Reason + Pythagoras contest - practice problems
Number of problems found: 33
- 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. - 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 - 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. - 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.
- 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 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 - Yesterday 13711
If the day before yesterday was the day of the week, what day of the week would it be from today in 50 days? (0 = Monday, 6 = Sunday) - 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
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Reason - practice problems. Pythagoras contest - practice problems.