Think differently: the riddle journey

Take one puzzle at a time. Try it yourself, ask for a hint if you want one, and bring the insight back to something you want to do with AI. Paper and a pen are enough. An AI assistant is optional.

Your rhythm: try → notice an assumption → explore another approach → check → apply. Allow about 10 minutes per riddle, with more time when you want to explore. You can stop and return; this browser remembers the steps you mark complete.

If you already know a solution, change a rule and see whether it still works. There is no speed test. The useful result is a new way of approaching your own problem.

1. Nine dotsLink to step

Try: Copy the dots. Draw at most four connected straight line segments that pass through every dot, without lifting your pen. A line may continue past a dot.

Text alternative: the dots have coordinates (0,0), (1,0), (2,0), (0,1), (1,1), (2,1), (0,2), (1,2), (2,2). You may describe the line endpoints instead of drawing.

Bring it to your project: Name one restriction you assumed that nobody actually required.

Success: You can trace a valid route and distinguish a written rule from an imagined rule.

2. The candle boxLink to step

Try: Imagine a candle, matches and a small box holding thumbtacks. How would you support the candle on a cork wall so wax does not fall onto the table underneath? You may use every supplied object. Sketch your answer; there is no need to light a candle.

Bring it to your project: Could a spreadsheet, template or application you already have do the job you thought required a new AI app?

Success: You can explain what changed when you stopped treating the box only as a container.

3. Three wrong labelsLink to step

Try: Three opaque boxes contain only apples, only oranges, and a mixture of both. Their labels read apples, oranges and mixed, but every label is wrong. You may draw one fruit from one box. How can that single observation let you correct all three labels?

Bring it to your project: What one question would remove the most uncertainty from your current request?

Success: You can explain why you chose that box and identify all three boxes for either possible draw.

4. The barometerLink to step

Try: You have a barometer—an instrument that measures air pressure—and may use ordinary additional materials. Suggest three different ways to estimate a building's height. Choose one for a real situation and explain its limitations. This is a thought experiment: stay on the ground.

Bring it to your project: Suggest three ways to get your desired result, including one that does not use AI. Choose on usefulness and effort, not novelty alone.

Success: Your alternatives really use different methods, and you can defend your choice for the situation.

5. The missing cornersLink to step

Try: Can 31 dominoes cover this board? Each domino must cover two edge-adjacent squares, without overlap or extending outside the remaining board.

Text alternative: start with an 8 × 8 board of alternating light and dark squares. Remove diagonally opposite corners. There are 62 squares left.

Bring it to your project: Could a proposed solution be impossible under your constraints? What simple check could reveal that before you start building?

Success: You can explain why the task is impossible, rather than only saying that your attempts failed.

6. Seven bridgesLink to step

Try: Walk across every bridge exactly once. You may start and finish anywhere, but travel between places is only by bridge. Is there a route?

Text alternative: draw four places A, B, C and D. Connect A–C twice, A–D twice, A–B once, B–C once and B–D once. Each connection is a separate bridge.

Bring it to your project: Redraw a complicated process as boxes and connections. What becomes clearer when you remove the decoration?

Success: You can explain the failed route using connections, rather than trying every possible walk.

7. Four travellersLink to step

Try: Four travellers each use a different mode of transport: car, train, plane or ship. Cindy uses the car. Jones does not fly. John does not take the ship. Must Rachel use one particular mode of transport?

Bring it to your project: Give AI a brief and ask it for two different solutions that satisfy all the stated requirements. What extra information would help you choose?

Success: You can show at least two valid assignments without inventing another clue.

8. Test the ruleLink to step

Try: Each card has a letter on one side and a number on the other. The visible faces are A, D, 4, 7. Which cards must you turn over to test this rule?

If a card has a vowel on one side, it has an even number on the other.

Bring it to your project: Write one test that could disprove a claim in an AI answer, instead of only finding an example that agrees.

Success: You can say why each of the four cards does or does not need checking.

9. Switch the doorLink to step

Try: A prize is placed uniformly behind one of three doors. You choose a door. A host knows where the prize is, always opens another door without a prize, and always offers you a switch to the remaining unopened door. Is switching better?

Bring it to your project: Change the host's rule—for example, let them open a random other door without knowing where the prize is. Does the old explanation still apply? Ask the same question about how examples or data were selected in your project.

Success: You can explain the original result and name the assumption that your changed version invalidates.

10. Uneven ropesLink to step

Try: You have two ropes. Each takes exactly 60 minutes to burn from one end, but burns unevenly along its length. Use the idealised puzzle model: lighting both ends consumes a whole rope in 30 minutes. You may light endpoints at the start and whenever you observe a rope finishing. How can you measure 45 minutes? Solve on paper.

Bring it to your project: Are you treating a convenient proxy—word count, token count or number of examples—as though it directly measured quality or usefulness?

Success: You can describe the sequence using observable events without measuring a rope's length.

11. Two liquidsLink to step

Try: Two glasses start with equal volumes: one water, one coloured liquid. Move a spoonful from the first to the second, stir, then return an equal-volume spoonful of the mixture. Assume additive volumes and no loss. Is there more water in the second glass or more coloured liquid in the first?

Bring it to your project: What should balance before and after a data transformation: totals, row counts, quantities or identifiers?

Success: You can explain the equality using what stays constant, rather than relying on a guessed percentage.

12. Break the chocolateLink to step

Try: A chocolate bar has 4 × 6 small squares. Each break splits exactly one existing piece into two along a grid line. You cannot stack pieces. How many breaks separate every square?

Bring it to your project: Before optimising a complicated procedure, ask whether a simple count or equation tells you what improvement is actually possible.

Success: You can explain the general rule and predict what would change if stacking were allowed.

Bring one insight back

Choose a real task you care about. Finish these four sentences:

• I had assumed…
• Another way to approach this is…
• I can check that by…
• My next small step is…

If you want an AI partner, copy this request:

Help me explore this problem without giving away the answer immediately.
Ask one question that helps me examine an assumption.
After I propose a solution, check it against the exact rules.
Say if information is missing or more than one answer fits.

Then continue with your own first working result, frame a real problem, or check an AI answer.

Sources and more puzzles

These are course-written versions and original diagrams based on classic puzzles. Source pages can reveal the answers. Try the puzzle first if you want the surprise.

1. Nine Dots — Math Is Fun (opens in a new tab)
2. Duncker's Candle Problem (opens in a new tab)
3. Crates of Fruit — Math Is Fun (opens in a new tab)
4. The Barometer Question (opens in a new tab)
5. Mutilated Chessboard (opens in a new tab)
6. Seven Bridges of Königsberg (opens in a new tab)
7. Four People Travel — Math Is Fun (opens in a new tab)
8. Wason Selection Task (opens in a new tab)
9. Monty Hall — Math Is Fun (opens in a new tab)
10. Con Fusing — Math Is Fun (opens in a new tab)
11. Lemonink — Math Is Fun (opens in a new tab)
12. Breaking Up a Chocolate Bar — Math Is Fun (opens in a new tab)

For further challenges, explore NRICH (opens in a new tab), TED-Ed riddles (opens in a new tab) and Math Is Fun puzzles (opens in a new tab).