Brain teasers and logic puzzles

Fifteen classics with worked answers. Some need logic, some need a sideways look. Each card tells you which.

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  1. Logic

    You have two ropes. Each takes exactly one hour to burn, but they burn unevenly. How do you measure 45 minutes?

  2. Logic

    You have a 3-litre jug and a 5-litre jug and a tap. How do you measure exactly 4 litres?

  3. Lateral

    Three light switches outside a closed room control one bulb inside. You may enter the room once. How do you tell which switch works the bulb?

  4. Logic

    A farmer must cross a river with a wolf, a goat and a cabbage. The boat carries him and one item. Left alone, the wolf eats the goat and the goat eats the cabbage. How does he do it?

  5. Math

    There are 100 lockers, all closed. Student 1 opens every locker, student 2 toggles every 2nd, student 3 every 3rd, and so on up to student 100. Which lockers end up open?

  6. Math

    You have 8 balls; one is slightly heavier. With a balance scale, what is the fewest weighings that guarantees finding it?

  7. Math

    A snail is at the bottom of a 10 m well. Each day it climbs 3 m and each night it slides back 2 m. On which day does it get out?

  8. Pattern

    What is the next letter? O, T, T, F, F, S, S, E, …

  9. Logic

    A man looks at a portrait and says: "Brothers and sisters I have none, but that man's father is my father's son." Who is in the portrait?

  10. Lateral

    If you are running a race and pass the person in second place, what place are you in?

  11. Lateral

    Two coins add up to 30 cents, and one of them is not a nickel. What are they?

  12. Math

    A doctor gives you three pills and says take one every half hour. How long do they last?

  13. Math

    What is half of two plus two?

  14. Logic

    On an island, knights always tell the truth and knaves always lie. A says: "We are both knaves." What are A and B?

  15. Lateral

    How can you drop a raw egg onto a concrete floor without cracking it?

Try it by hand: the water jug puzzle

You have a 3-litre jug, a 5-litre jug and a tap. Get exactly 4 litres into either jug. The shortest solution takes six moves.

0 / 3 L
0 / 5 L

Moves: 0

Why it works: the two jugs differ by 2 litres, and pouring the big one into the small one leaves that difference behind. Repeat the trick and you step through 2, then 4. Mathematicians describe this with Bézout's identity: with jugs of 3 and 5, whose greatest common divisor is 1, you can measure any whole number of litres up to 5.

Questions people ask

What is the difference between a brain teaser and a logic puzzle?

A logic puzzle can be solved step by step from the facts given (river crossings, knights and knaves). A brain teaser often relies on a trick of wording or a lateral leap. We tag each one so you know which kind you are facing.

Are brain teasers good for your brain?

They are good practice at the specific kind of reasoning they use. Research, including large trials of commercial brain-training apps, has found little evidence that puzzles raise general intelligence, but they are a fine way to stay curious.

What is the hardest classic brain teaser here?

The 100 lockers puzzle. The answer (perfect squares) makes sense only once you realise each locker is toggled once for every divisor of its number.

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