Logic Puzzles
All 45 of these free logic puzzles play right in your browser, with hints when you're stuck and scoring the moment you answer. You'll meet the classics: river crossings, knights and knaves, weighing problems, and number traps that punish fast guesses. Logic puzzle books are great on a long flight, but paper can't check your work, and here every card tells you right away whether your reasoning holds.
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1. A farmer must ferry a wolf, a goat, and a cabbage across a river. The boat holds the farmer plus one passenger. Left alone together, the wolf eats the goat and the goat eats the cabbage. How does everything cross safely?
Need a hint?
Nothing says a passenger can't ride the boat twice.
Show answer
Take the goat over first. Return empty, bring the wolf across, and take the goat back with you. Leave the goat, ferry the cabbage over, then return one last time for the goat. Seven crossings, nothing gets eaten.
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2. On an island, knights always tell the truth and knaves always lie. An islander points at his friend and says, 'We are both knaves.' What are they?
Need a hint?
Could a truth teller ever say that sentence about himself?
Show answer
The speaker is a knave and his friend is a knight. A knight could never truthfully call himself a knave, so the sentence must be a lie. If it's a lie, they are not both knaves, so the friend has to be a knight.
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3. Three boxes are labeled Apples, Oranges, and Mixed, and every single label is wrong. You may pull one piece of fruit from one box without looking inside. How do you fix all three labels?
Need a hint?
Start with the label that tells you the most when it's wrong.
Show answer
Draw from the box labeled Mixed. It can't actually be mixed, so whatever fruit you pull is all that box contains. Since the other two labels are also wrong, they now have only one legal way to swap.
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4. A hunter walks one mile south, one mile east, and one mile north, and ends up exactly where she started. She sees a bear. What color is it?
Need a hint?
Where on Earth can that walk bring you home?
Show answer
White. That route only loops back to its start at the North Pole, so it has to be a polar bear.
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5. I have two coins in my pocket that add up to 30 cents. One of them is not a nickel. What are the two coins?
Need a hint?
The statement is true. Read it very literally.
Show answer
A quarter and a nickel. One of them, the quarter, is not a nickel. The other one is.
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6. Two ducks swim in front of a duck, two ducks swim behind a duck, and one duck swims in the middle. What is the smallest number of ducks that makes this true?
Show answer
Three ducks, swimming in a single line. The front duck has two behind it, the back duck has two in front, and the middle duck is in the middle.
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7. A drawer holds 10 black socks and 10 blue socks, all loose. The room is pitch dark. How many socks must you grab to guarantee a matching pair?
Need a hint?
Plan for the worst case, not the lucky one.
Show answer
Three. With only two colors, any three socks must include at least two of the same color.
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8. Three friends pay 30 dollars for a room. The clerk realizes it costs 25 and sends 5 back with a bellhop, who pockets 2 and returns 1 to each friend. The friends paid 27, the bellhop has 2, and 27 plus 2 is 29. Where did the missing dollar go?
Need a hint?
Is that final addition even a sum that should equal 30?
Show answer
Nowhere. The 27 the friends paid already includes the bellhop's 2, so adding it again counts that money twice. The honest ledger reads 25 to the hotel, 2 to the bellhop, 3 refunded, which is exactly 30.
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9. During a race you somehow overtake the runner in last place. Why is that impossible?
Need a hint?
Where were you standing a second before the pass?
Show answer
To pass the last runner you'd have to be behind them. But if you were behind them, you were the one in last place, not them.
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10. In one family, each boy has as many brothers as sisters, but each girl has twice as many brothers as sisters. How many boys and girls are there?
Need a hint?
Try small numbers and count from one child's point of view. Kids don't count themselves.
Show answer
Four boys and three girls. Each boy sees three brothers and three sisters. Each girl sees four brothers and only two sisters.
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11. You have a 5 liter jug, a 3 liter jug, and a tap with unlimited water. How do you measure exactly 4 liters?
Need a hint?
The leftover after a pour is the whole trick.
Show answer
Fill the 5 and pour it into the 3, leaving 2 liters in the big jug. Empty the 3 and pour those 2 liters in. Refill the 5, then top up the 3. Exactly 1 liter leaves the big jug, and 4 liters remain.
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12. A fork in the road leads to Truthville, where everyone tells the truth, and Liarburg, where everyone lies. A local stands at the fork, but you don't know her hometown. What single question reveals the road to Truthville?
Need a hint?
Design a question where the lie and the truth point the same way.
Show answer
Ask, 'Which road leads to your town?' A Truthville local points to Truthville honestly. A Liarburg local also points to Truthville, since she must lie about her own home. Either way, take the road she picks.
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13. A census taker asks a woman for her three children's ages. She says they multiply to 36 and add up to the house number next door. He checks the number and says he still can't tell. She adds, 'My oldest loves chess.' Now he knows. What are the ages?
Need a hint?
Why would knowing the sum still leave him stuck?
Show answer
Nine, two, and two. Only two sets multiplying to 36 share a sum, 13: the sets 9, 2, 2 and 6, 6, 1. That's why the house number wasn't enough. The word 'oldest' kills the 6, 6, 1 option, because twins can't give you one single oldest child.
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14. Two fathers and two sons go fishing. Each catches exactly one fish, yet only three fish are caught in total. How?
Show answer
They are three people: a grandfather, his son, and his grandson. The middle man is both a father and a son.
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15. Four prisoners are buried up to their necks. A wall separates the first from the other three, who stand in a line facing the wall. They wear two black and two white hats and can only look forward. If any one of them correctly names his own hat color, all go free. Who speaks, and why?
Need a hint?
Silence is information too.
Show answer
The man standing second from the wall. The man at the back sees the two hats ahead of him. If they matched, he'd know his own color and speak. His silence tells the man in front of him that their two hats differ, so that man calls the opposite of the color he sees ahead.
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16. Four people must cross a bridge at night with one flashlight. At most two may cross at once, and every crossing needs the light. They take 1, 2, 5, and 10 minutes, and a pair moves at the slower person's speed. What is the fastest total time?
Need a hint?
Make the two slowest people share a single trip.
Show answer
17 minutes. The 1 and 2 cross together (2), the 1 runs back (1), the 5 and 10 cross together (10), the 2 returns (2), and finally the 1 and 2 cross again (2).
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17. A hundred kids stand in a circle playing an elimination game. Starting the count at player 1, every second player still standing is tagged out, round after round, until one remains. Which player wins?
Need a hint?
Solve it for 2, 4, 8, and 16 players first and watch the pattern.
Show answer
Player 73. The pattern depends on powers of two: with exactly 64 players, player 1 would win. The 36 extra players shift the winner by two spots each, and 2 times 36 plus 1 is 73.
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18. A driver changing a flat tire drops all four lug nuts down a storm drain. A kid walking past gets the car back on the road within minutes. What did the kid suggest?
Need a hint?
The car has more than one wheel.
Show answer
Borrow one lug nut from each of the other three wheels. Three nuts per wheel holds fine for a careful drive to the garage.
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19. You're stranded on an island covered in dry forest. A fire starts at the west end, and a steady wind pushes it east toward you. Cliffs drop into rough sea on every side. How do you survive?
Need a hint?
Fight fire with fire, literally.
Show answer
Light your own fire and let the wind carry it east ahead of you. Then walk onto the freshly burned ground and wait. When the main fire arrives, it finds nothing left to burn around you.
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20. Back on the island of knights and knaves, islander A says, 'B and I are the same type.' What is B?
Need a hint?
Test both possibilities for A and watch what happens to B.
Show answer
B is a knight, no matter what A is. If A tells the truth, they're both knights. If A lies, they're different types, which still makes B the knight.
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21. A bat and a ball cost 1.10 together. The bat costs one dollar more than the ball. How much is the ball?
If the ball were 10 cents, the bat would be 1.10 and the pair 1.20. At 5 cents the bat is 1.05 and the total is exactly 1.10.
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22. A patch of lily pads doubles in size every day and covers the whole lake on day 48. On which day does it cover half the lake?
It doubles daily, so the day before full coverage it was at exactly half.
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23. If 5 machines take 5 minutes to make 5 widgets, how long do 100 machines take to make 100 widgets?
One machine makes one widget in 5 minutes. A hundred machines make a hundred widgets in the same 5 minutes, all at once.
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24. On a game show you pick one of three doors; one hides a car. The host, who knows what's where, opens a different door showing a goat and offers a swap. What should you do?
Your first pick wins only 1 time in 3. Switching wins whenever your first pick was wrong, which is 2 times in 3.
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25. In a race you overtake the runner in second place. What position are you in now?
You take the spot of the person you passed. Passing second place makes you second, not first.
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26. When I was 6, my sister was half my age. Now I am 70. How old is my sister?
Half my age back then was 3, so she is 3 years younger. 70 minus 3 is 67, not half of 70.
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27. Nine identical balls, but one is slightly heavier. You have a balance scale. What's the minimum number of weighings that guarantees you find the heavy ball?
Weigh 3 against 3. The heavy group reveals itself (or it's the group left out). Then weigh 1 against 1 from that group.
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28. Four cards show A, K, 4, and 7. Rule: if a card has a vowel on one side, it has an even number on the other. Which cards must you flip to test the rule?
The A could hide an odd number, and the 7 could hide a vowel; both would break the rule. The 4 proves nothing either way, and the K is irrelevant.
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29. What number comes next: 2, 3, 5, 9, 17, ...?
The gaps double: 1, 2, 4, 8. Add 16 to 17 and you get 33.
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30. The doctor hands you three pills and says to take one every half hour. How long until you've taken all three?
Pill one at zero, pill two at 30 minutes, pill three at 60. Only two gaps, so one hour.
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31. Two trains 100 miles apart head toward each other, each at 50 mph. A bird shuttles between them at 75 mph until they meet. How far does the bird fly?
Skip the zigzags. The trains close at 100 mph, so they meet in one hour, and the bird flies 75 mph for that hour.
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32. How many times do a clock's hour and minute hands overlap in a full 24 hours?
The hands overlap 11 times every 12 hours, not 12, because the hour hand keeps creeping forward. That makes 22 in a day.
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33. Ten people at a meeting each shake hands with every other person exactly once. How many handshakes happen?
Show answer
45
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34. This sequence describes itself out loud: 1, 11, 21, 1211, 111221. What number comes next?
Show answer
312211
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35. What letter comes next: O, T, T, F, F, S, S, ...?
Show answer
E
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36. A frog sits at the bottom of a 30 foot well. Each day it climbs 3 feet, and each night it slips back 2. On which day does it finally hop out?
Show answer
Day 28
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37. How many times does the digit 9 appear when you write out every number from 1 to 100?
Show answer
20
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38. If it rains, the street gets wet. The street is wet this morning. Therefore it must have rained last night.
A sprinkler, a street cleaner, or a burst pipe wets streets too. Wet streets are consistent with rain, but they don't prove it.
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39. Every square is also a rectangle.
A rectangle needs four right angles with opposite sides equal. A square meets all of that; it just adds equal sides.
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40. If all Zips are Zaps, and no Zaps are Zops, then no Zips are Zops.
Every Zip sits inside the Zap group, and that whole group is walled off from the Zops. No Zip can sneak through.
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41. All roses are flowers. Some flowers fade quickly. Therefore some roses fade quickly.
The quick faders might all be tulips. Nothing forces the two groups to overlap, so the conclusion doesn't follow.
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42. What shape comes next in this pattern?
Show answer
A triangle. The pattern repeats in threes: circle, square, triangle. The sixth slot restarts nothing; it finishes the second set.
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43. One of these four shapes does not belong. Which one?
Show answer
Shape 4, the triangle. Shapes 1, 2, and 3 all have four sides; even the tilted diamond is a four sided shape. The triangle only has three.
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44. How many squares can you find in this figure in total?
Show answer
Five. Four small squares, plus the big outer square that most people forget to count.
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45. The scale balances: one circle weighs the same as two triangles. How many triangles would balance two circles?
Show answer
Four triangles. Each circle is worth two triangles, so two circles need two plus two.