The Collection
Every logic puzzle here is machine-checked by a solver before it is published: one provable solution, no ambiguous clues. Classic imports from the public domain are labeled until they pass review.
Showing 48 of 48 puzzles
The Ferryman’s Troublesome Cargo
A traveller reaches a river with three awkward pieces of cargo: a wolf, a goat, and a basket of cabbages. His small boat can carry only the traveller and one of them at a time. He may also cross alone. Whenever the trave…
The Expanding Lily
A single water lily is growing across a quiet pond. Each day, the total surface area covered by the lily becomes exactly twice what it covered the day before. The growth continues at this steady rate, and at the end of t…
The Traveling Spoonful
Two glasses sit on a table. One contains only water, and the other contains only wine. A full spoonful is taken from the wine glass, poured into the water glass, and stirred until the liquids are evenly mixed. Next, usin…
The Warden’s Unmarked Morning
At noon on Sunday, a judge tells a prisoner: “On exactly one weekday next week, you will be taken to the courtyard and hanged. The date will not be announced beforehand, and when you wake that morning you will not be abl…
The Fly’s Final Commute
Two trains are travelling toward each other along the same straight track. At the start, the fronts of the trains are 120 kilometres apart, and each train moves at a constant speed of 40 kilometres per hour. A fly begins…
The Four-Litre Finish
You have two unmarked jugs. One holds exactly three litres, and the other holds exactly five litres. A water supply and a drain are both available, so you may use as much water as needed. Each of the following actions c…
The Last Question at the Gate
You stand in a stone chamber with two closed doors. One door leads safely outside; the other opens onto a fatal trap. A guard stands beside each door. Both guards know which exit is safe. One guard always speaks truthful…
The Counterfeit Dozen
Twelve coins are visually indistinguishable. Eleven have exactly the same weight; the remaining coin is either heavier or lighter, but you do not know which. You have a two-pan balance scale that reports only whether the…
The Eight-Disc Transfer
A tower of eight discs rests on the left peg. Every disc has a different diameter, and the discs are arranged from largest at the bottom to smallest at the top. Two other pegs stand empty. Your task is to rebuild the ent…
The Dark Door Test
A closed room contains one working incandescent bulb. Outside the room are three switches, labeled A, B, and C. Exactly one switch controls the bulb; the other two are disconnected. The door is sealed well enough that yo…
The Third Sage Speaks
Three sages are shown a collection of five hats: three are white and two are black. While their eyes are closed, each sage is given one hat to wear. The two unused hats are hidden. Once they open their eyes, each sage c…
A Pair in the Dark
A bedroom drawer contains a jumble of socks in exactly two colors: black and blue. There are plenty of socks of each color, but the room is completely dark, so you cannot tell one color from the other by looking. You mus…
The Borrowed Camel
A herder dies and leaves his seventeen camels to his three sons. His instructions say that the eldest must receive one half of the herd, the middle son one third, and the youngest one ninth. The camels cannot be sold, ki…
The Midnight Cellar Test
A vintner has 1,000 sealed barrels. Exactly one contains a fatal poison; the rest are harmless. Anyone who tastes the poisoned liquid dies exactly 24 hours later, with no earlier symptoms. You have a group of tasters ava…
The Heavy Ninth
Nine coins are indistinguishable in size and appearance. Eight have exactly the same weight, while the remaining coin is slightly heavier. You have a balance scale with two pans, but no standard weights. Each use of the …
Three Uneven Heaps
Three heaps of counters sit on a table. One heap contains 3 counters, another contains 4, and the last contains 5. You and an opponent alternate turns. On each turn, a player must choose exactly one heap and remove one o…
The Warder’s Coin
Arin, Bela, and Corin are awaiting execution. The governor has secretly selected exactly one of them for a pardon, choosing each prisoner with equal probability. Arin asks a warder, who knows the decision, to name eithe…
The Missing Corners
Begin with an ordinary 8-by-8 chessboard, colored in the usual alternating pattern. Remove two squares: one corner and the corner diagonally opposite it. The remaining board has sixty-two squares. You also have thirty-o…
The Perilous River Crossing
Three missionaries and three cannibals are waiting on the west bank of a river. They have one small boat, which can carry either one or two people. Every trip must have at least one passenger, and anyone in the group—mis…
The Knight’s Grand Circuit
Place a knight on any square of a standard 8×8 chessboard. It then makes ordinary knight moves: two squares in one direction and one square at right angles. The starting square counts as visited. Can the knight travel t…
The Forty-One Circle
Forty-one soldiers stand in a circle, numbered 1 through 41. Beginning with soldier 1, a count proceeds clockwise: the first soldier is spared, the second is killed, the third is spared, the fourth is killed, and so on. …
The Suspicious Six
Three married couples are waiting on the west bank of a river. A small boat can carry either one or two people, and everyone can row it. The couples are unusually jealous. At no time may a wife be on either bank with an…
The Last Hat Signal
Ten prisoners are placed in a single-file line. Each is given either a black hat or a white hat. Everyone can see the hats worn by the people ahead, but nobody can see their own hat or any hat behind them. Starting with …
Sixty-Six Greetings
At a small evening party, every guest greets every other guest with exactly one handshake. No one shakes their own hand, no pair meets twice, and nobody skips anyone. By the time all the introductions are complete, the h…
The Million-Grain Square
A ruler offers a clever scholar a reward measured out on a standard 64-square chessboard. One grain of wheat is placed on the first square. The second square receives two grains, the third receives four, and every later …
The Frog’s Final Climb
A frog is trapped at the bottom of a well that is 30 feet deep. Every day, it climbs 3 feet up the wall. Each night, while resting, it slips 2 feet back down. The frog begins its first climb at dawn, and once it reaches …
Fifteen Puzzle: One Bad Swap
A square tray has sixteen spaces arranged in four rows of four. Fifteen tiles, numbered 1 through 15, can slide within the tray; the remaining space is empty. A move consists of sliding one tile horizontally or verticall…
The Riverboat Relay
A marching column reaches a river with no bridge. On the bank, two boys have a tiny boat. The boat can safely carry either both boys together or one soldier alone. It cannot carry a soldier with either boy, and nobody ca…
Eight Queens, No Truce
Place eight queens on a standard 8×8 chessboard. Every queen attacks along its row, its column, and both diagonals. Your placement must leave every pair of queens unable to attack each other. Count arrangements by exact…
The Stone’s Fractional Life
An old gravestone describes a man’s life in numbers rather than dates. He spent one sixth of his entire lifetime in childhood. After another one twelfth of his lifetime, his youth ended. A further one seventh of his life…
The Missing Grams
A mint has arranged coins into ten separate stacks. Nine stacks contain ordinary coins weighing exactly 10 grams each. Every coin in the remaining stack is counterfeit and weighs exactly 9 grams, but that stack looks ide…
Three Valves, One Cistern
A caretaker needs to fill an empty cistern. The first inlet, working alone at a steady rate, can fill the entire cistern in three hours. A second inlet also runs steadily and would fill the cistern by itself in four hour…
Tracks in the Farmyard
At feeding time, a farmer counts every chicken and rabbit in a small enclosed yard. Each animal has one head, so the farmer can tell that there are thirty-five animals altogether. The animals will not stay still long eno…
Chameleons at Dusk
A secluded colony contains 45 chameleons: 13 are red, 15 are green, and 17 are blue. Whenever two chameleons of different colours meet, they both immediately change to the third colour. For example, a red chameleon meeti…
The Vanishing Coin at Room 12
Three travelers rent a hotel room and pay $30 altogether, each contributing $10. Later, the desk clerk realizes the room should have cost only $25 and sends a porter upstairs with a $5 refund. The porter decides that $5 …
The Census Taker’s Last Clue
A census taker knocks at a house and asks a parent for the ages of her three daughters. She replies, “Their ages are whole numbers, and if you multiply them together, you get thirty-six.” “That does not tell me enough,”…
The Desert Banana Relay
A trader has 3,000 bananas at the edge of a desert. His camel must transport as many as possible to a market 1,000 miles away. The camel can carry no more than 1,000 bananas at once, and it eats one banana for every mile…
The Last Minute Before the Hour
You have two ropes and a supply of matches. Each rope takes exactly 60 minutes to burn from one end to the other, but neither burns at a steady rate: one section might vanish quickly while another smolders for much longe…
Bridges of Königsberg
Königsberg is divided by a river into four land areas: a north bank, a south bank, and two islands. Seven bridges connect them. The larger island has two bridges to the north bank, two to the south bank, and one to the s…
The Lantern on Blackwater Bridge
Four hikers reach a narrow bridge after dark. Their lantern is the only safe source of light, and everyone—including anyone returning—must carry it while crossing. The bridge can support no more than two hikers at once. …
The Visitor’s Blue-Eye Announcement
On an island live perfect logicians. Each person can see everyone else’s eye colour but cannot see their own, and nobody may discuss eye colours. Every islander knows these rules and knows that everyone reasons flawlessl…
The Crowded Calendar
A host gathers a group of people in one room and wonders whether any two of them celebrate their birthdays on the same date. Assume there are 365 possible birthdays, each date is equally likely, birthdays are independent…
The Gilded Draw
Three identical boxes sit on a table. One contains two gold coins, another contains two silver coins, and the third contains one gold coin and one silver coin. You choose one of the three boxes uniformly at random. Witho…
The Full Feathered Purse
A poultry keeper has exactly 100 coins to spend and wants to return with exactly 100 birds. Roosters cost 5 coins each, hens cost 3 coins each, and chicks are sold at the rate of 3 chicks for 1 coin. The keeper must buy …
The Razor Rule
In a remote village, a notice outside the only barbershop describes its male barber’s duty with perfect precision: he shaves every man in the village who does not shave himself. The notice also insists that he shaves no …
The Uneven Pack Train
A mule and an ass are walking to market, each carrying a whole number of sacks. The mule notices that their loads could be rearranged in two revealing ways. “If I took one sack from you,” the mule tells the ass, “I woul…
The Last Ant Off
A straight pole is exactly one metre long. Several ants stand at arbitrary points along it. Each ant chooses one of the two directions and walks steadily at one metre per minute. Whenever two ants meet, both instantly tu…
The Vanishing Lead
Achilles races a tortoise along a straight track. Because Achilles runs much faster, he allows the tortoise a head start of 100 metres. To overtake it, Achilles must first reach the tortoise’s starting point. During tha…
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