MathProblem 💙💛

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Updated: May 25, 2026 at 12:37 PM

MathProblem 💙💛

Recreational mathematics. Of the 12 coins, only 1 is false, and it is a different weight than the real coin. How do you find a counterfeit coin in 3 weighings on a two-cup scale without weights? Reddit: https://bit.ly/3P4rr92.

@mathematicalproblem is a growing community focused on coin and coins and related topics

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MathProblem 💙💛

Apr 23, 2026, 04:01 PM

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

🌐 https://en.m.wikipedia.org/wiki/Modular_arithmetic

✍ Write your answer in the comments!

553

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

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 coin because it is made of a cheaper and heavier metal. What is the minimum number of weighings needed on a cup scale to find a counterfeit coin? (Real gold coins weigh the same and real silver coins weigh the same.)

📜 Leaflet #weighing

✍ Write your answer in the comments!

404

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

https://en.m.wikipedia.org/wiki/Chip_'n'_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 your answer in the comments!

489

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

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 were erased during the storm. He needs to prove to the captain how much each bag weighs, using only two-cup scales that show the difference between the bowls (in grams).

a) Prove that 4 weighings are enough for him for this purpose.
b) Prove that three weighings are not enough.

📜 Leaflet #weighing

✍ Write your answer in the comments!

476

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

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!

474

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

https://en.m.wikipedia.org/wiki/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 cabin boy brings a bag with a fake coin to the captain of the ship, he will be executed.
How can you find a sack with all the real coins in it in 1 weighing on a cup scale without weights?

📜 Leaflet #weighing

✍ Write your answer in the comments!

521

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

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!

296

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

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?

📜 Leaflet #weighing

✍ Write your answer in the comments!

329

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

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 #weighing

✍ Write your answer in the comments!

475

MathProblem 💙💛

Apr 23, 2026, 04:01 PM

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!

384

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