Pythagoras contest - practice for 14 year olds
Number of problems found: 23
- Two-digit 82521
Karel had to multiply two two-digit numbers. Out of care, he changed the order of the digits in one of the factors and got a product that was 4,248 less than the correct result. What is the correct result? How much should Karl have earned? - Rectangle 82087
A 9cm × 15cm rectangle is divided into unit squares. How many paths are there from one rectangle vertex to the opposite vertex if one can only go to the right and up the sides of the squares? - Position 81987
Find a number with six digits. If you put the last digit before the first, you get a new number that is five times larger. The digits between must not change their position. - Determine 80714
Three different numbers are given. The average of the average of two smaller numbers and the average of the two larger numbers is equal to the average of all three numbers. The average of the smallest and largest number is 2022. Determine the sum of the t - Nightmares 80568
At the dream market, she offered the Sphinx to a traveler for four dreams, seven illusions, two naps, and one nightmare. Another has seven dreams, four illusions, four naps, and two nightmares. The Sphinx always measures the same for all travelers. How ma - Distribute 70244
We have to distribute the keys to the safe among four people so that no two of them can open the safe but in such a way that any three can open the safe. How many minimum keys do we need? How to divide them? How many minimum locks must be on the safe? All - Three-digit 58943
The vortex of the three given digits formed different three-digit numbers. When she added up all these numbers, she published 1554. What numbers did Vierka use? - Four-digit 55481
Find all four-digit abcd numbers to which: abcd = 20. ab + 16. cd, where ab and cd are double digits numbers from digits a, b, c, and d. - The isosceles
The isosceles trapezoid ABCD has bases of 18 cm and 12 cm. The angle at apex A is 60°. What is the circumference and area of the trapezoid? - Five-digit number
Anna thinks of a five-digit number not divisible by three or four. If he increments each digit by one, it gets a five-digit number divisible by three. If he reduces each digit by one, he gets a five-digit number divisible by four. If it swaps any two digi - Candles
Before Christmas, Eva bought two cylindrical candles - red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 PM, lit a green candle at 7:00 PM, and left them on fire until it burned. At 9:30 PM, both candles were the - Apples and pears
Apples cost 50 cents a piece, pears 60 cents a piece, bananas cheaper than pears. Grandma bought five pieces of fruit. There was only one banana, and I paid 2 euros 75 cents. How many apples and how many pears? - Two cars on ring
There were two cars on the round track (ring) in the adjacent tracks, the first car on the inner track and the second on the outer track. Both cars started at the same time from one starting track. The first toy car drove four laps simultaneously, and the - 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 - 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 point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl - Special watch
Fero bought a special watch on the market. They have only one (minute) hand and a display showing the angle between the hour and minute hand. How many hours was his watch shown - the minute hand points to number 2; the display shows 125°. - Two rectangles
I cut out two rectangles with 54 cm² and 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together, I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your - Triplets
Three years ago, the triplets Pavel, Petr, Luke, and their five-year-old sister Jane had been together for 25 years. How old is Jane today? - 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. - Skiing meeting
Four friends came to the skiing meeting 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
Do you have homework that you need help solving? Ask a question, and we will try to solve it.