# Pythagoras contest - practice problems

#### Number of problems found: 32

- Grandma

Grandma is 57 years older than her two twin granddaughters. If we add the ages of an old woman with both granddaughters, we get the number 99. How old is her old woman? - 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? - Different 55491

Add the same numbers after the same letters and different numbers after the other letters so that equality applies: KRAVA + KRAVA = MLIEKO, where K is an odd digit. - Four-digit 55481

Find all four-digit abcd numbers to which: abcd = 20. ab + 16. cd, where ab, cd is double digits numbers from digits a, b, c, 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? - Phone number

Ivan's phone number ends with a four-digit number: When we subtract the first from the fourth digit of this four-digit number, we get the same number as when we subtract the second from the third digit. If we write the four-digit number from the back and - Five-digit number

Anna thinks of a five-digit number that is not divisible by three or four. If he increments each digit by one, it gets a five-digit number that is divisible by three. If he reduces each digit by one, he gets a five-digit number divisible by four. If it sw - All pairs

Find 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. - Different 29943

Vojta added five different prime numbers to the top row of the census pyramid. Their sum was 50. What was the biggest number he could get "down"? - 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 p. M. , lit a green candle at 7:00 p. M. , and left them both on fire until they burned. At 9:30 p. M. , bo - Yesterday 13711

If the day before yesterday was what day of the week it will be from today in 50 days. (0 = Monday, 6 = Sunday) - Apples and pears

Apples cost 50 cents piece, pears 60 cents piece, bananas cheaper than pears. Grandma bought 5 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 in 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 as the s - 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 - Special watch

Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which 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, 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 calc - Triplets

Three years ago, the triplets Pavel, Petr, and Luke, and their five-year-old sister Jane had together 25 years. How old is Jane today? - Solutions 5453

Tongue twister. Replace the letters with numbers to get the correct sum: ŠKRZ KRK STRČ ______ PRST How many solutions does the task have? - 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.

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