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 50 of 189 puzzles
Knights and Knaves: Frank, Rupert, and Carol
On an island, every inhabitant is either a knight, who always tells the truth, or a knave, who always lies. You meet Frank, Rupert, and Carol. Rupert says: "I am a knave and Frank is a knave." Carol says: "Rupert is a k…
The Four Seats: Farid, Chiara, Dmitri, and Bao
Four guests (Farid, Chiara, Dmitri, and Bao) each have exactly one wine, hometown, and dish, and no two share any of them. Match each guest to their wine, hometown, and dish from these clues: 1. The guest from Lisbon is…
The Four Houses: The Gardener, the Tea Drinker, and the Pole
Four houses stand in a row, numbered 1 to 4 from left to right. Each holds exactly one of each attribute, and no attribute repeats. Work out the full arrangement from these clues: 1. The person in the red house is immed…
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…
Nicarete's Nuts
Nicarete shared out her nuts: a third to Cleis, a quarter to Sappho, a fifth to Aristodice, a twentieth and a twelfth to Theano, and a twenty-fourth to Philinnis. That left her 50 nuts. How many did she start with?
Seen Only by the Sleeping
No one sees me while they are awake, but they see me when asleep. I speak without a voice and move without walking. I am a deceiver, and yet I tell nothing but the truth.
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 Shared Apples
A girl shared out her apples: a fifth to Chrysis, a fourth to Hero, a nineteenth to Psamathe, a tenth to Cleopatra and a twentieth to Parthenope; twelve went to Evadne, and she kept 120 for herself. How many apples were …
Drink Me Young, Eat Me Old
If you had taken me in my youth you might have drunk my blood. Now that I am old, eat me wrinkled and dry, and crush my bones together with my flesh.
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 Bronze Lion
I am a bronze lion, and my spouts are my two eyes, my mouth, and the flat of my right foot. My right eye fills a jar in 48 hours, my left eye in 72 hours, and my foot in 96 hours. My mouth fills it in 6 hours. How long d…
One Father, Twelve Children
There is one father and twelve children. Each of the twelve has twice thirty children of two kinds: some are white and some are black, and though they never die, they all pass away.
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 Rectangular Field
A rectangular field covers 864 square paces, and it is 12 paces longer than it is wide. How wide is the field?
Two Feet, Four Feet, Three Feet
There is a creature on earth that is two-footed, four-footed and three-footed, and goes by one name. Alone of all that move on land, in the air or in the sea, it changes its nature; and when it walks on the most feet, it…
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 Door and Its Diagonal
A door is 6.8 feet taller than it is wide, and its diagonal measures 10 feet. How wide is the door?
Hairy Under My Cover
I am very hairy, but my covering hides my hairs unless there is a hole in it. I amuse many boys, and if one of them throws me badly he stands there looking a fool.
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 Remainder Problem
Find the smallest whole number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 2 when divided by 7.
Born in the Mountains
I was born in the mountains; my mother was a tree and my father is fire. I am a blackened mass, but if my father melts me in a deep vessel, I keep the chariot of the sea from harm.
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 Weaving Woman
A woman weaves 5 feet of cloth on the first day, and each day after that she weaves the same amount less than the day before, until she weaves 1 foot on the thirtieth and last day. How much cloth does she weave altogethe…
Silent When Shut
Wood gave birth to me and iron reshaped me. I am the secret keeper of the Muses. When I am shut I am silent; when I am opened, I speak.
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 Sea Island
Two poles 30 feet high stand 1,000 paces apart, in line with an island out at sea. An observer who walks 123 paces back from the near pole sees the island's summit in line with the top of that pole. Walking 127 paces bac…
A Brain Without a Head
I have a brain but no head; I am green and grow out of the ground on a long neck. I am like a ball set upon a flute, and if you look inside me you will find my grandfather.
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 Three Sisters
Three sisters come home every 5, 4 and 3 days. Today all three are at home together. In how many days will they next all be at home on the same day?
Sweeter Than My Mother
I bear the same name as my mother and I am sweeter than she is, but she is tall and I am tiny. She cannot be eaten except for her head; I can be eaten whole except for my insides.
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 Broken Bamboo
A bamboo 10 feet tall snaps part way up, and the top touches the ground 3 feet from the foot of the stem. How high above the ground is the break?
Lips That Open in Vain
If you look at me, I look at you too. You look with eyes, but I have none. You have a voice, but I speak without one, for I have only lips that open in vain.
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…
Three Classes of Corn
Three bundles of first-class corn, two of second class and one of third yield 39 measures. Two of first, three of second and one of third yield 34 measures. One of first, two of second and three of third yield 26 measure…
Black, White and Yellow
I am black, white, yellow, dry and wet; and when I am spread on plains of wood, I speak without uttering a sound.
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…
Buying It Together
A group of people are buying something between them. If each puts in 8 coins they have 3 coins too many; if each puts in 7 they are 4 coins short. How many people are in the group?
The Virgin That Bears Fruit
I am a virgin woman and the child of a virgin woman, and as a virgin I bear fruit every year.
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 Hare and the Hound
A hare is 100 paces ahead of a hound. The hound chases it for 250 paces, and by then only 30 paces separate them. How many more paces must the hound run to catch the hare?
Two Sisters
There are two sisters: one gives birth to the other, and having given birth she is in turn born of her. They are sisters of one blood, and both sisters and mothers.
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 Good Runner and the Bad Runner
A good runner covers 100 paces in the time a bad runner covers 60. The bad runner starts 100 paces ahead. How many paces must the good runner run to draw level with him?
The Friend of Pallas
I am the friend of Pallas and bring forth countless children, which men crush under stones. When they perish there is light for the lamp, medicine for the sick, and oil for the athlete in the games.
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 …
Bitter Life, Sweet Death
Bitter is my life and sweet is my death, and both of them are water. I die pierced by bloodless spears; and if I am buried in a living tomb, I am first moistened by the blood of my kin.
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 Beast in the Wood
I once saw a beast running on its back through a wood cut by steel, and its feet never touched the earth.
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…
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