Riddle Archive

Browse 100+ logic riddles, brain teasers, and math puzzles with clear statements, optional hints, and step-by-step solutions.

The thousand bottles poisoned

Master plays · 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.

The hundred boxes numbered

Master plays · 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.

The hundred prisoners with hats

Master plays · 3/5

There are 100 prisoners in line. Each one is randomly placed with a red or blue hat.

The light-bulb room

Master plays · 4/5

There are 100 prisoners. Before you start, you can agree on a strategy.

The veinticinco horses

Master plays · 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 within each race.

The Monty Hall Problem

Chance and uncertainty · 2/5

In a contest there are three doors. Behind one there is a car and behind the other two there are goats.

Albert and Bernardo have just met Cheryl. She tells them that her birthday is one of these ten dates: - May 15, May 16, May 19 - June 17, June 18 - July 14, July 16 - August 14, August 15, August 17 Afterwards, Cheryl secretly tells Albert the month and Bernardo the day. Then this conversation occurs: 1. Albert: “I don't know when Cheryl's birthday is, but I know Bernardo doesn't know either.” 2. Bernardo: “At first I didn't know, but now I know.” 3.…

The five pirates: empate favorable

Master plays · 3/5

Five pirates, ordered from oldest to youngest, must divide 100 coins. The oldest proposes a distribution and everyone votes, including him.

The five pirates: strict majority

Master plays · 3/5

Five pirates, ordered from oldest to youngest, must divide 100 coins. The oldest proposes a distribution and everyone votes, including him.

The guardianes of the two doors

Pure logic · 2/5

You are faced with two doors: one leads to the exit and the other to perdition. Next to them are two guardians.

The three switches

Visual traps · 2/5

In a room there are three switches. In another room, which you can't see from the first, there is a light bulb connected to only one of them.

The three mislabeled boxes

Pure logic · 1/5

You have three closed boxes with these labels: “Apples”, “Oranges” and “Mixed”. You know all three labels are wrong. You can take a single fruit out of a single box, without looking inside. How do you find out the correct contents of the three boxes?

The boat and the ladder

Visual traps · 1/5

A boat is moored to the dock. On its side there is a ladder with 10 steps visible above the water, separated by 20 cm. The tide rises 15 cm per hour. In 2 hours, how many steps will still be visible above the water?

The jugs of agua

Pure logic · 1/5

You have two unmarked jugs: one with 3 liters and one with 5 liters. You have a tap with unlimited water. How can you measure exactly 4 liters?

The bridge and the lantern

Timeless ingenuity · 2/5

Four people must cross a bridge at night. They only have one flashlight, and no one can cross without it. A maximum of two people can cross at a time. Each person takes a different time to cross: - 1 minute - 2 minutes - 5 minutes - 10 minutes When two cross together, they take as long as the slower one takes. What is the shortest total time in which the four can cross?

The hourglasses

Timeless ingenuity · 1/5

You have two hourglasses: one measures 7 minutes and the other measures 11 minutes. You have no other instrument to measure time. How can you measure exactly 15 minutes?

The two broken clocks

Pure logic · 1/5

You have two watches: - clock A is completely stopped; - Clock B works, but it goes back exactly 1 minute every hour. Which of the two keeps the correct time more times?

The ages in a temporal mirror

Pure logic · 1/5

Someone says:

The tercer wise man ciego

Pure logic · 3/5

Three perfectly logical wise men are sitting in a circle. The king informs them that he has five hats: three white and two black.

The most difficult logic puzzle in the world

Pure logic · 5/5

Three gods, A, B and C, are called Truth, Falsehood and Random, in some order. - Truth always answers with the truth. - Falsehood always responds with a lie. - Random answers at random. They understand your language, but they respond using the words “da” and “ja,” and you don't know which means “yes” and which means “no.” You can ask exactly three questions, each directed to a single god and with a yes/no answer. How do you identify with certainty which…

The hats of Ebert

Master plays · 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.

The bus of Conway

Numerical territory · 4/5

Two mathematicians travel by bus. One says to the other: —I have at least two children.

Sum and product

Numerical territory · 4/5

two different integers $x$ and $y$ satisfy $2 \le x < y \le 99$. one mathematician is told the sum $S=x+y$, and the other is told the product $P=xy$. conversation: 1. Product: “I do not know what the numbers are.” 2.

The switches and the million of light bulbs

Numerical territory · 3/5

In a hallway there are a million light bulbs, numbered from 1 to 1,000,000. At first, they are all turned off.

The three prisoners and the red hats

Pure logic · 3/5

Three prisoners perfectly logical are in row. Each one can ver the hats of the that has delante, but no the suyo nor the of quienes are behind.

Two prisoners, 64 coins and a escaque secreto

Master plays · 4/5

There are two prisoners and a guard. On a chess board there is a coin in each square, showing heads or tails.

The two ropes

Timeless ingenuity · 2/5

You have two ropes and a lighter. Each rope takes exactly one hour to burn completely, but it does not burn evenly: one half can take much longer than the other. How can you measure exactly 45 minutes?

Trunks and padlocks without shared key

Master plays · 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.

The nine-dot puzzle

Pure logic · 2/5

Draw these 9 points forming a $3\times 3$ grid: Nine dots in a 3x3 grid Can you join the 9 dots with only 4 consecutive straight lines, without lifting the pencil from the paper?

Missionaries and cannibals

Pure logic · 2/5

Three missionaries and three cannibals must cross a river in a boat that only accepts one or two people. On no shore can there remain a group in which the cannibals outnumber the missionaries, unless there are no missionaries on that shore.

The caballero, the escudero and the spy

Pure logic · 2/5

On an island there are three types of inhabitants: - gentlemen, who always tell the truth; - squires, who always lie; - spies, who can tell truth or lie. You meet three people: A, B and C. - A says: “B is a gentleman.” - B says: “A is a gentleman.” - C says: “A is a knave.” Knowing that there is exactly one knight, one squire and one spy, who is who?

The elimination tournament

Pure logic · 2/5

1024 players participate in a tennis tournament in a direct elimination format. Each match eliminates exactly one player. How many games must be played to determine the champion?

The coin false between doce

Master plays · 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.

The round sewers

Visual traps · 2/5

Many manhole covers are circular. They could have other flat shapes—square, rectangular, triangular, or oval—but the round shape repeats for some reason. What is the decisive advantage of the circle in this case?

The clock and its hands

Visual traps · 2/5

On an analog watch, how many times a day do the hour hand and minute hand matches exactly? Count each match only once.

The 100-story building and the two eggs

Visual traps · 2/5

You have two identical eggs and access to a 100-story building. There is a critical floor such that: - if an egg is dropped from that floor or from a higher one, it breaks; - if dropped from a lower floor, it does not break. You need to determine that critical floor by minimizing, in the worst case, the number of launches. What is the optimal strategy?

The rope alrededor of the Tierra

Visual traps · 2/5

A rope surrounds the Earth adjusted to the equator. It is then lengthened exactly $2\pi$ meters and placed again forming a concentric circle, uniformly separated from the ground. How high does the rope rise above the surface?

The wolf, the goat and the cabbage

Timeless ingenuity · 2/5

A farmer must cross a river with a wolf, a goat and a cabbage. The boat can only carry the farmer and one of the other three.

The tower of Hanoi

Timeless ingenuity · 3/5

There are three rods and a tower of 7 discs of different sizes, stacked from largest to smallest on one of them. You can only move one disk at a time and you can never place a large disk on top of a small one.

The island of the ojos azules

Pure logic · 4/5

On an island live perfectly logical people. Exactly 100 of them have blue eyes. The others have brown eyes, but no one knows the color of their own eyes.

The three vessels of the wise man (India antigua)

Timeless ingenuity · 2/5

A wise man has three vessels of 12, 8 and 5 liters. The 12 is full; the other two, empty. You must divide the contents into two equal parts, using only transfers between vessels and without intermediate marks. How do you get it?

The inheritance of the 17 camels (Arab tradition)

Timeless ingenuity · 2/5

A father leaves 17 camels to his three children with these conditions: - the oldest corresponds to $1/2$; - to the second, $1/3$; - to the minor, $1/9$. No camels are allowed to split. How can the distribution be made respecting the will?

The Chinese Farmer's Riddle

Timeless ingenuity · 2/5

A farmer buys 100 animals for exactly 100 coins. - Each buffalo costs 10 coins. - Each pig costs 3 coins. - Each chicken costs 1/2 coin. How many animals of each type can you buy?

The wise men and the perlas (Persia antigua)

Timeless ingenuity · 2/5

A sultan has 9 seemingly identical pearls, but one weighs a little more than the others. You have a two-pan scale and want to identify the heaviest pearl using the fewest possible weighings. What is the optimal strategy?

The Lo Shu magic square (China)

Timeless ingenuity · 2/5

Place the numbers 1 through 9 in a $3\times 3$ grid, using each number only once, so that the sum of each row, each column, and each diagonal is 15. 3x3 grid for the Lo Shu construction Give a valid arrangement of the magic square.

Ten bags and a weighing

Master plays · 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 you identify the different bag?

The combined weight lift

Master plays · 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: - any 3 boxes together weigh less than 100 kg; - any 4 boxes together weigh more than 150 kg; - there are at least two different pairs that weigh exactly 100 kg. Does it necessarily follow that there is some trio that weighs exactly 150 kg?

Nim (3,4,5) in modo misère

Master plays · 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.

The envious dice

Chance and uncertainty · 3/5

There are four special dice: - A: 4, 4, 4, 4, 0, 0 - B: 3, 3, 3, 3, 3, 3 - C: 6, 6, 2, 2, 2, 2 - D: 5, 5, 5, 1, 1, 1 You choose a die first. The dealer then chooses one of the remaining three. You both roll your says once and whoever gets the highest number wins. Is there one die better than all the others? What should the second player choose?

The row ganadora

Master plays · 3/5

Eight chess players play a free-for-all tournament. Each pair faces off once and no game ends in a draw.

The tournament of ties

Numerical territory · 3/5

Five teams play a round-robin league, with a single round. Score: - victory: 3 points; - tie: 1 point for each team; - defeat: 0 points. In the end, the five teams end up with different scores. What is the highest possible score for the fourth place finisher?

The mentira of the monday

Pure logic · 2/5

One person says: —Yesterday I lied. You know that this person always lies on Mondays, Tuesdays and Wednesdays, and always tells the truth on other days. What day of the week could it be today?

The desert expedition

Master plays · 3/5

Crossing the entire desert requires exactly 6 days of walking. Each explorer can carry supplies for a maximum of 4 days.

The door that it opens sola

Master plays · 3/5

A safe uses a 4-digit code, from 0000 to 9999. You can type an arbitrarily long sequence of digits.

The last passenger

Chance and uncertainty · 3/5

An airplane has $n$ seats and $n$ passengers, each with their assigned seat. Passenger 1 loses his card and sits randomly in any seat. Starting with passenger 2, each one acts like this: - if your seat is free, you sit in it; - if it's busy, choose randomly from free seats. What is the probability that the last passenger ends up in his or her own seat?

The relay of messages

Master plays · 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. What is the minimum number of calls necessary for the four of them to know the four secrets?

White balls in two boxes

Chance and uncertainty · 3/5

You have 50 white balls and 50 black balls. You must divide them into two boxes, with the only condition that neither is left empty.

Impossible coloring from 1 to 5

Master plays · 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 $x,y,z$ that satisfy $x+y=z$ (repeating numbers is allowed if equality requires it). Is it possible to do it?

Synchronized sources

Numerical territory · 2/5

Three sources activate every 4, 6 and 9 minutes. At 12:00 the three of them coincided. A visitor arrives between 12:00 and 12:30 and observes that: - the first and second will match again in 3 minutes; - the second and third will match again in 6 minutes. What time did you arrive?

The height shelf

Master plays · 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 than it has to its left.

The binary bells

Master plays · 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 D; - W changes that of D. Playing a string reverses the state of the bells that correspond to it: if they were ringing, they stop ringing; If they were silent, they start ringing. Is it possible to get only bell C to ring at the end? If you think so, indicate which ropes need to be pulled; If…

Corredores with a hint false

Master plays · 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 the first.” - Beto: “Ana came second.” - Cora: “Diego arrived immediately before me.” - Diego: “Beto came second.” In what order did they arrive?

The triple rotation

Master plays · 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: \[ abc\to bca \quad\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\text{or}\quad abc\to cab. \] Is it possible to obtain any permutation of the five cards in this way?

The coin of two heads

Pure logic · 1/5

There are two coins in a bag: - a coin has heads on both sides; - the other is a normal coin, with heads and tails. You draw one at random, toss it, and it comes up heads. What is the probability that the other side of that same coin is also heads?

Ten tokens and the black impossible

Pure logic · 1/5

You start with 10 white chips on the table. In each move you must choose exactly two pieces and turn them over: white goes to black and black goes to white. Is it ever possible to get into a situation with exactly one black piece?

The traffic light that it reprograma only

Pure logic · 1/5

An experimental traffic light has three lights: red $R$, yellow $A$ and green $V$. Each light is worth 1 if it is on and 0 if it is off.

Mutilated board and dominoes

Visual traps · 3/5

On a $8\times 8$ chessboard, two opposite corners are eliminated. Diagrama del tablero mutilado 8x8 Is it possible to cover exactly the remaining 62 squares with $1\times 2$ dominoes, without overlaps or gaps?

Chameleons with a possible ending

Pure logic · 4/5

On an island there are 4 red, 7 green and 10 blue chameleons. Every time two chameleons of different colors meet, they both change to the third color. 1. Is it possible to reach a state where everyone has the same color? 2. If yes, what color or colors?

The modular oracle

Master plays · 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.

The invisible submarine

Numerical territory · 4/5

An invisible submarine moves along the infinite line of integer positions: $$ \ldots,-2,-1,0,1,2,\ldots $$ Its initial position is an unknown integer $X$. Its speed is also an unknown integer $V$ and remains constant. At instant $t=0,1,2,\ldots$, the submarine is in position: $$ X+tV. $$ Each day you can choose a single entire position and shoot there. If you get it right, the search ends; If you fail, the submarine keeps moving. Is there a strategy that…

Dashboard infection

Pure logic · 4/5

On a $100\times100$ board, exactly 99 squares start out infected. Every minute, a healthy square becomes infected if it shares a side with at least two infected squares.

The urn bet

Pure logic · 4/5

An urn starts with 1 red and 1 blue ball. In each turn: 1. a ball is drawn at random; 2. is returned to the urn; 3.

The executioner and the hats (3 colores)

Pure logic · 4/5

There are 10 people in a row, numbered 1 to 10, where 10 is behind everyone. Each hat can be red, blue or green.

The cursed chocolate

Master plays · 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 chooses a square and eats that square along with all the squares below and to the right of it.

The magician and the five cards

Master plays · 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 fifth.

The code with checksum and reverse

Numerical territory · 4/5

A code has four different digits. It is known that: - is a multiple of 9; - the last figure is the remainder by dividing the sum of the first three by 10; - By reversing the order of its figures, the number obtained exceeds the original by 369 units. What is the code?

The scale and the bola distinta

Pure logic · 2/5

You have a balance with two pans and three visually identical balls. You know that one of them weighs differently than the other two, but you don't know if it is heavier or lighter. Can the different ball be identified with certainty using a single weighing?

The mosca between two trenes

Visual traps · 2/5

Two trains are 300 km apart and moving towards each other, each at 60 km/h. A fly leaves the first train towards the second at 90 km/h.

12-step ladder

Numerical territory · 2/5

You climb a 12-step ladder. With each movement you can advance 1 or 2 steps. How many different ways can you get to the top?

The cadena of mentiras (7 in circle)

Pure logic · 2/5

There are 7 people sitting in a circle. Each one says exactly: > “My neighbor on the right is a liar.” It is known that each person belongs to one of these two types: - truthful, if he always tells the truth; - liar, if he always lies. Is such a distribution possible?

The squeeze party

Pure logic · 2/5

At a party there are $n$ people, with $n\ge2$. Each person writes down how many handshakes they gave during the party. Is it possible that the $n$ numbers noted are all different?

Six personas and a triangle social

Pure logic · 2/5

In any meeting of 6 people, does at least one of these two things always happen? - there are 3 people who know each other; - there are 3 people who are mutual strangers. Explain why.

The number that it describes a yes mismo

Numerical territory · 2/5

Search for a 10 digit number \[ d_0\ d_1\ d_2\ d_3\ d_4\ d_5\ d_6\ d_7\ d_8\ d_9 \] with this property: - $d_0$ indicates how many zeros the number contains; - $d_1$ indicates how many ones it contains; - $d_2$ indicates how many twos it contains; - and so on; - $d_9$ indicates how many nines it contains. What is that number?

The row impossible of cards

Pure logic · 2/5

You start with the row of cards 4, 2, 6, 1, 5, 3. The only operation allowed is to exchange two adjacent cards whose sum is odd. Can this be achieved 1, 2, 3, 4, 5, 6?

The merchant's weights

Numerical territory · 1/5

A merchant wants to be able to weigh any whole quantity from 1 to 40 kilos using only four weights. You can place weights either on the same plate as the object or on the opposite one. How much should the four weights weigh?

The 100 coins a ciegas

Master plays · 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 from the other by touch.

The last ball

Pure logic · 2/5

In an urn there are black and white balls. You repeatedly draw two balls: - if they are the same color, you remove them and insert a black one; - If they are a different color, you remove them and insert a white one. When there is only one ball left, what will its color depend on?

A cyclic elimination

Timeless ingenuity · 3/5

The positions of a circle are numbered from 1 to $n$. Position 2 is eliminated first, then 4, then 6, and so on, continuing in a circular manner between the positions that are still alive, until only one remains. Which position survives in the end?

The messenger and the provisions

Master plays · 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 supplies.

The "look and say" sequence

Numerical territory · 2/5

Observe the sequence: \[ 1,\ 11,\ 21,\ 1211,\ 111221,\ 312211,\ 13112221 \] What is the next term?

The four prisoners and the wall

Pure logic · 3/5

Four prisoners, A, B, C and D, are lined up. There is a wall between C and D. - A goes to B and C. - B sees C. - C and D don't see anyone on the other side of the wall. Four hats are distributed, two black and two white, one for each prisoner. Everyone knows that information. In order, they are asked if they can deduce the color of his hat. After a moment, one of them answers yes. Who can know and how do you deduce it?

The plane and the conveyor belt

Visual traps · 2/5

An airplane is on a runway that is, in reality, a conveyor belt. The belt moves rearward and adjusts its speed to match the speed of the plane forward.

The boat and the marbles in the lake

Visual traps · 2/5

You are in a boat in the middle of a lake. Inside the boat is a box full of very heavy steel marbles. If you throw all the marbles into the water, does the lake level rise, fall, or stay the same?

The envelope and the banknotes

Chance and uncertainty · 3/5

There are two envelopes. One contains twice as much money as the other.

Chess and the grain of rice

Numerical territory · 2/5

On a board of 64 squares, grains of rice are placed like this: - 1 in the first box, - 2 in the second, - 4 in the third, - and so on, always doubling the amount in the previous box. How many grains of rice would there be in total at the end of the board?

The equation of the term cruzado

Numerical territory · 3/5

Find all continuous functions $f:\mathbb{R}\to\mathbb{R}$ such that $$ f(x+y)=f(x)+f(y)+2xy $$ for all $x,y\in\mathbb{R}$.

Hilbert II's Hotel

Master plays · 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 $g_1, g_2, g_3, \dots$. How can you accommodate them all?

Hilbert I's Hotel

Numerical territory · 2/5

A hotel has infinite rooms numbered 1, 2, 3,…, and they are all occupied. A new guest arrives. Is it possible to host it without kicking anyone out?

The shared birthday

Chance and uncertainty · 3/5

There are several people in a room. We will assume that birthdays are distributed evenly over the 365 days of the year and that there are no leap years.

The choice optimal

Chance and uncertainty · 3/5

You interview candidates for a job, one by one and in random order. You can only choose one, and once you reject a candidate you can't go back. You want to maximize the probability of choosing the best of all. What is the optimal strategy?

The triangle of coins

Numerical territory · 2/5

There are 10 coins forming an equilateral triangle: 4 at the base, 3 on top, then 2 and 1 on top. Moving only three coins, reverse the triangle so that it points downward.

The marriage handshake

Pure logic · 2/5

At a party there are several married couples. No one shakes hands with themselves or their own spouse. You ask everyone else how many hands they have shaken and you get all different answers. How many hands has your spouse shaken?

The snail in the well

Pure logic · 1/5

A snail climbs 3 meters each day and, while sleeping at night, slides 2 meters. If the well is 10 meters deep, in how many days will it come out?

The mixed pills

Pure logic · 1/5

A person must take one blue and one red pill each day. He has exactly two blue and two red left.

The four cards

Pure logic · 2/5

There are four cards on the table. Each one has a letter on one side and a number on the other.

Agua and wine

Numerical territory · 2/5

You have a glass full of water and another full of wine, both with the same amount. You add a tablespoon of water to the glass of wine and mix.

Who has the pez?

Master plays · 4/5

There are five houses in a row, each one a different color. A person of different nationality lives in each house.

The fair counting of the loaves

Pure logic · 2/5

Two travelers cross the desert. One carries 5 loaves.

The carrera impossible

Master plays · 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 city will win it. As soon as they hear the rule, the two princes stop moving.

The elephant and the boat

Timeless ingenuity · 2/5

A rajah wants to find out how much his elephant weighs, but he doesn't have a scale capable of supporting it. It does have the following: - a boat that perfectly supports the weight of the elephant, - a pier, - and as many 1 kilo stones as you need. How can you find out the weight of the elephant using only those things?

Watermelons in the sun

Numerical territory · 2/5

A shipment of watermelons weighs 100 kilos and is made up of 99% water. After several days in the sun, it is still the same cargo, but now it is made up of 98% water. How much do you weigh now?

SEND + MORE = MONEY

Numerical territory · 4/5

A young mathematician, the are of a mathematician, writes to his father to ask for money, but decides to do it his own way. Instead of typing the amount directly, it sends you this sum: SEND + MORE --- MONEY Each letter represents a different number, and no word can start with 0.

The square doble

Visual traps · 2/5

You have a square drawn on a sheet. Someone challenges you to draw another square that has exactly twice the area, but with one condition: you cannot measure lengths or use formulas. How can you build it using only the square itself as a guide?

The trial of the cadi

Master plays · 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 represents to them.

The alpinista and the rope corta

Master plays · 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 below. How can he go down to the ground wearing only that?

The coin justa

Chance and uncertainty · 3/5

You have a skewed coin, but you don't know how much. It can come up heads more times than tails, or the other way around; all you know is that its bias is fixed.

The nativos in circle

Pure logic · 3/5

An anthropologist is surrounded by a circle of natives. Each one belongs to one of two tribes: - those who always tell the truth; - those who always lie. He asks each native the same question: “Does the person on your right always tell the truth?” After hearing all the answers, the anthropologist still does not know who belongs to which tribe. But he does discover something surprising: the proportion of liars is determined in a unique way. What is that…

The seven eslabones

Master plays · 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 gold link per day.

Six vasos

Timeless ingenuity · 1/5

Six identical glasses are lined up on a table. The first three are full of water and the last three are empty: full, full, full, empty, empty, empty You can only move a glass, and do it only once.

The divided loot

Numerical territory · 3/5

You start with 10 chips in a single pile. In each step you choose a pile, divide it into two non-empty piles, and write down the product of the sizes of those two new piles.

Penney's game

Master plays · 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 time as a consecutive block.

The three logical in the bar

Pure logic · 2/5

A waiter approaches a table where there are three logicians and asks them: “Do you three want beer?” The first one answers: “I don't know.” The second answers: “I don't know.” The third answers: “Yes.” Why can you say this with certainty?

The hundred logical numerados

Pure logic · 3/5

In a room there is a hundred logicians. The first one says: “There is exactly 1 liar here.” The second says: “There are exactly 2 liars here.” The third says: “There are exactly 3 liars here.” And so on, until the last one, which says: “There are exactly 100 liars here.” Every logician is either truthful, and always tells the truth, or a liar, and always lies.

The two islanders

Pure logic · 2/5

A judge visits an island where everyone belongs to one of two tribes: - the truthful, who always tell the truth; - the liars, who always lie. He meets two islanders, A and B. He asks A: “Are you both liars?” A responds in a low voice, and the judge cannot hear him. Then B says: “He said no.” What tribe does each one belong to?