# Mathematical Olympiad + Pythagoras contest - math problems

#### Number of problems found: 8

- All pairs

Determine all pairs (m, n) of natural numbers for which is true: m s (n) = n s (m) = 70, where s (a) denotes the digit sum of the natural number a. - Self-counting machine

The self-counting machine works exactly like a calculator. The innkeeper wanted to add several three-digit natural numbers on his own. On the first attempt, he got the result in 2224. To check, he added these numbers again and he got 2198. Therefore, he a - Equilateral triangle ABC

In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont - One million

Write the million number (1000000) using only nine numbers and algebraic operations plus, minus, times, divided, powers, and squares. Find at least three different solutions. - Alarm clock

The old watchmaker has a unique digital alarm in its collection that rings whenever the sum of digits of the alarm is equal to 21. Find out when the alarm clock will ring. What is their number? List all options . .. - Bicycles

You're the owner of the transport 's learning playground. Buy bicycles of two colors but you've got to spend accurately 120000 Kč. Blue bike costs 3600Kč and red bicycle 3200Kč. - Skiing meeting

On the skiing meeting came four friends from 4 world directions and led the next interview. Charles: "I did not come from the north or from the south." Mojmir "But I came from the south." Joseph: "I came from the north." Zdeno: "I come from the south." We - Fluid

We have vessels containing 7 liters, 5 liters, and 2 liters. The largest container is filled with fluid, the others empty. Can you only by pouring get 5 liters and two 1 liter of fluid? How much pouring is needed?

We apologize, but in this category are not a lot of examples.

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Do you have an exciting math question or word problem that you can't solve? Ask a question or post a math problem, and we can try to solve it.

Mathematical Olympiad - math problems. Pythagoras contest - math problems.