Riddles

20 Math Riddles and Logic Puzzles (With Answers)

Twenty math riddles and logic puzzles with hidden answers and clear explanations, from quick number tricks to classic river-crossing and weighing puzzles.

Colorful wooden tangram pieces, a pair of dice and a small brass balance scale on a desk
Illustration: WhiteFool / AI-generated.
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Math riddles are jokes for the logical brain: the answer is usually simpler than it looks, and the fun is in spotting the trap. These twenty start with quick number tricks and build to classic logic puzzles. Answers are hidden, each with a short explanation so nobody feels cheated.

Quick number riddles

1. If two’s company and three’s a crowd, what are four and five?

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Nine.

2. I’m an odd number. Take away one letter and I become even. What number am I?

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Seven. Remove the S and you get “even.”

3. How can you add eight 8s to get 1,000?

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888 + 88 + 8 + 8 + 8 = 1,000.

4. When I was 6, my sister was half my age. Now I’m 70. How old is my sister?

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67. She was 3 when you were 6, so she is always three years younger.

5. Divide 30 by half and add 10. What do you get?

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70. Dividing by a half is the same as multiplying by 2: 30 ÷ ½ = 60, plus 10.

6. A farmer has 17 sheep. All but 9 run away. How many are left?

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Nine. “All but 9” means nine stayed put.

7. Which three positive whole numbers give the same answer whether you add or multiply them?

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1, 2 and 3. Both 1 + 2 + 3 and 1 × 2 × 3 equal 6.

Trick questions that fool grown-ups

8. A bat and a ball cost $1.10 together. The bat costs $1.00 more than the ball. How much is the ball?

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5 cents. The bat is then $1.05. If the ball were 10 cents, the bat would be $1.10 and the total $1.20.

9. If 5 machines take 5 minutes to make 5 widgets, how long do 100 machines take to make 100 widgets?

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5 minutes. Each machine makes one widget in 5 minutes.

10. A patch of lily pads doubles in size every day and covers the whole lake in 48 days. When was the lake half covered?

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Day 47. It doubles on the last day, so it was half the size the day before.

11. A clock strikes six times in 5 seconds. How long does it take to strike twelve?

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11 seconds. Six strikes have five one-second gaps; twelve strikes have eleven.

Classic logic puzzles

12. A snail at the bottom of a 10-foot well climbs 3 feet each day and slides back 2 feet each night. When does it get out?

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On day 8. After seven days and nights it is 7 feet up. On day 8 it climbs the last 3 feet and escapes before it can slide back.

13. A farmer must row a fox, a goose and a bag of grain across a river. The boat holds him and one item. Left alone, the fox eats the goose and the goose eats the grain. How does he do it?

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Take the goose across. Return and take the fox, then bring the goose back. Take the grain across and leave it with the fox. Finally, go back for the goose.

14. You have a 3-liter jug, a 5-liter jug and a tap. How do you measure exactly 4 liters?

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Fill the 5-liter jug and pour it into the 3-liter jug, leaving 2 liters. Empty the small jug and pour the 2 liters in. Refill the big jug and top up the small one, which takes 1 liter. Exactly 4 liters remain.

15. Three switches outside a closed room control three bulbs inside. You may open the door only once. How do you match them?

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Turn on switch 1 for a few minutes, turn it off and turn on switch 2. Go in. The lit bulb is switch 2, the warm dark bulb is switch 1 and the cold dark bulb is switch 3.

16. Two ropes each take exactly an hour to burn, but they burn unevenly. How can you time 45 minutes?

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Light rope A at both ends and rope B at one end. When A burns out after 30 minutes, light the other end of B. It burns out 15 minutes later.

17. Eight identical-looking balls include one that’s slightly heavier. How do you find it with only two uses of a balance scale?

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Weigh three against three. If they balance, weigh the last two against each other. If one side is heavier, weigh two balls from that side; if they balance, the third is the heavy one.

What comes next?

18. 1, 1, 2, 3, 5, 8, …

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13. Each number is the sum of the two before it: the Fibonacci sequence.

19. 1, 4, 9, 16, 25, …

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36. These are the square numbers: 1², 2², 3² and so on.

20. O, T, T, F, F, S, S, E, …

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N, for Nine. They are the first letters of One, Two, Three…

Which puzzles suit which players?

Puzzle typeGood forWhat it trains
Quick number riddlesAges 7 and upReading carefully
Trick questionsTeens and adultsSlowing down before answering
Logic puzzlesAges 10 and upStep-by-step planning
SequencesEveryoneSpotting patterns

Stuck? Draw it. A quick sketch of the riverbank or the jugs makes most logic puzzles click. For more head-scratchers, try our brain teasers for adults, or for younger solvers, riddles for kids.

Frequently asked questions

Are math riddles good for kids?

Yes. They teach children to read a problem carefully, test an idea and explain their thinking. Start with the quick number riddles and save the logic puzzles for ages ten and up.

Why do so many adults get the bat-and-ball question wrong?

The fast answer, 10 cents, feels right, so most people never check it. It’s a famous example of intuition beating careful reasoning.

How can I make these puzzles easier?

Use real objects: coins for the weighing puzzle, cups for the jugs and toy animals for the river crossing.

Every article is edited by a human and checked against our editorial policy. Spotted a mistake? Tell us.

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