The bus of Conway
4/5
Two mathematicians travel by bus. One says to the other: —I have at least two children. Their ages are positive integers. The sum of their ages is the number...
Numerical territory
Number-driven challenges in arithmetic, patterns, counting, and step-by-step reasoning.
Sum and product
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=x...
The switches and the million of light bulbs
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. A person walks down the hallway many times. In...
The tournament of ties
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...
Synchronized sources
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...
The invisible submarine
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...
The code with checksum and reverse
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 r...
12-step ladder
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 number that it describes a yes mismo
2/5
Search for a 10 digit number \[ d0\ d1\ d2\ d3\ d4\ d5\ d6\ d7\ d8\ d9 \] with this property: - \(d0\) indicates how many zeros the number contains; \(d1\) i...
The merchant's weights
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 obj...
The "look and say" sequence
2/5
Observe the sequence: \[ 1,\ 11,\ 21,\ 1211,\ 111221,\ 312211,\ 13112221 \] What is the next term?
Chess and the grain of rice
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 i...
The equation of the term cruzado
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 I's Hotel
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 triangle of coins
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 po...
Agua and wine
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. Then you pour...
Watermelons in the sun
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 9...
SEND + MORE = MONEY
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 dire...
The divided loot
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 thos...
The numbers consecutivos
1/5
Choose three consecutive whole numbers and multiply them. Why is the result always divisible by 6?
Empty a cubo
3/5
There are three buckets with marbles. In each move you can choose one of them and double its number of marbles, taking from the other two cubes, between them...