# Pythagoras contest - practice problems

Direction: Solve each problem carefully and show your solution in each item.#### Number of problems found: 46

- Consecutive 83266

Consecutive natural numbers on the number line are always 1 cm apart. Write the sum of the numbers 9 cm away from 517 on the number line. - Different 82683

There are candies from 1 to 10 in ten different packages. Each child took two packages. They got so many candies: Anka: 5 Zuzka: 7 Katka: 9 Monica: 15 How many candies does Lucka have? - 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? - Kilometers 82408

The longest Brazilian river, the Amazon, is ten times longer than the two Czech rivers, Vltava and Berounka. The ratio of the lengths of the Vltava and Berounka is 9:5. At the same time, the length ratio of the Vltava and Morava rivers is 5:4. How many ki - 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. - Classroom 81621

On a classroom clock, the large (minute) hand on the clock will travel through an angle of 120 degrees in some time. What angle does the small (hour) hand pass in this time? - 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 - Seven-liter 80518

Happy Mom needs to measure exactly 6 liters of water. It only has a five-liter and a seven-liter container. How can a mother measure exactly 6 liters of water by gradually pouring? He doesn't care about other containers. - 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 - Beginning 66104

The kangaroo always jumps three steps up. Each time he jumps, the bunny jumps down two steps. On which stairs will they meet? The kangaroo stands on the 1st step at the beginning and the bunny on the 100th. - Grandma

Grandma is 57 years older than her two twin granddaughters. If we add the ages of an older 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 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? - 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 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 - 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.

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