# 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?

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