Natural numbers + Pythagoras contest - practice problems
Number of problems found: 17
- 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 - 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 - 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 - 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?
- 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. - 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 - Five-crowns 4879
Eva had seven coins. Crowns, two-crowns, and five-crowns. At least two of each. How many did she have if she could buy three packs of gum for six crowns? - 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? - 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.
- 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. - 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. - 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"? - Equation algebraogram
Solve the equation: oco + ivo = cita How much has the task of solutions?
- Alarm clock
The old watchmaker has a unique digital alarm in its collection that rings whenever the sum of the alarm's digits equals 21. Find out when the alarm clock will ring. What is their number? List all options. - 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? - 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.
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Natural numbers - practice problems. Pythagoras contest - practice problems.