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10 Best Problem-Solving Therapy Worksheets & Activities

Cognitive science tells us that we regularly face not only well-defined problems but, importantly, many that are ill defined (Eysenck & Keane, 2015).

Sometimes, we find ourselves unable to overcome our daily problems or the inevitable (though hopefully infrequent) life traumas we face.

Problem-Solving Therapy aims to reduce the incidence and impact of mental health disorders and improve wellbeing by helping clients face life’s difficulties (Dobson, 2011).

This article introduces Problem-Solving Therapy and offers techniques, activities, and worksheets that mental health professionals can use with clients.

Before you continue, we thought you might like to download our three Positive Psychology Exercises for free . These science-based exercises explore fundamental aspects of positive psychology, including strengths, values, and self-compassion, and will give you the tools to enhance the wellbeing of your clients, students, or employees.

This Article Contains:

What is problem-solving therapy, 14 steps for problem-solving therapy, 3 best interventions and techniques, 7 activities and worksheets for your session, fascinating books on the topic, resources from positivepsychology.com, a take-home message.

Problem-Solving Therapy assumes that mental disorders arise in response to ineffective or maladaptive coping. By adopting a more realistic and optimistic view of coping, individuals can understand the role of emotions and develop actions to reduce distress and maintain mental wellbeing (Nezu & Nezu, 2009).

“Problem-solving therapy (PST) is a psychosocial intervention, generally considered to be under a cognitive-behavioral umbrella” (Nezu, Nezu, & D’Zurilla, 2013, p. ix). It aims to encourage the client to cope better with day-to-day problems and traumatic events and reduce their impact on mental and physical wellbeing.

Clinical research, counseling, and health psychology have shown PST to be highly effective in clients of all ages, ranging from children to the elderly, across multiple clinical settings, including schizophrenia, stress, and anxiety disorders (Dobson, 2011).

Can it help with depression?

PST appears particularly helpful in treating clients with depression. A recent analysis of 30 studies found that PST was an effective treatment with a similar degree of success as other successful therapies targeting depression (Cuijpers, Wit, Kleiboer, Karyotaki, & Ebert, 2020).

Other studies confirm the value of PST and its effectiveness at treating depression in multiple age groups and its capacity to combine with other therapies, including drug treatments (Dobson, 2011).

The major concepts

Effective coping varies depending on the situation, and treatment typically focuses on improving the environment and reducing emotional distress (Dobson, 2011).

PST is based on two overlapping models:

Social problem-solving model

This model focuses on solving the problem “as it occurs in the natural social environment,” combined with a general coping strategy and a method of self-control (Dobson, 2011, p. 198).

The model includes three central concepts:

• Social problem-solving
• The problem
• The solution

The model is a “self-directed cognitive-behavioral process by which an individual, couple, or group attempts to identify or discover effective solutions for specific problems encountered in everyday living” (Dobson, 2011, p. 199).

Relational problem-solving model

The theory of PST is underpinned by a relational problem-solving model, whereby stress is viewed in terms of the relationships between three factors:

• Stressful life events
• Emotional distress and wellbeing
• Problem-solving coping

Therefore, when a significant adverse life event occurs, it may require “sweeping readjustments in a person’s life” (Dobson, 2011, p. 202).

• Enhance positive problem orientation
• Decrease negative orientation
• Foster ability to apply rational problem-solving skills
• Reduce the tendency to avoid problem-solving
• Minimize the tendency to be careless and impulsive

D’Zurilla’s and Nezu’s model includes (modified from Dobson, 2011):

• Initial structuring Establish a positive therapeutic relationship that encourages optimism and explains the PST approach.
• Assessment Formally and informally assess areas of stress in the client’s life and their problem-solving strengths and weaknesses.
• Obstacles to effective problem-solving Explore typically human challenges to problem-solving, such as multitasking and the negative impact of stress. Introduce tools that can help, such as making lists, visualization, and breaking complex problems down.
• Problem orientation – fostering self-efficacy Introduce the importance of a positive problem orientation, adopting tools, such as visualization, to promote self-efficacy.
• Problem orientation – recognizing problems Help clients recognize issues as they occur and use problem checklists to ‘normalize’ the experience.
• Problem orientation – seeing problems as challenges Encourage clients to break free of harmful and restricted ways of thinking while learning how to argue from another point of view.
• Problem orientation – use and control emotions Help clients understand the role of emotions in problem-solving, including using feelings to inform the process and managing disruptive emotions (such as cognitive reframing and relaxation exercises).
• Problem orientation – stop and think Teach clients how to reduce impulsive and avoidance tendencies (visualizing a stop sign or traffic light).
• Problem definition and formulation Encourage an understanding of the nature of problems and set realistic goals and objectives.
• Generation of alternatives Work with clients to help them recognize the wide range of potential solutions to each problem (for example, brainstorming).
• Decision-making Encourage better decision-making through an improved understanding of the consequences of decisions and the value and likelihood of different outcomes.
• Solution implementation and verification Foster the client’s ability to carry out a solution plan, monitor its outcome, evaluate its effectiveness, and use self-reinforcement to increase the chance of success.
• Guided practice Encourage the application of problem-solving skills across multiple domains and future stressful problems.
• Rapid problem-solving Teach clients how to apply problem-solving questions and guidelines quickly in any given situation.

Success in PST depends on the effectiveness of its implementation; using the right approach is crucial (Dobson, 2011).

Problem-solving therapy – Baycrest

The following interventions and techniques are helpful when implementing more effective problem-solving approaches in client’s lives.

First, it is essential to consider if PST is the best approach for the client, based on the problems they present.

Is PPT appropriate?

It is vital to consider whether PST is appropriate for the client’s situation. Therapists new to the approach may require additional guidance (Nezu et al., 2013).

Therapists should consider the following questions before beginning PST with a client (modified from Nezu et al., 2013):

• Has PST proven effective in the past for the problem? For example, research has shown success with depression, generalized anxiety, back pain, Alzheimer’s disease, cancer, and supporting caregivers (Nezu et al., 2013).
• Is PST acceptable to the client?
• Is the individual experiencing a significant mental or physical health problem?

All affirmative answers suggest that PST would be a helpful technique to apply in this instance.

Five problem-solving steps

The following five steps are valuable when working with clients to help them cope with and manage their environment (modified from Dobson, 2011).

Ask the client to consider the following points (forming the acronym ADAPT) when confronted by a problem:

• Attitude Aim to adopt a positive, optimistic attitude to the problem and problem-solving process.
• Define Obtain all required facts and details of potential obstacles to define the problem.
• Alternatives Identify various alternative solutions and actions to overcome the obstacle and achieve the problem-solving goal.
• Predict Predict each alternative’s positive and negative outcomes and choose the one most likely to achieve the goal and maximize the benefits.
• Try out Once selected, try out the solution and monitor its effectiveness while engaging in self-reinforcement.

If the client is not satisfied with their solution, they can return to step ‘A’ and find a more appropriate solution.

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Positive self-statements

When dealing with clients facing negative self-beliefs, it can be helpful for them to use positive self-statements.

Use the following (or add new) self-statements to replace harmful, negative thinking (modified from Dobson, 2011):

• I can solve this problem; I’ve tackled similar ones before.
• I can cope with this.
• I just need to take a breath and relax.
• Once I start, it will be easier.
• It’s okay to look out for myself.
• I can get help if needed.
• Other people feel the same way I do.
• I’ll take one piece of the problem at a time.
• I can keep my fears in check.
• I don’t need to please everyone.

5 Worksheets and workbooks

Problem-solving self-monitoring form.

Answering the questions in the Problem-Solving Self-Monitoring Form provides the therapist with necessary information regarding the client’s overall and specific problem-solving approaches and reactions (Dobson, 2011).

Ask the client to complete the following:

• Describe the problem you are facing.
• What is your goal?
• What have you tried so far to solve the problem?
• What was the outcome?

Reactions to Stress

It can be helpful for the client to recognize their own experiences of stress. Do they react angrily, withdraw, or give up (Dobson, 2011)?

The Reactions to Stress worksheet can be given to the client as homework to capture stressful events and their reactions. By recording how they felt, behaved, and thought, they can recognize repeating patterns.

What Are Your Unique Triggers?

Helping clients capture triggers for their stressful reactions can encourage emotional regulation.

When clients can identify triggers that may lead to a negative response, they can stop the experience or slow down their emotional reaction (Dobson, 2011).

The What Are Your Unique Triggers ? worksheet helps the client identify their triggers (e.g., conflict, relationships, physical environment, etc.).

Problem-Solving worksheet

Imagining an existing or potential problem and working through how to resolve it can be a powerful exercise for the client.

Use the Problem-Solving worksheet to state a problem and goal and consider the obstacles in the way. Then explore options for achieving the goal, along with their pros and cons, to assess the best action plan.

Getting the Facts

Clients can become better equipped to tackle problems and choose the right course of action by recognizing facts versus assumptions and gathering all the necessary information (Dobson, 2011).

Use the Getting the Facts worksheet to answer the following questions clearly and unambiguously:

• Who is involved?
• What did or did not happen, and how did it bother you?
• Where did it happen?
• When did it happen?
• Why did it happen?
• How did you respond?

2 Helpful Group Activities

While therapists can use the worksheets above in group situations, the following two interventions work particularly well with more than one person.

Generating Alternative Solutions and Better Decision-Making

A group setting can provide an ideal opportunity to share a problem and identify potential solutions arising from multiple perspectives.

Use the Generating Alternative Solutions and Better Decision-Making worksheet and ask the client to explain the situation or problem to the group and the obstacles in the way.

Once the approaches are captured and reviewed, the individual can share their decision-making process with the group if they want further feedback.

Visualization

Visualization can be performed with individuals or in a group setting to help clients solve problems in multiple ways, including (Dobson, 2011):

• Clarifying the problem by looking at it from multiple perspectives
• Rehearsing a solution in the mind to improve and get more practice
• Visualizing a ‘safe place’ for relaxation, slowing down, and stress management

Guided imagery is particularly valuable for encouraging the group to take a ‘mental vacation’ and let go of stress.

Ask the group to begin with slow, deep breathing that fills the entire diaphragm. Then ask them to visualize a favorite scene (real or imagined) that makes them feel relaxed, perhaps beside a gently flowing river, a summer meadow, or at the beach.

The more the senses are engaged, the more real the experience. Ask the group to think about what they can hear, see, touch, smell, and even taste.

Encourage them to experience the situation as fully as possible, immersing themselves and enjoying their place of safety.

Such feelings of relaxation may be able to help clients fall asleep, relieve stress, and become more ready to solve problems.

We have included three of our favorite books on the subject of Problem-Solving Therapy below.

1. Problem-Solving Therapy: A Treatment Manual – Arthur Nezu, Christine Maguth Nezu, and Thomas D’Zurilla

This is an incredibly valuable book for anyone wishing to understand the principles and practice behind PST.

Written by the co-developers of PST, the manual provides powerful toolkits to overcome cognitive overload, emotional dysregulation, and the barriers to practical problem-solving.

Find the book on Amazon .

2. Emotion-Centered Problem-Solving Therapy: Treatment Guidelines – Arthur Nezu and Christine Maguth Nezu

Another, more recent, book from the creators of PST, this text includes important advances in neuroscience underpinning the role of emotion in behavioral treatment.

Along with clinical examples, the book also includes crucial toolkits that form part of a stepped model for the application of PST.

3. Handbook of Cognitive-Behavioral Therapies – Keith Dobson and David Dozois

This is the fourth edition of a hugely popular guide to Cognitive-Behavioral Therapies and includes a valuable and insightful section on Problem-Solving Therapy.

This is an important book for students and more experienced therapists wishing to form a high-level and in-depth understanding of the tools and techniques available to Cognitive-Behavioral Therapists.

For even more tools to help strengthen your clients’ problem-solving skills, check out the following free worksheets from our blog.

• Case Formulation Worksheet This worksheet presents a four-step framework to help therapists and their clients come to a shared understanding of the client’s presenting problem.
• Understanding Your Default Problem-Solving Approach This worksheet poses a series of questions helping clients reflect on their typical cognitive, emotional, and behavioral responses to problems.
• Social Problem Solving: Step by Step This worksheet presents a streamlined template to help clients define a problem, generate possible courses of action, and evaluate the effectiveness of an implemented solution.

If you’re looking for more science-based ways to help others enhance their wellbeing, check out this signature collection of 17 validated positive psychology tools for practitioners. Use them to help others flourish and thrive.

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While we are born problem-solvers, facing an incredibly diverse set of challenges daily, we sometimes need support.

Problem-Solving Therapy aims to reduce stress and associated mental health disorders and improve wellbeing by improving our ability to cope. PST is valuable in diverse clinical settings, ranging from depression to schizophrenia, with research suggesting it as a highly effective treatment for teaching coping strategies and reducing emotional distress.

Many PST techniques are available to help improve clients’ positive outlook on obstacles while reducing avoidance of problem situations and the tendency to be careless and impulsive.

The PST model typically assesses the client’s strengths, weaknesses, and coping strategies when facing problems before encouraging a healthy experience of and relationship with problem-solving.

Why not use this article to explore the theory behind PST and try out some of our powerful tools and interventions with your clients to help them with their decision-making, coping, and problem-solving?

We hope you enjoyed reading this article. Don’t forget to download our three Positive Psychology Exercises for free .

• Cuijpers, P., Wit, L., Kleiboer, A., Karyotaki, E., & Ebert, D. (2020). Problem-solving therapy for adult depression: An updated meta-analysis. European P sychiatry ,  48 (1), 27–37.
• Dobson, K. S. (2011). Handbook of cognitive-behavioral therapies (3rd ed.). Guilford Press.
• Dobson, K. S., & Dozois, D. J. A. (2021). Handbook of cognitive-behavioral therapies  (4th ed.). Guilford Press.
• Eysenck, M. W., & Keane, M. T. (2015). Cognitive psychology: A student’s handbook . Psychology Press.
• Nezu, A. M., & Nezu, C. M. (2009). Problem-solving therapy DVD . Retrieved September 13, 2021, from https://www.apa.org/pubs/videos/4310852
• Nezu, A. M., & Nezu, C. M. (2018). Emotion-centered problem-solving therapy: Treatment guidelines. Springer.
• Nezu, A. M., Nezu, C. M., & D’Zurilla, T. J. (2013). Problem-solving therapy: A treatment manual . Springer.

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30 Challenging Math Riddles For High School Students With Answers

Solving riddles with your child is a terrific method to develop problem-solving skills. The ability to persevere through challenging tasks can be a better predictor of successful outcomes than intelligence, according to research on “grit” or mental toughness. Children have the opportunity to try again if they fail. 

The key to developing grit is learning to keep going after failing or, in the instance of a riddle, not knowing the solution. Math riddles have the advantage of not having any negative consequences if the answer is wrong; this teaches children that making mistakes is okay and prepares them to take calculated chances in the future. 

Hence, some challenging math riddles for high school students can act favorable and advantageous in many ways. In this post, we will talk about a few of these riddles, and provide you with the answer as well, so that it can make the learning process more fun and definitely much easier. 

How can Math Riddles help high schoolers?

While it’s a known fact that math riddles and puzzles are a great method to get any learner interested in a subject since they make them listen actively rather than passively. Working with arithmetic puzzles, however, can also raise the environment for learning as a whole.

• These issues call on various abilities and provide meaning to abstract ideas. A question or statement “intentionally crafted to require imagination in finding its answer or meaning” is a math riddle.
• Since math riddles are frequently written in a way that applies to real-life circumstances, they can help pupils understand complex concepts.
• Students must also concentrate on and develop their critical thinking skills to solve challenges. Although it may seem obvious, there is a straightforward explanation for why kids respond well to arithmetic riddles: they have heard them before, in other contexts, and are therefore familiar with the idea. When you are comfortable with the subject, learning is more fun.
• Additionally, math riddles are appropriate for younger kids. And lastly, arithmetic puzzles are fun! Students are significantly more likely to focus and maintain motivation if they appreciate the topic of the debate.

 Riddles with answers

1. Riddle: How many apples do you have if there are four and you take away three?

Answer: You have three apples because you took three!

2. Riddle: A 300-foot tunnel must be traversed by a 300-foot Travis moving 300 feet per minute. How much time will the train need to pass through the tunnel?

Answer: The time is two minutes. The front of the train clears the tunnel in one minute, and the remainder takes two minutes.

3. Riddle: An iPhone and a cover are $110 each. The phone case is $100 more expensive than the cell phone. How much did the phone cost?

Answer: One hundred five dollars, not 110.

4. Riddle: Over a week, Robert and David competed in several golf matches. At each game, they competed for a pizza, but no pizzas were bought until the end of the week. Those pizza orders were canceled if David and Robert tied in wins. David earned three pizzas, whereas Robert won four matches (but no pizzas). How many golf rounds were completed?

Answer: 11. Because David prevailed in seven games—four to offset Robert’s four victories and three more to take home the pizzas.

5. Riddle: My three-digit number identity. My third digit is four times smaller than my second. The difference between my first and second digits is three. I, who?

Answer: 141

6. Riddle: When I multiply five by nine, I get two. The right response is given, but how?

Answer: You can get to 2 p.m. by adding five hours to the time at 9 a.m.

7. Riddle: There are 100 couples of dogs at a zoo, and each pair has two puppies. Unluckily, 23 of the dogs have perished. How many dogs are still there overall?

Answer: 977 dogs. Because 100 x 2 = 200; 200 + 800 = 1,000; 1,000 – 23 = 977.

8. Riddle: At a march past occasion, a group of students faces due west in the scorching sun. Right turn, the leader yelled at the group. Right turn! Turn left! Which way are the pupils facing after these commands?

Answer: East, because they will turn 90 degrees to the right, 180 degrees to the left, and then 90 degrees to the right again. The students are now facing east as a result.

9. Riddle: A third of it is a half. It is what?

Answer: 1 ½

10. Riddle: Tom can fit either eight large boxes or ten little boxes into a carton while shipping. In all, 96 boxes were shipped together in one consignment. Few little boxes were present than huge boxes. How many cartons in total did he ship?

Answer: 11 containers because four little boxes (410 = 40 boxes) plus seven large boxes (78 = 56 boxes). Therefore, 96 boxes and 11 cartons altogether.

11. Riddle: When Miguel was six years old, his little sister Leila was half of his age. If Miguel is 40 years old today how old is Leila?

Answer: She is 37 years old, to be exact.

12. Riddle: Three positive numbers are presented to you. These figures can be multiplied and added together. Your outcome will be the same. What numbers are there?

Answer: There are three options.

13. Riddle: How many eggs would six chickens lay in six days if each lays one egg every day and a half?

Answer: Twelve

14. Riddle: What may be placed between a seven and an eight to produce a result higher than a seven but lower than an eight?

Answer: 7.8 is larger than seven but less than 8, the answer is a decimal.

15. Riddle: Tom will have to paint numbers one through 100 because he was instructed to paint numbers outside 100 apartments. He’ll have to paint the number eight how many times?

Answer: Twenty times because 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98

16. Riddle: How often can you take five away from twenty-five?

Answer: Just once.

17. Riddle: A pound of solid gold or 16 ounces of soda, which is heavier?

Answer: None is the reply. They both have the same weight! 

18. Riddle: Leon works at an aquarium. He has one turtle extra when trying to put each turtle in its tank. If he places two turtles in each tank, he has an excess of one tank. Leon has how many turtles and tanks.

Answer: He has four turtles and three aquariums.

19. Riddle: A hoodie and sneakers cost $150. $100 more was spent on the sweatshirt than the sneakers. What is the price of each item?

Answer: The response is that the hoodie is $125, and the sneakers are $25.

20. Riddle: You have two American coins worth 30 cents. Not a nickel is one of them. Which two coins are they? 

Answer: One is a nickel, and one is a quarter.

21. Riddle: A dozen eggs cost 12 cents. The number of eggs you can get for a dollar?

Answer: One penny per egg for 100 eggs.

22. Riddle: A spider received $36, a bee received $27, and a duck received $9. How much cash would you offer a cat in light of this information?

Amount: $18 ($4.50 for each leg).

23. Riddle: “How much is this bag of potatoes?” the man inquired. The grocer answered, “Thirty-two pounds divided by half its weight.” What was the weight of the potatoes?

Answer: 8 lbs.

24. Riddle: I’m a three-digit number. The difference between my one and tens digits is six. Eight fewer than my tens digit is my hundred digits. What digit am I?

Answer: 193

25. Riddle: His younger sister is twice as old as a man. He is also half his father’s age. His sister’s age will eventually match their father’s in 50 years. What is the man’s current age?

Answer: A 50-year-old person.

26 Riddle: How do you multiply eight fours together so that the result is 500?

Answer: 500 = 444 + 44 + 4 + 4 + 4.

27. Riddle: How many handshakes occur if seven people meet and each shakes hands just once with the others?

28. Riddle: How many tables can eight guys construct in eight hours if four men can construct four in four?

Answer: 16 tables

29. Riddle: Lisa’s sister Lucy was half her age when she was six. How old is Lucy if Lisa is 40 years old today?

Answer: 37 because Lucy is three years younger than Lisa as justification.

30. Riddle: How many eggs would you have after three weeks if you buy a rooster to lay eggs and anticipate getting three eggs every day for breakfast?

Answer: None. Eggs aren’t laid by roosters

A problem can be difficult even if it seems ludicrous or strange; presenting a mathematical concept as a riddle challenges students to employ critical and analytical thinking in unexpected ways, which enhances their overall grasp. A lot of people are inclined towards myths like mathematical riddles are like child’s play! However, these can also be baffling for a few adult. But, pushing the right buttons and brainstorming can give you the right answer. For all our readers, here’s a fun riddle to solve: There were some folks on a train. Nineteen people get off the train at the first station, while 17 get aboard. There are now 63 people on the train. First of all, how many people were aboard the train?

Drop in your answers in the comments below, with an explanation as to how you reached the figure! 

Sananda Bhattacharya, Chief Editor of TheHighSchooler, is dedicated to enhancing operations and growth. With degrees in Literature and Asian Studies from Presidency University, Kolkata, she leverages her educational and innovative background to shape TheHighSchooler into a pivotal resource hub. Providing valuable insights, practical activities, and guidance on school life, graduation, scholarships, and more, Sananda’s leadership enriches the journey of high school students.

Explore a plethora of invaluable resources and insights tailored for high schoolers at TheHighSchooler, under the guidance of Sananda Bhattacharya’s expertise. You can follow her on Linkedin

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Two Riddles To Get Students Practicing Problem Solving Tricks

Please try again

Riddles are a great way to get kids thinking logically, testing predictions, using math and even collaborating. They're fun and often quite challenging. Many riddles sound confusing at first, forcing students to think about ways to isolate information or simplify a problem. These are useful skills for all problem solving. TED-Ed and its educator contributors have put together great animated riddles that make the presentation of the riddle fun and walk through the solutions once kids have tried to solve them.

Seven Planets Riddle:

In this puzzle students are intergalactic police trying to find rebels who are hiding out on seven faraway planets. Various rules govern how the police ship can move between planets and how rebels can move. Students have to figure out a sequence of moves the police ship can make that will guarantee they'll find the rebels before reinforcements arrive (the answer starts at 1:11). The solution also offers some problem solving tips that students can apply to other challenges. Students might also enjoy the bonus Harry Potter-themed video at the end of this video.

Penniless Pilgrim Riddle:

This is a great riddle for both logic and the order of operations. As pilgrims to Duonia, students are caught in a complicated tax scheme. They have to figure out how to get to the temple without paying any money or breaking the rules of their pilgrimage (answer is at 1:58).

Unravel the Mystery: 42 Mind-Bending Math Riddles to Challenge and Entertain You

1. Riddle: Three people check into a hotel room that costs $30. They each contribute $10, handing $30 to the hotel clerk. Later, the hotel clerk realizes there was a mistake and the room only cost $25. The hotel clerk gives $5 to the bellboy to return to the guests. The bellboy, however, decides to keep $2 for himself and gives $1 back to each guest. Now, each guest has paid $9 (a total of $27) and the bellboy kept $2, which adds up to $29. What happened to the missing dollar? 2. Riddle: A snail is at the bottom of a 30-foot well. Each day, the snail climbs up 3 feet, but at night, it slides back down 2 feet. How many days will it take for the snail to reach the top of the well? 3. Riddle: You have 10 stacks of coins with 10 coins in each stack. All the coins in one stack are counterfeit, and all the other coins are genuine. A genuine coin weighs 10 grams, and a counterfeit coin weighs 11 grams. You have a digital scale that you can use only once. How can you determine which stack contains the counterfeit coins? 4. Riddle: What has a hundred legs but cannot stand, a long neck but no head, and is responsible for making everyone late? 5. Riddle: A boy was asked to multiply a certain number by 25. He accidentally multiplied it by 52 instead and got the answer 2600. What was the original number? 6. Riddle: A clock with a regular 12-hour display loses two minutes every hour. It was last set to the correct time at midnight. When the clock shows 6:00 AM, what is the actual time? 7. Riddle: The ages of a father and his son add up to 66 years. The father's age is the son's age reversed. How old are the father and son? 8. Riddle: You have two containers: one holds five liters and the other holds three liters. Using only these containers, how can you measure exactly four liters of water? 9. Riddle: There are 100 light bulbs lined up in a row, all turned off. You start by switching on every second bulb. Then, you go back and toggle every third bulb (turning off if it's on, turning on if it's off). You continue this process with every fourth bulb, every fifth bulb, and so on, until you finish with the 100th bulb. After you've gone through this process, how many light bulbs will be on? 10. Riddle: Two trains are 250 miles apart, traveling toward each other along the same track. Train A travels at 65 miles per hour, and Train B travels at 85 miles per hour. A fly is hovering just above the nose of Train A and decides to fly to Train B. When it reaches Train B, it immediately flies back to Train A. The fly continues this back-and-forth journey until the two trains collide. If the fly travels at 120 miles per hour, how far will it have flown when the trains collide? 11. Riddle: A square room has a width of 8 meters. A spider is located at one of the bottom corners, while a fly is at the diagonally opposite top corner. If the spider can only walk on the walls, ceiling, and floor, what is the shortest distance it must travel to reach the fly? 12. Riddle: A shepherd has 17 sheep. All but nine of them run away. How many sheep does the shepherd have left? 13. Riddle: At a party, everyone shook hands exactly once with every other person present. There were 66 handshakes in total. How many people were at the party? 14. Riddle: I am a three-digit number. My tens digit is five more than my ones digit, and my hundreds digit is eight less than my tens digit. What number am I? 15. Riddle: A man has 53 socks in his drawer: 21 identical blue, 15 identical black, and 17 identical red. The room is dark, and he cannot see the color of the socks. What is the minimum number of socks he must take out of the drawer to guarantee he has a matching pair? 16. Riddle: You have three boxes: one labeled "Apples," another labeled "Oranges," and the third labeled "Apples and Oranges." Each label is placed incorrectly. You are allowed to pick one fruit from one box without looking inside. How can you determine the correct labels for all three boxes? 17. Riddle: A ladder is leaning against a vertical wall, with its bottom 4 feet from the wall. The ladder touches the top of a 6-foot fence that is 2 feet from the wall. How tall is the ladder? 18. Riddle: A man gave one of his five sons a gift of $100. He divided the rest of the money equally among the remaining four sons. If each of the other sons received $80, how much money did the man originally have? 19. Riddle: A gardener plants 100 trees in a perfect square grid, with each tree equidistant from its neighbors. The gardener plants one more tree directly in the center of the square, making the distance between it and each of the four center trees equal to the distance between any two neighboring trees. How many trees are in each row of the square grid? 20. Riddle: In a certain country, half of the people who live there are 25 years old or younger, and ⅔ of the people are 35 years old or younger. What percentage of the population is between 26 and 35 years old? 21. Riddle: A palindrome is a word, phrase, number, or other sequences of characters that reads the same forward and backward. If a number is a palindrome and the sum of its digits is equal to the product of its digits, what is the number? 22. Riddle: A group of people is traveling to a mountain cabin that is 100 miles away. They can travel at an average speed of 50 miles per hour. If they leave at noon, stop halfway for an hour to eat lunch, and then continue to the cabin, what time will they arrive? 23. Riddle: There is a number that is 3 times the sum of its digits. When the digits are reversed, the number increases by 396. What is the number? 24. Riddle: A store is selling apples and oranges at the same price per pound. A customer buys 3 pounds of apples and 5 pounds of oranges for $16. Another customer buys 8 pounds of apples and 2 pounds of oranges for $18. What is the price per pound of apples and oranges? 25. Riddle: A clock chimes 5 times in 4 seconds. How long will it take to chime 12 times? 26. Riddle: A factory produces 500 units of a product every 8 hours. Each unit requires 10 minutes of labor from a worker. How many workers are needed to maintain this production rate? 27. Riddle: A circle with a radius of 10 cm is inscribed in a square. What is the difference between the areas of the square and the circle? 28. Riddle: In a class of 40 students, 12 students play soccer, 14 students play basketball, and 18 students play neither sport. How many students play both soccer and basketball? 29. Riddle: A bus leaves from City A to City B, which is 240 miles away. At the same time, another bus leaves City B to City A. The bus from City A travels at an average speed of 60 miles per hour, while the bus from City B travels at an average speed of 40 miles per hour. At what distance from City A will the two buses meet? 30. Riddle: If a number is divisible by both 9 and 12, it must also be divisible by which other number? 31. Riddle: A person walks up a moving escalator in 60 steps. When the person stands still on the escalator, it takes 90 steps to reach the top. How many steps would the person take if they walked up the non-moving escalator? 32. Riddle: There are 3 consecutive numbers that add up to 57. What are the numbers? 33. Riddle: A man buys a sandwich for $10 and a drink for $5. He gives the cashier a $20 bill. How much change should he receive? 34. Riddle: I am a two-digit number. If you subtract my digits from me, the result is 9. If you add my digits together, the result is also 9. What number am I? 35. Riddle: A train travels 20 miles per hour for 2 hours and then 30 miles per hour for 3 hours. What is the train's average speed during the entire trip? 36. Riddle: A triangle has side lengths of 10 cm, 24 cm, and 26 cm. Is the triangle a right triangle? 37. Riddle: A car rental company charges a flat fee of $20 per day and an additional 15 cents per mile driven. How much will a customer pay if they rent a car for 3 days and drive 150 miles? 38. Riddle: A baker uses 1 cup of sugar for every 2 cups of flour when making a cake. If the baker uses 6 cups of flour, how many cups of sugar are needed? 39. Riddle: At a fruit stand, 5 oranges cost the same as 3 apples. If 15 oranges cost $9, how much do 9 apples cost? 40. Riddle: A number is divisible by 4 and 6. If the number is also divisible by 5, what is the smallest possible value for the number? 41. Riddle: A man gives half of his money to his wife and one-third to his son. He has $200 left. How much money did he originally have? 42. Riddle: A movie theater charges $7 for adults and $5 for children. If 25 people attend a movie and the theater collects $150, how many adults and children attended the movie?

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100+ Clever Riddles for High School Students

Encourage creativity, critical thinking, and problem-solving.

Good riddles can leave high school students both stumped and laughing. Trying to solve them and find the answer encourages creativity, critical thinking, and problem-solving. It’s also a lot of fun! Want to share some with your class? Here’s a list of riddles for high school students to bring some energy to the classroom.

Riddles for High School Students

Which month has 28 days.

All months have 28 days.

A woman builds a house with all four walls facing south. A bear walks past the house. What color is the bear?

White. It is a polar bear.

Which is the sweetest and most romantic fruit?

I grow richer with alcohol but die with water. what am i, what do you break before you use it, what problem does a teacher with uncontrollable eyes have.

He cannot control his pupils.

What do you get when you mix sulfur, tungsten, and silver?

Trees are my home, but i never go inside. when i fall off a tree, i am dead. what am i, what can make an octopus laugh.

Ten-tickles.

How many books can you pack inside an empty backpack?

One. It is no longer empty after that.

I have hands, but I cannot shake your hands. I have a face, but I cannot smile at you. What am I?

What kind of food do mummies eat, i have no doors, but i have keys. i have no rooms, but i have space. you can enter, but you cannot leave. what am i.

A keyboard.

If you drop me on the ground, I survive. But if you drop me in water, I die. What am I?

What has a bottom at the top, you can hear me, but you cannot see or touch me. what am i, what is the similarity between “2 + 2 = 5” and your left hand.

Neither is right.

What sounds like a war machine but is a piece of clothing?

What is black and white and read all over.

A newspaper.

What has a thumb and fingers but is not alive?

How can a man go for eight days without sleeping.

He sleeps at night.

You live in a one-story house made entirely of redwood. What color are the stairs?

What stairs? It is a one-story house.

What do you find at the end of a line?

The letter “E.”

Name three consecutive days that aren’t the days of the week.

Yesterday, today, and tomorrow.

What is a snowman called in summer?

There are two fathers and two sons in a car. how many people are in the car.

Three people—a grandfather, a father, and a son.

What is full of holes but holds water?

My first letter is in chocolate but not in ham. my second letter is in cake and jam, and my third is in tea but not in coffee. what am i, a man shaves throughout the day, yet he has a beard. how.

He is a barber.

What has a head and a tail but no body?

An electric train is traveling from east to west, and the wind is blowing from north to south. in which direction does the smoke go.

None. Electric trains don’t produce smoke.

Which windows can’t you open literally?

The Windows on your laptop.

Kate’s mother has four daughters: Monday, Tuesday, Wednesday, and _____. What is the name of the fourth daughter?

I can fill up a room but take no space. what am i, where does divorce come before marriage.

In the dictionary.

What starts with a P and ends with an X and has hundreds of letters in between?

It is lighter than a feather, but you can’t hold it for more than two minutes. what is it.

Your breath.

What type of music do rabbits like?

What gets wetter the more it dries, which weighs more, a pound of iron bars or a pound of feathers.

They both weigh the same.

What has a neck but no head?

I am made of water, but i die when you put water on me. what am i, what is the ancient invention that allows people to see through walls, what can’t be kept until it is given, what did the math book say to the pencil.

I have a lot of problems.

What gets sharper the more you use it?

Your brain.

A farmer walks toward his field and he sees three frogs sitting on the shoulders of two rabbits. Three parrots and four mice run toward him. How many pairs of legs are going toward the field?

One pair—the farmer’s.

What goes up but never comes down?

What room has no windows or doors.

A mushroom.

Which fruit is always sad?

A blueberry.

When I am young, I am tall. I grow shorter as I become older. What am I?

What has a mouth but cannot eat and runs but has no legs, what is a teenager’s favorite phrase during math class.

“I can’t even.”

What has branches but no leaves or fruits?

What has 13 hearts but no brains.

A pack of playing cards.

Which tree can you carry in your hand?

A palm tree.

If you are running a race and you pass the person who is running second, which position are you in?

When do you go at red and stop at green.

While eating a watermelon.

What is the center of gravity?

The letter “V.”

What has no beginning, end, or middle?

What grows bigger the more you take away from it, i am smooth as silk and can be hard or soft. i fall but cannot climb. what am i, what did the angry electron say when it was repelled.

Let me atom!

What do you place on the table and cut but never eat?

What did the english book say to the algebra book.

Don’t change the subject.

What vehicle is a palindrome?

What breaks the moment you say its name, what becomes shorter when you add two letters to it.

The word “short.”

During which month do people sleep the least?

February—it has the fewest days.

The person who buys me cannot use me, and the person who uses me cannot buy or see me. What am I?

Which english word has three consecutive double letters.

Bookkeeper.

You can hear me but cannot see me. I don’t speak until you do. What am I?

What can you find in a minute or an hour but never in a day or a month.

The letter “U.”

What is the only English word with “ii” in it?

You are alone at home and sleeping. your friends ring the doorbell. they have come for breakfast. you have cornflakes, bread, jam, a carton of milk, and a bottle of juice. what will you open first, what is the only english word with “uu” in it, i am hard to find, difficult to leave, and impossible to forget. what am i, i have seas with no water, mountains with no land, and towns with no people. what am i, what did the beach say when the tide came in.

Long time, no sea.

When you have me, you want to share me. But if you share me, you don’t have me any longer. What am I?

Find the number less than 100 that is increased by one-fifth of its value when its digits are reversed..

45 (1/5*45 = 9, 9+45 = 54)

What goes all around the world but stays in one place?

Forwards i am heavy, but backward i am not. what am i, an apple is 40 cents, a banana is 60 cents, and a grapefruit is 80 cents. how much is a pear.

40 cents. The price of each fruit is calculated by multiplying the number of vowels by 20 cents.

What has one eye but cannot see?

Everyone has me but nobody can lose me. what am i, there was a plane crash and every single person died. who survived, what invention lets you look right through a wall, they come out at night without being called and are lost in the day without being stolen. what are they, what has four legs but can’t walk, what goes up when rain comes down.

An umbrella.

I am your mother’s brother’s brother-in-law. Who am I?

Your father.

What has a tongue but never talks, and has no legs but sometimes walks?

I am a vegetable that bugs stay away from. what am i, born in an instant, i tell all stories. i can be lost, but i never die. what am i, with shiny fangs, my bloodless bite will bring together what’s mostly white. what am i, a plane crashed on the border of the united states and canada. where do they bury the survivors.

Nowhere—the survivors are alive.

What type of bow can never be tied?

What can be found at the beginning of eternity, the end of time and space, and the beginning of every end, there is only one word spelled wrong in the dictionary. what is it, what begins with t, finishes with t, and has t in it, what room do ghosts avoid.

The living room.

Bonus: Christmas Riddles for High School Students

What do you call a person who is scared of santa claus.

Claustrophobic.

If a lion had a Christmas music album, what would it be called?

Jungle bells.

What keeps a Christmas tree smelling fresh?

Orna-mints.

What do elves learn in school?

The elfabet.

Which reindeer can you see in outer space?

What is your parents’ favorite christmas carol.

“Silent Night.”

Can Christmas trees knit well?

No, they always drop their needles.

Share your riddles for high school students in our WeAreTeachers HELPLINE group  on Facebook!

Enjoy these riddles for high school students for more laughs, check out our favorite grammar jokes  and  science jokes..

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Interactive Mathematics Miscellany and Puzzles

20 Tough Riddles for Adults That Will Have You Scratching Your Head

Put your logic and math skills to the test. No cheating!

So go grab a pencil and a piece of scratch paper and prepare to rip your hair out (and we really do mean that in the best way possible). When you think you’ve got the right answer, click the link at the bottom of each riddle to find the solution. Got it wrong? No worries, you have 19 other riddles to test out.

Navigate Through Our Riddles:

Puzzmo / The King’s Orders / How Many Eggs? / The Gold Chain / Pickleball / Circuit Breaker / Two Trains, Two Grandmas / Ant Math / Peppermint Patty / Great American Rail Trail / A Cruel SAT Problem / Movie Stars Cross a River / Tribute to a Math Genius / One Belt, One Earth / Elbow Tapping / Whiskey Problem / Doodle Problem / Stumping Scientists / What ’ s On Her Forehead? / Keanu for President / Who Opened the Lockers?

Riddle No. 1: The King’s Orders Make for One Hell of a Brain Teaser

Difficulty: easy.

King Nupe of the kingdom Catan dotes on his two daughters so much that he decides the kingdom would be better off with more girls than boys, and he makes the following decree: All child-bearing couples must continue to bear children until they have a daughter!

But to avoid overpopulation, he makes an additional decree: All child-bearing couples will stop having children once they have a daughter! His subjects immediately begin following his orders.

After many years, what’s the expected ratio of girls to boys in Catan?

The likelihood of each baby born being a girl is, of course, 50 percent.

Ready for the solution? Click here to see if you’re right .

Riddle No. 2: How Many Eggs Does This Hen Lay?

This problem is in honor of my dad, Harold Feiveson. It’s due to him that I love math puzzles, and this is one of the first problems (of many) that he gave me when I was growing up.

A hen and a half lays an egg and a half in a day and a half. How many eggs does one hen lay in one day?

Riddle No. 3: The Gold Chain Math Problem Is Deceptively Simple

Difficulty: moderate.

You’re rummaging around your great grandmother’s attic when you find five short chains each made of four gold links. It occurs to you that if you combined them all into one big loop of 20 links, you’d have an incredible necklace. So you bring it into a jeweler, who tells you the cost of making the necklace will be $10 for each gold link that she has to break and then reseal.

How much will it cost?

Riddle No. 4: Try to Solve This Pickleball Puzzle

Difficulty: 🚨hard🚨.

Kenny, Abby, and Ned got together for a round-robin pickleball tournament, where, as usual, the winner stays on after each game to play the person who sat out that game. At the end of their pickleball afternoon, Abby is exhausted, having played the last seven straight games. Kenny, who is less winded, tallies up the games played:

Kenny played eight games

Abby played 12 games

Ned played 14 games

Who won the fourth game against whom?

How many total games were played?

Riddle No. 5: Our Circuit Breaker Riddle Is Pure Evil. Sorry.

The circuit breaker box in your new house is in an inconvenient corner of your basement. To your chagrin, you discover none of the 100 circuit breakers is labeled, and you face the daunting prospect of matching each circuit breaker to its respective light. (Suppose each circuit breaker maps to only one light.)

To start with, you switch all 100 lights in the house to “on,” and then you head down to your basement to begin the onerous mapping process. On every trip to your basement, you can switch any number of circuit breakers on or off. You can then roam the hallways of your house to discover which lights are on and which are off.

What is the minimum number of trips you need to make to the basement to map every circuit breaker to every light?

The solution does not involve either switching on or off the light switches in your house or feeling how hot the lightbulbs are. You might want to try solving for the case of 10 unlabeled circuit breakers first.

Riddle No. 6: Two Trains. Two Grandmas. Can You Solve This Tricky Math Riddle?

Jesse’s two grandmothers want to see him every weekend, but they live on opposite sides of town. As a compromise, he tells them that every Sunday, he’ll head to the subway station nearest to his apartment at a random time of the day and will hop on the next train that arrives.

If it happens to be the train traveling north, he’ll visit his Grandma Erica uptown, and if it happens to be the train traveling south, he’ll visit his Grandma Cara downtown. Both of his grandmothers are okay with this plan, since they know both the northbound and southbound trains run every 20 minutes.

But after a few months of doing this, Grandma Cara complains that she sees him only one out of five Sundays. Jesse promises he’s indeed heading to the station at a random time each day. How can this be?

The trains always arrive at their scheduled times.

Riddle No. 7: Here’s a Really F@*#ing Hard Math Problem About Ants

Max and Rose are ant siblings. They love to race each other, but always tie, since they actually crawl at the exact same speed. So they decide to create a race where one of them (hopefully) will win.

For this race, each of them will start at the bottom corner of a cuboid, and then crawl as fast as they can to reach a crumb at the opposite corner. The measurements of their cuboids are as pictured:

If they both take the shortest possible route to reach their crumb, who will reach their crumb first? (Don’t forget they’re ants, so of course they can climb anywhere on the edges or surface of the cuboid.)

Remember: Think outside the box.

Riddle No. 8: This Peppermint Patty Riddle Is Practically Impossible

You’re facing your friend, Caryn, in a “candy-off,” which works as follows: There’s a pile of 100 caramels and one peppermint patty. You and Caryn will go back and forth taking at least one and no more than five caramels from the candy pile in each turn. The person who removes the last caramel will also get the peppermint patty. And you love peppermint patties.

Suppose Caryn lets you decide who goes first. Who should you choose in order to make sure you win the peppermint patty?

First, solve for a pile of 10 caramels.

Riddle No. 9: Can You Solve the Great American Rail-Trail Riddle?

This problem was suggested by the physicist P. Jeffrey Ungar.

Finally, the Great American Rail-Trail across the whole country is complete! Go ahead, pat yourself on the back—you’ve just installed the longest handrail in the history of the world, with 4,000 miles from beginning to end. But just after the opening ceremony, your assistant reminds you that the metal you used for the handrail expands slightly in summer, so that its length will increase by one inch in total.

“Ha!” you say, “One inch in a 4,000 mile handrail? That’s nothing!” But … are you right?

Let’s suppose when the handrail expands, it buckles upward at its weakest point, which is in the center. How much higher will pedestrians in the middle of the country have to reach in summer to grab the handrail? That is, in the figure below, what is h ? (For the purposes of this question, ignore the curvature of the Earth and assume the trail is a straight line.)

Pythagoras is a fascinating historical figure.

Riddle No. 10: This Riddle Is Like an Especially Cruel SAT Problem. Can You Find the Answer?

Amanda lives with her teenage son, Matt, in the countryside—a car ride away from Matt’s school. Every afternoon, Amanda leaves the house at the same time, drives to the school at a constant speed, picks Matt up exactly when his chess club ends at 5 p.m., and then they immediately return home together at the same constant speed. But one day, Matt isn’t feeling well, so he leaves chess practice early and starts to head home on his portable scooter.

After Matt has been scooting for an hour, Amanda comes across him in her car (on her usual route to pick him up), and they return together, arriving home 40 minutes earlier than they usually do. How much chess practice did Matt miss?

Consider the case where Amanda meets Matt exactly as she’s leaving their house.

Riddle No. 11: Can You Get These 3 Movie Stars Across the River?

Three movie stars, Chloe, Lexa, and Jon, are filming a movie in the Amazon. They’re very famous and very high-maintenance, so their agents are always with them. One day, after filming a scene deep in the rainforest, the three actors and their agents decide to head back to home base by foot. Suddenly, they come to a large river.

On the riverbank, they find a small rowboat, but it’s only big enough to hold two of them at one time. The catch? None of the agents are comfortable leaving their movie star with any other agents if they’re not there as well. They don’t trust that the other agents won’t try to poach their star.

For example, Chloe’s agent is okay if Chloe and Lexa are alone in the boat or on one of the riverbanks, but definitely not okay if Lexa’s agent is also with them. So how can they all get across the river?

There isn’t just one way to solve this problem.

Riddle No. 12: This Ludicrously Hard Riddle Is Our Tribute to a Late Math Genius. Can You Figure It Out?

On April 11, John Horton Conway , a brilliant mathematician who had an intense and playful love of puzzles and games, died of complications from COVID-19. Conway is the inventor of one of my favorite legendary problems (not for the faint of heart) and, famously, the Game of Life . I created this problem in his honor.

Carol was creating a family tree, but had trouble tracking down her mother’s birthdate. The only clue she found was a letter written from her grandfather to her grandmother on the day her mother was born. Unfortunately, some of the characters were smudged out, represented here with a “___” . (The length of the line does not reflect the number of smudged characters.)

“Dear Virginia,

Little did I know when I headed to work this Monday morning, that by evening we would have a beautiful baby girl. And on our wedding anniversary, no less! It makes me think back to that incredible weekend day, J___ 27th, 19___ , when we first shared our vow to create a family together, and, well, here we are! Happy eighth anniversary, my love.

Love, Edwin”

The question: When was Carol’s mother born?

This problem is inspired by Conway’s Doomsday Rule .

Riddle No. 13: To Solve This Twisty Math Riddle, You Just Need One Belt and One Earth

Imagine you have a very long belt. Well, extremely long, really … in fact, it’s just long enough that it can wrap snugly around the circumference of our entire planet. (For the sake of simplicity, let’s suppose Earth is perfectly round, with no mountains, oceans, or other barriers in the way of the belt.)

Naturally, you’re very proud of your belt. But then your brother, Peter, shows up—and to your disgruntlement, he produces a belt that’s just a bit longer than yours. He brags his belt is longer by exactly his height: 6 feet.

If Peter were also to wrap his belt around the circumference of Earth, how far above the surface could he suspend the belt if he pulled it tautly and uniformly?

Earth’s circumference is about 25,000 miles, or 130 million feet … but you don’t need to know that to solve this problem.

Riddle No. 14: This Elbow Tapping Riddle Is Diabolical. Good Luck Solving It.

In some future time, when the shelter-in-place bans are lifted, a married couple, Florian and Julia, head over to a bar to celebrate their newfound freedom.

They find four other couples there who had the same idea.

Eager for social contact, every person in the five couples enthusiastically taps elbows (the new handshake) with each person they haven’t yet met .

It actually turns out many of the people had known each other prior, so when Julia asks everyone how many elbows they each tapped, she remarkably gets nine different answers!

The question: How many elbows did Florian tap?

What nine answers did Julia hear?

Riddle No. 15: You’ll Need a Drink After Trying to Solve This Whisky Riddle

Alan and Claire live by the old Scottish saying, “Never have whisky without water, nor water without whisky!” So one day, when Alan has in front of him a glass of whisky, and Claire has in front of her a same-sized glass of water, Alan takes a spoonful of his whisky and puts it in Claire’s water. Claire stirs her whisky-tinted water, and then puts a spoonful of this mixture back into Alan’s whisky to make sure they have exactly the same amount to drink.

So: Is there more water in Alan’s whisky, or more whisky in Claire’s water? And does it matter how well Claire stirred?

The size of the spoon does not matter.

Riddle No. 16: The Doodle Problem Is a Lot Harder Than It Looks. Can You Solve It?

This week’s riddle is relatively simple—but sinister all the same.

The question: Can you make 100 by interspersing any number of pluses and minuses within the string of digits 9 8 7 6 5 4 3 2 1? You can’t change the order of the digits! So what’s the least number of pluses and minuses needed to make 100?

For instance, 98 - 7 - 6 + 54 - 32 shows one way of interspersing pluses and minuses, but since it equals 107, it’s not a solution.

I call this a “doodle problem”: one that’s best worked on during meetings where you might be doodling otherwise.

You might want to start looking for solutions that use a total of seven pluses and minuses (although there are ways to use fewer).

Ready for the solution? Click here to see if you’re right.

Riddle No. 17: This Math Puzzle Stumped Every Scientist but One. Think You Can Crack It?

Difficulty: hard.

In honor of Freeman Dyson, the renowned physicist who died last month , here’s a legendary tale demonstrating his quick wit and incredible brain power.

One day, in a gathering of top scientists, one of them wondered out loud whether there exists an integer that you could exactly double by moving its last digit to its front. For instance, 265 would satisfy this if 526 were its exact double—which it isn’t.

After apparently just five seconds , Dyson responded, “Of course there is, but the smallest such number has 18 digits.”

This left some of the smartest scientists in the world puzzling over how he could have figured this out so quickly.

So given Dyson’s hint, what is the smallest such number?

My second grader has recently learned how to add a 3-digit number to itself using the classic vertical method:

18-digit numbers, of course, can be added in the same way.

Riddle No. 18: Figure Out What’s on Her Forehead

Cecilia loves testing the logic of her very logical friends Jaya, Julian, and Levi, so she announces:

“I’ll write a positive number on each of your foreheads. None of the numbers are the same, and two of the numbers add up to the third.”

She scribbles the numbers on their heads, then turns to Jaya and asks her what her number is. Jaya sees Julian has 20 on his forehead, and Levi has 30 on his. She thinks for a moment and then says, “I don’t know what my number is.” Julian pipes in, “I also don’t know my number,” and then Levi exclaims, “Me neither!” Cecilia gleefully says, “I’ve finally stumped you guys!”

“Not so fast!” Jaya says. “Now I know my number!”

What is Jaya’s number?

Jaya could be one of two numbers, but only one of those numbers would lead to Julian and Levi both not knowing their numbers. Why?

Riddle No. 19: Can You Get Keanu Reeves Elected As President?

It’s 2024, and there are five candidates running in the democratic primary: Taylor Swift, Oprah Winfrey, Mark Cuban, Keanu Reeves, and Dwayne Johnson. (Hey, it could happen.) As usual, the first primary is in Iowa.

In an effort to overcome its embarrassment after the 2020 caucus debacle , the Iowa Democratic Party has just announced a new, foolproof way of finding the best candidate: there will be four consecutive elections.

First, candidate 1 will run against candidate 2. Next, the winner of that will run against candidate 3, then that winner will run against candidate 4, and finally the winner of that election will run against the final candidate. By the transitive property, the winner of this last election must be the best candidate ... so says the Iowa Democratic Party.

Candidate Keanu has been feeling pretty low, as he knows he is ranked near the bottom by most voters, and at the top by none. In fact, he knows the Iowa population is divided into five equal groups, and that their preferences are as follows:

Keanu is childhood friends with Bill S. Preston, Esq., the new head of the Iowa Democratic Party. Preston, confident that the order of the candidates doesn’t matter for the outcome, tells Keanu he can choose the voting order of the candidates.

So what order should Keanu choose?

How would Keanu fare in one-to-one races against each candidate?

Riddle No. 20: Who Opened All These Damn Lockers?

There are 100 lockers that line the main hallway of Chelm High School. Every night, the school principal makes sure all the lockers are closed so that there will be an orderly start to the next day. One day, 100 mischievous students decide that they will play a prank.

The students all meet before school starts and line up. The first student then walks down the hallway, and opens every locker. The next student follows by closing every other locker (starting at the second locker). Student 3 then goes to every third locker (starting with the third) and opens it if it’s closed, and closes it if it’s open. Student 4 follows by opening every fourth locker if it’s closed and closing it if it’s open. This goes on and on until Student 100 finally goes to the hundredth locker. When the principal arrives later in the morning, which lockers does she find open?

Make sure you pay attention to all of the factors.

Laura Feiveson is an economist for the government, a storyteller, and a lifelong enthusiast of math puzzles.  She lives in Washington, DC with her husband and two daughters. 

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Alexander picks up a piece of wood and lights it from the fire on the west end of the island. He then quickly carries it near the east end of he island and starts a new fire. The wind will cause that fire to burn out the eastern end and he can then shelter in the burnt area. Alexander survives the fire, but dies of starvation, with all the food in the forest burnt....lolzzz

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