MathProblem @MathProblem314

Can the sum of three different natural numbers be divisible by each summand? Leaflet #divisibility Write your answer in the comments! ift.tt/o7ha9PY

John wrote several different natural numbers on the board and divided the sum of these numbers by their product. Then he erased the smallest number and divided the sum of the remaining numbers by their product. The second result was 3 times as many as th… ift.tt/jM7eKVX

In a 3×3 square all integers from 1 to 9 are arranged in some way. First, we counted the arithmetic mean of the numbers in four different 2×2 squares (they all turned out to be integers), and then we calculated the arithmetic mean of the four numbers obt… ift.tt/yajfckz

Find the sum of 123456789 + 234567891 + 345678912 + ... + 912345678. Leaflet #calculation Write your answer in the comments! ift.tt/qSwoil8

Is it possible to arrange the chips in the cells of an 8×8 board so that in any two columns the number of chips is the same, and in any two rows different? Leaflet #can Write your answer in the comments! ift.tt/62Sz4Bh

David conceived a natural number, multiplied all its digits, and multiplied the result by the conceived number. Could he have gotten 1716? Leaflet #can Write your answer in the comments! Happy Pi Day! ift.tt/AQgrIpE

Can 4 sticks of length 1 cm, 4 sticks of length 2 cm, 7 sticks of length 3 cm, and 5 sticks of length 4 cm make a rectangle? (All sticks must be used, they must not be broken.) Leaflet #can Write your answer in the comments! ift.tt/LbWijY6

The natural numbers x, y, z are such that x² + y² + z² is divisible by 9. Prove that one can choose two of these three numbers such that the difference of their squares is also divisible by 9. Leaflet #modular_arithmetic Wikipedia Write your answer in… ift.tt/EeClgDG

The cabin boy found a new treasure chest, this time it contained 80 bags of gold of various weights. His real weight was written on each bag. Just in case, the cabin boy wrote down all the weights, and for good reason, since the inscriptions on the bags … ift.tt/6fJnT2B

Dale accidentally broke an electronic scale, but he has a cup scale. He wants to learn how to measure every number of grams from 1 to 10. Chip says he can give him three screws of any weight. Can you help Dale decide on a scale? Leaflet #weighing Write… ift.tt/KjvkQeB

There are 25 gold and 26 silver coins, of which exactly one is false. It is known that if the counterfeit coin is gold, it is lighter than the real coin because it is made of less gold, and if the counterfeit coin is silver, it is heavier than the real c… ift.tt/mWB9kVS

The cabin boy dug out the treasure chest and found three bags of coins in it. The bags contained 18, 22, and 28 coins. There was a note in the chest that one of the bags contained a fake coin that, which differs in weight from the real ones. If the cabi… ift.tt/rqBUAmF

There are 60 identical coins, one of which is a counterfeit of a different weight. How can you tell if a counterfeit coin is lighter or heavier in two weighings on a cup scale? Leaflet #weighing Write your answer in the comments! ift.tt/zBiUYwK

Four coins and a cup scale are given. It is known that among them there is 1 counterfeit coin, which somehow differs in weight from the real one, but looks the same. What is the least amount of weighing that can be done to determine it? Leaflet #weighin… ift.tt/YUKFfHP

There are 30 real coins and 31 counterfeit coins. A real coin is 3 grams heavier than a counterfeit coin. The magician chooses a random coin and then determines in one weighing on a scale with an arrow whether it is real or not. How does he do this? Lea… ift.tt/gkY2P5p

From which of the largest number of coins will it be possible to find a fake coin, which is lighter than the rest, in 4 weighings? Leaflet #weighing Write your answer in the comments! ift.tt/Wfj9vd5

Find all pairs of prime numbers p and q such that (p + q)² - pq is a complete square. Leaflet #prime_numbers Write your answer in the comments! ift.tt/OvgSZE0

Is there such a number p that all three numbers p-2023, p, p+2023 are prime? Leaflet #prime_numbers Write your answer in the comments! ift.tt/FQYZqUh

Find all prime p such that p = a + b, where a, b are composite. Leaflet #prime_numbers Write your answer in the comments! ift.tt/eYFgiDy

Find all prime numbers p for which the following holds: p = a + b = c - d, where a, b, c, d are prime numbers (not necessarily distinct). Leaflet #prime_numbers Write your answer in the comments! ift.tt/CBTthJS