The water jugs
Level 1 · Starter · ●○○○○
You have two jugs: one with 3 liters and one with 5 liters. You have a tap with unlimited water. How can you measure exactly 4 liters of water? There are no...
Numerical territory
Number-driven challenges in arithmetic, patterns, counting, and step-by-step reasoning.
The hourglasses (7 and 11 minutes)
Level 1 · Starter · ●○○○○
You have two hourglasses: one for 7 minutes and one for 11 minutes. How can you measure exactly 15 minutes?
The two broken clocks
Level 1 · Starter · ●○○○○
You have two watches: Clock A: is completely stopped. Clock B: works, but goes back exactly 1 minute every hour. Which of the two keeps the correct time more...
The ages in a temporal mirror
Level 1 · Starter · ●○○○○
Now I am 40 years old. I tell you: “I am 4 times the age you were when I was the age you are now.” How old are you currently?
The Bus Wizard (Conway)
Level 5 · Expert · ●●●●●
Two mathematicians ride a bus and read the line number. One says to the other: “I have at least two children.” “Their ages are positive integers.” “The sum o...
Sum and product (two mathematicians)
Level 5 · Expert · ●●●●●
Two different integers x,y satisfy 2 \le x < y \le 99 . You say to one person S=x+y (they only know the sum) and to another P=xy (they only know the product)...
The switches and the million light bulbs
Level 5 · Expert · ●●●●●
There are a million light bulbs in a row, all initially turned off. There are a million people. Person 1 activates all switches (1, 2, 3, ...). Person 2 acti...
The 12 coins and the scales
Level 3 · Intermediate · ●●●○○
You have 12 coins identical to the naked eye. One is false and may be heavier or lighter (you don't know which of the two cases). You have a two-pan scale an...
The inheritance of the 17 camels (Arab tradition)
Level 2 · Core · ●●○○○
A father leaves 17 camels to his three sons with these conditions: the oldest gets \frac{1}{2} , the second gets \frac{1}{3} and the youngest gets \frac{1}{9...
The Chinese Farmer's Riddle
Level 2 · Core · ●●○○○
A farmer buys 100 animals for exactly 100 silver coins. Buffaloes cost 10 coins each, pigs cost 3 coins each, and chickens cost 0.5 coins each. Buy at least...
The wise men and the pearls (ancient Persia)
Level 2 · Core · ●●○○○
A sultan has 9 pearls that look identical, but one is slightly heavier. It has a two-pan scale. You must identify the heaviest pearl by using the scale the M...
The magic square of Lo Shu (China)
Level 2 · Core · ●●○○○
Place the numbers 1 through 9 on a 3 \times 3 grid so that the sum of each row, each column, and each diagonal is exactly 15. This is the legendary magic squ...
Ten bags and one heavy
Level 4 · Advanced · ●●●●○
There are 10 bags with coins. In 9 bags each coin weighs 10 g. In 1 bag, they all weigh 11 g. With a single weighing on a digital scale, how do you identify...
The combined weight lift
Level 4 · Advanced · ●●●●○
A forklift only starts if the total load is exactly 100 kg or exactly 150 kg. You have 5 indivisible boxes with unknown weights. An operator wrote down the s...
Delivery men with a false lead
Level 4 · Advanced · ●●●●○
Four distributors—Ana, Beto, Cora and Diego—came in positions from 1 to 4, without ties. Exactly one of these notes is known to be false: Ana: “I was first.”...
Ten pieces and the black impossible
Level 1 · Starter · ●○○○○
You start with 10 white chips on the table. In each movement you are obliged to: choose exactly two tiles, and flip them (white to black, black to white). Qu...
Chameleons with a possible ending
Level 5 · Expert · ●●●●●
On an island there are: 4 red chameleons, 7 green, 10 blue. When two of different colors are found, both change to the third color. Is it possible to reach a...
The Oracle Who Knows Himself
Level 5 · Expert · ●●●●●
There are 100 people. On each front an integer from 1 to 100 is written (they can be repeated). Each person sees everyone else's 99 numbers, but not their ow...
The scales of Babel
Level 5 · Expert · ●●●●●
You have a scale with two pans and four weights: 1,\ 3,\ 9,\ 27\ \text{kg}. You can put weights on either side. How many different whole weights between 1 an...
The executioner and the hats (3 colors)
Level 5 · Expert · ●●●●●
There are 10 people in a row, numbered from 1 (front) to 10 (behind). Each hat can be red, blue or green. Vision and turn rules: person 10 speaks first and s...
The code with checksum and reverse
Level 5 · Expert · ●●●●●
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 rev...
The number that describes itself
Level 3 · Intermediate · ●●●○○
Search for a 10 digit number d0d1d2d3d4d5d6d7d8d9 such that: d0 = number of zeros in the number, d1 = number of ones, d2 = number of twos, -... d9 = number o...
The impossible row of cards
Level 3 · Intermediate · ●●●○○
You have the row: 4,\ 2,\ 6,\ 1,\ 5,\ 3. The only operation allowed is to exchange two adjacent cards whose sum is odd. Can you reach: 1,\ 2,\ 3,\ 4,\ 5,\ 6?
The shredded password
Level 3 · Intermediate · ●●●○○
A 6 letter password was hashed. All its consecutive fragments of length 3 were preserved, out of order: \texttt{ABA},\ \texttt{BAC},\ \texttt{ACB},\ \texttt{...
Los cuatro pesos
Level 1 · Starter · ●○○○○
Dispones de una balanza de dos platos y de cuatro pesas de 1 g, 3 g, 9 g y 27 g. En cada pesada puedes colocar cada pesa en el plato izquierdo, en el derecho...
Una eliminación cíclica
Level 4 · Advanced · ●●●●○
Se numeran del 1 al n las posiciones de un círculo. Se elimina primero al 2, luego al 4, luego al 6, y así sucesivamente, continuando de manera circular entr...
El mensajero y las provisiones
Level 5 · Expert · ●●●●●
Entre la casa de un mensajero y su destino hay siete jornadas. Al final de cada jornada hay una casa donde puede dormir. Puede llevar provisiones para cuatro...
La sucesión "mira y di"
Level 3 · Intermediate · ●●●○○
Observa la sucesión: 1 11 21 1211 111221 312211 13112221 ¿Cuál es el patrón y cuál es el siguiente término?