The thousand bottles poisoned
4/5
You have 1000 bottles of wine. One of them is poisoned, and a single drop is enough to kill a rat exactly 24 hours later. You have 10 lab rats and you can on...
Master plays
Strategy and game-theory puzzles where planning multiple moves ahead matters.
The hundred boxes numbered
4/5
There are 100 prisoners numbered 1 to 100 and 100 boxes also numbered 1 to 100. Inside each box is a different number from 1 to 100, placed at random. Before...
The hundred prisoners with hats
3/5
There are 100 prisoners in line. Each one is randomly placed with a red or blue hat. Each prisoner can see the hats of everyone in front of him, but not his...
The light-bulb room
4/5
There are 100 prisoners. Before you start, you can agree on a strategy. Then, each day, the guard chooses one and takes him to a room with a light bulb, whic...
The veinticinco horses
3/5
You have 25 horses and a track with 5 lanes. Only 5 horses can compete in each race, and you do not have a stopwatch: you can only know the order of finish w...
The five pirates: empate favorable
3/5
Five pirates, ordered from oldest to youngest, must divide 100 coins. The oldest proposes a distribution and everyone votes, including him. If the distributi...
The five pirates: strict majority
3/5
Five pirates, ordered from oldest to youngest, must divide 100 coins. The oldest proposes a distribution and everyone votes, including him. To be approved, t...
The hats of Ebert
3/5
Three players randomly and independently receive a red or blue hat. Each can see the other two's hats, but not their own. Before you start, you can agree on...
Two prisoners, 64 coins and a escaque secreto
4/5
There are two prisoners and a guard. On a chess board there is a coin in each square, showing heads or tails. Before starting, the prisoners can agree on a s...
Trunks and padlocks without shared key
2/5
You and another person are far away and can only send each other a trunk by courier. Each one has their own lock and their own key. Neither can open the othe...
The coin false between doce
3/5
You have 12 seemingly identical coins. One of them is fake, and you don't know if it weighs more or less than the others. You have a two-pan scale. What is t...
Ten bags and a weighing
3/5
There are 10 bags of coins. In 9 of them, each coin weighs 10 g. In the rest, all the coins weigh 11 g. You have only one weighing on a digital scale. How do...
The combined weight lift
3/5
A forklift only starts if the total load is exactly 100 kg or exactly 150 kg. You have 5 indivisible boxes of unknown weights. An operator left these notes:...
Nim (3,4,5) in modo misère
3/5
There are three piles with 3, 4 and 5 chips. On each turn you can withdraw any positive number of tokens, but from a single pile. It is played in misère mode...
The row ganadora
3/5
Eight chess players play a free-for-all tournament. Each pair faces off once and no game ends in a draw. Someone claims that, no matter what happens in the t...
The desert expedition
3/5
Crossing the entire desert requires exactly 6 days of walking. Each explorer can carry supplies for a maximum of 4 days. Explorers can walk together, exchang...
The door that it opens sola
3/5
A safe uses a 4-digit code, from 0000 to 9999. You can type an arbitrarily long sequence of digits. The box opens as soon as the last four digits typed match...
The relay of messages
2/5
Four spies—A, B, C and D—each have a different secret. Every time two spies talk on the phone, they both tell each other everything they know at that moment....
Impossible coloring from 1 to 5
3/5
You want to color the numbers \(\{1,2,3,4,5\}\) with two colors, red and blue. The condition is that there are no three numbers of the same color \(x,y,z\) t...
The height shelf
2/5
Five books of different heights 1, 2, 3, 4 and 5—where 1 is the shortest and 5 the tallest—are placed in a row. Each book writes down how many books taller t...
The binary bells
3/5
Four bells A, B, C and D begin silently. There are four strings: X changes the state of A and B; And change the one of B and C; Z changes the one of A, C and...
Corredores with a hint false
2/5
Four runners—Ana, Beto, Cora and Diego—came in positions from 1 to 4, without ties. Exactly one of these statements is known to be false: - Ana: “I wasn't th...
The triple rotation
3/5
You start with the line \[ 1,\ 2,\ 3,\ 4,\ 5. \] The only operation allowed is to choose three consecutive cards and rotate them cyclically: \[ abc\to bca \q...
The modular oracle
4/5
There are 100 people numbered from 0 to 99. An integer between 0 and 99 is written on the forehead of each one. There may be repetitions. Each person sees ev...
The cursed chocolate
4/5
A rectangular bar of chocolate is divided into squares, and the square in the upper left corner is poisoned. Two players take turns: each turn, the player ch...
The magician and the five cards
4/5
A spectator chooses 5 different cards from a standard deck of 52. The assistant sees the 5 cards, hands 4 to the magician in the order he wants and hides the...
The 100 coins a ciegas
2/5
There are 100 coins on a table. You know that exactly 20 are facing up and 80 are facing down, but you are completely in the dark and cannot distinguish one...
The messenger and the provisions
4/5
Between a messenger's house and his destination there are seven days of travel. At the end of each day there is a house where you can sleep and leave supplie...
Hilbert II's Hotel
4/5
A hotel has infinite rooms numbered 1, 2, 3,…, and they are all occupied. An infinite queue of new guests now arrives, numbered \(g1, g2, g3, \dots\) . How c...
Who has the pez?
4/5
There are five houses in a row, each one a different color. A person of different nationality lives in each house. Each one drinks a different drink, smokes...
The carrera impossible
2/5
A sultan promises his inheritance to one of his two sons, but imposes a strange condition: The owner of the horse that arrives the latest in the neighboring...
The trial of the cadi
3/5
Two heirs dispute a ruby that cannot be broken. To avoid arguments, the cadi brings each person in separately and asks them how much money that ruby repr...
The alpinista and the rope corta
3/5
A mountaineer is on a ledge 20 meters above the ground. It has: a 15 meter rope, a knife, a firm ring next to him, and another similar ring located 10 meters...
The seven eslabones
2/5
A blacksmith agrees to pay a laborer with a small gold chain made up of 7 closed links. The deal is this: for 7 days, you'll need to hand him exactly one gol...
Penney's game
4/5
Two players take turns choosing a sequence of three coin outcomes. A fair coin is then tossed repeatedly until one of the two sequences appears for the first...
Guess the biggest
3/5
Two different numbers between 0 and 1 are chosen at random. You see only one of them. Then, without knowing the other one, you must decide if the hidden numb...