Logic Puzzles

All 44 of these free logic puzzles play right in your browser, with a hint on the harder classics. You'll meet the ones everybody knows: 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 the option, typed and drawn cards here mark your answer the moment you commit.

Logic puzzles reward a plan and punish the answer that arrives fast

These are not one line riddles with a pun at the end. A river crossing, two jugs and a tap, four walkers and one flashlight: each card hands you a rule set and asks for a sequence of moves that survives it. So do not answer the opening clue, restate it. Name the constraint that clue creates, then ask what the constraint actually forbids. The river card bans exactly two pairings and says nothing about how often a passenger may ride.

The second habit is to check what each number in the puzzle is really doing. Ten black socks and ten blue ones bind nothing; the color count does the job. A thirty foot well against a three foot climb invites a division that the nightly slip cancels. Where a card grades your tap on the spot, the first press is the one it records, so commit to the option your reasoning predicts and read the mark as a verdict on it.

Logic riddles carries many of these same classics, the river crossing, the jugs, the frog in the well, and every card there is text you read and grade yourself. What changes is the form: some cards hand you options, some want a typed answer, and some ask you to count what is drawn. Lateral thinking puzzles run the other way, hiding part of the story for a group to dig out with yes or no questions, and nothing here waits on one.

Riddle 5: most people say No such pair exists. One of them is a phrase about a single coin, and it leaves the second coin unmentioned. Read as a blanket ban it makes thirty cents unreachable with two coins, which is why solvers call the pair impossible instead of calling the sentence generous.
Riddle 8: most people say The bellhop pocketed it. Two dollars did go to the bellhop, and nothing is missing. Plus is the word that breaks the ledger: it joins two amounts that overlap, since the twenty seven the friends are out of pocket already contains the bellhop's share.
Riddle 17: most people say Player 50. Halving feels right because half the players are gone after one lap. Still standing is the phrase that rules the middle out: each lap counts only the survivors, and seat one wins a crowd of exactly sixty four, so each of the thirty six extra players pushes the winner two seats further along.
Riddle 35: most people say Day 30. Thirty feet at a net gain of one foot a day gives thirty days, and slips is the word that breaks the sum. A slip only follows a climb that leaves the frog inside the well, so the climb that clears the rim is never undone.

Name the constraint each number creates, then build the order of moves that satisfies every one of them.

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?

Most people first say: Take the wolf across first

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.

Forbid a second ride and the puzzle turns impossible, which is how you find the rule nobody wrote. Nothing on the card bans one, and the goat is the one item in both dangerous pairings, so it is the passenger that keeps crossing.
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?

Most people first say: They are both knaves

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.

Both is the word that drags the speaker into his own accusation. A truth teller saying it would be branding himself a liar, so the line is a lie, and a lie about both of them leaves the friend honest.
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?

Most people first say: Draw from the Apples box

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.

One label is worth more than the others: Mixed, because being wrong strips it of its ambiguity. One fruit then names that whole box, and the all wrong rule leaves exactly one legal way to place the other two labels.
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?

Most people first say: A brown bear

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.

The route is there to fix a place, not to be measured, and the card asks for a color. That makes the fact the whole answer: polar bears live in the far north, and a polar bear is white.
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?

Most people first say: No such pair exists

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.

Hearing it as a ban on nickels is fair, and that reading is what puts thirty cents out of reach for two coins. The wording covers one coin and leaves its partner unspoken, so the nickel was never ruled out.
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?

Most people first say: Five ducks

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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.

In front of and behind are relative positions, so one bird can satisfy several at once. A single file of three gives the lead duck two followers and the rear duck two leaders.
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?

Most people first say: Eleven socks

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.

Every sock you pull lands in one of only two color slots, so the first two can fill both and the third has to double up, which leaves the drawer totals out of the arithmetic entirely.
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?

Most people first say: The bellhop pocketed it

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.

Two ledgers run at once here, one for money the friends handed over and one for where it ended up. The bellhop's share already sits inside the twenty seven, so adding it again invents a total nobody owes.
9. During a race you somehow overtake the runner in last place. Why is that impossible?

Most people first say: It is perfectly possible

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.

What rank did you hold a step earlier? Behind the runner you overtook, and anyone behind the last runner is the last one, so the pass in the question never had a place to start from.
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?

Most people first say: Three boys and four girls

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.

One boy more than the girls is what equal counts force, since a boy does not count himself among his brothers. Then the girl's doubled view fixes the size, and four against three is the pair that fits both sentences.
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.

Stop watching the small jug and read the big one, because what fails to fit is the measurement. The first pour strands two liters, and carrying that leftover into the empty jug is what makes the final top up leave four.
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?

Most people first say: Ask where Truthville is

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.

What does a liar have to get wrong? Her own address, so a question about where she lives forces her to point at the other town, which is exactly where an honest local points too.
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?

Most people first say: Six, six, and one

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.

An offhand remark does the narrowing here, and the chess in it is decoration. A census taker still stuck after reading the house number tells you two triples share that total, and one oldest child is something a pair of sixes cannot supply.
14. Two fathers and two sons go fishing. Each catches exactly one fish, yet only three fish are caught in total. How?

Most people first say: One fish got thrown back

Show answer

They are three people: a grandfather, his son, and his grandson. The middle man is both a father and a son.

The scene needs only three people, because family words let one of them wear two titles at once. Being someone's son and someone else's father at the same moment costs no extra body.
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?

Most people first say: The man at the back

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.

Refusing to answer is itself a clue. The rear prisoner would have spoken instantly had the two hats before him matched, so his quiet proves they differ and the next man calls the reverse of the hat he sees.
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?

Most people first say: Nineteen minutes

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).

The flashlight has to come home after every forward trip but the last, so the real question is who walks back. Send the two slowest across together once, and let the quickest walker and his partner carry the light on every return.
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?

Most people first say: Player 50

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.

Shrink the problem before you touch a hundred. Seat one survives whenever the crowd is an exact power of two, so start at seat one and walk two seats forward for each of the thirty six players past sixty four.
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?

Most people first say: Call a tow truck

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.

Nothing in the scene says the replacement must come from outside the car. Once you drop that unwritten rule, the three wheels still bolted on are the nearest source of what the fourth one needs.
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?

Most people first say: Jump into the sea

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.

Fire stops where the fuel stops, so the thing to change is the ground you are standing on. Burn a patch while the wind still pushes flames away from you, then stand on the ash the main fire cannot use.
20. Back on the island of knights and knaves, islander A says, 'B and I are the same type.' What is B?

Most people first say: There is no way to tell

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.

The claim names the speaker, so his own type decides whether it is true. A true one makes the pair match as knights, a false one makes them differ, and the friend is a knight from either start.
21. A bat and a ball cost 1.10 together. The bat costs one dollar more than the ball. How much is the ball?

Show answer

5 cents

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.
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?

Show answer

Day 47

It doubles daily, so the day before full coverage it was at exactly half.
23. 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?

Show answer

Switch doors

Two doors left feels like an even split, but the host knows where the car is and never opens the one hiding it, so the goat he shows leaks information. Your first pick keeps its one in three and the other door absorbs the rest.
24. In a race you overtake the runner in second place. What position are you in now?

Show answer

Second

You take the spot of the person you passed. Passing second place makes you second, not first.
25. When I was 6, my sister was half my age. Now I am 70. How old is my sister?

Show answer

67

Half my age back then was 3, so she is 3 years younger. 70 minus 3 is 67, not half of 70.
26. 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?

Show answer

2

Weigh 3 against 3. The heavy group reveals itself (or it's the group left out). Then weigh 1 against 1 from that group.
27. 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?

Show answer

A and 7

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.
28. What number comes next: 2, 3, 5, 9, 17, ...?

Show answer

33

Work on the gaps rather than the terms themselves: each gap doubles the one before it, so adding sixteen gives the next value.
29. The doctor hands you three pills and says to take one every half hour. How long until you've taken all three?

Show answer

1 hour

Pill one at zero, pill two at 30 minutes, pill three at 60. Only two gaps, so one hour.
30. 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?

Show answer

75 miles

Skip the zigzags. The trains close at 100 mph, so they meet in one hour, and the bird flies 75 mph for that hour.
31. How many times do a clock's hour and minute hands overlap in a full 24 hours?

Show answer

22

The hands overlap 11 times every 12 hours, not 12, because the hour hand keeps creeping forward. That makes 22 in a day.
32. Ten people at a meeting each shake hands with every other person exactly once. How many handshakes happen?

Most people first say: Ninety handshakes

Show answer

45

Ten times nine measures the ends of handshakes, not handshakes, because each shake carries two people and a per person tally records it twice.
33. This sequence describes itself out loud: 1, 11, 21, 1211, 111221. What number comes next?

Most people first say: The number 311221

Show answer

312211

What is the input to the next line? The line before it, read aloud in runs: three ones, then two twos, then one one, and each run is written as its length followed by its digit.
34. What letter comes next: O, T, T, F, F, S, S, ...?

Most people first say: The letter N

Show answer

E

Seven letters are showing, and they are the openings of one through seven in order. The word after seven is eight, so a solver who loses the thread and jumps to nine plants an N where an E belongs.
35. 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?

Most people first say: Day 30

Show answer

Day 28

The nightly slide is a bill that comes due only when the frog is still inside at sundown, and day twenty eight begins at twenty seven feet with a three foot climb that clears the rim first.
36. How many times does the digit 9 appear when you write out every number from 1 to 100?

Most people first say: Ten nines

Show answer

20

The ones place supplies a nine every tenth number, and the tens place covers all ten of the nineties. Ninety nine sits in both blocks, which is why it earns two of the count and a round ten falls short.
37. If it rains, the street gets wet. The street is wet this morning. Therefore it must have rained last night.

Show answer

False.

A sprinkler, a street cleaner, or a burst pipe wets streets too. Wet streets are consistent with rain, but they don't prove it.
38. Every square is also a rectangle.

Show answer

True.

A rectangle needs four right angles with opposite sides equal. A square meets all of that; it just adds equal sides.
39. If all Zips are Zaps, and no Zaps are Zops, then no Zips are Zops.

Show answer

True.

Change the second premise to some Zaps are Zops and the conclusion stops following, because that overlap could miss every Zip. The word no makes the exclusion total, so anything sitting inside Zaps lands outside Zops.
40. All roses are flowers. Some flowers fade quickly. Therefore some roses fade quickly.

Show answer

False.

The quick faders might all be tulips. Nothing forces the two groups to overlap, so the conclusion doesn't follow.
41. What shape comes next in this pattern?

Most people first say: A circle

Show answer

A triangle. The pattern repeats in threes: circle, square, triangle. The sixth slot restarts nothing; it finishes the second set.

Read the five drawn shapes as a finished set and the gap looks like a fresh start, which is where a round shape comes from. Count in threes and the gap is the second group's last slot.
42. One of these four shapes does not belong. Which one?

Most people first say: Shape 3, the diamond

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.

Side count is the trait that splits these four, and tilting a figure leaves that count untouched, so the diamond keeps its four sides and the three sided figure stands alone.
43. How many squares can you find in this figure in total?

Most people first say: Four small squares

Show answer

Five. Four small squares, plus the big outer square that most people forget to count.

The question asks for squares in total, and the border around the grid is a square as well as a frame, so the four inside it are not the whole count.
44. The scale balances: one circle weighs the same as two triangles. How many triangles would balance two circles?

Most people first say: Two triangles

Show answer

Four triangles. Each circle is worth two triangles, so two circles need two plus two.

Once one round shape is worth a fixed number of pointed ones, doubling the left pan doubles whatever the right pan must carry, because the drawing states a swap rate and not a total.

FAQ about Logic Puzzles

What is a logic puzzle?

A puzzle whose answer is a procedure or a count rather than a clever word. River crossings, jug measurements, weighings, hat problems and self describing sequences are the standard shapes, and each one is judged by whether your steps obey every rule on the card.

What is the difference between a logic puzzle and a logic riddle?

A logic riddle is a short scene you settle in your head, and its reveal is a line of reasoning. A logic puzzle hands you its premises openly and asks you to produce the steps or the count, so the difficulty sits in the order of your moves and in the tally you keep.

How do you solve logic puzzles without guessing?

Turn each sentence into a constraint you can state plainly, then test one candidate answer against those constraints until something contradicts. On the counting puzzles, work the smallest version first: four players before a hundred, and two jugs before you worry about exact liters.

Which of these logic puzzles work for kids?

The sock drawer, the ducks in a line, the frog in the well and the drawn shape patterns land well from about nine years old. The census taker ages, the four prisoners in hats and the elimination circle suit teenagers and adults who want a longer sit down think.

The move you practice here, restating a rule before you obey it, carries straight into math brain teasers, where a missing fact and an added assumption trade places from card to card. For the same deduction dressed as a scene with a culprit, the murder mystery riddles hand you the evidence and let you argue from it.