Natural numbers + Mathematical Olympiad - practice problems - page 2 of 4
Number of problems found: 65
- Three-digit 80768
Nikola had one three-digit and one two-digit number written in her notebook. Each of these numbers was made up of different digits. The difference in Nicole's numbers was 976. What was their sum? - Three-digit 5524
Six cards with digits 1, 2, 3, 4, 5, and 6 are on the table. Agnes made a six-digit number from these cards, divisible by six. Then she gradually removed the cards from the right. A five-digit number divisible by five remained on the table when she remove - MO 2016 Numerical axis
Cat's school uses a special numerical axis. The distance between the numbers 1 and 2 is 1 cm, the distance between the numbers 2 and 3 is 3 cm, between the numbers 3 and 4 is 5 cm, and so on, and the distance between the next pair of natural numbers is al - 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?
- Definitely 7179
Ivan and Mirka shared pears in the mission. Ivan always takes two pears, and Mirka takes half of what remains in the mission. Thus, Ivan, Mirka, Ivan, Mirka, and finally Ivan, who took the last two pears, took them away. Definitely. Who had more pears, in - Remaining 5534
On the table lay eight cards with the numbers 2,3,5,7,11,13,17,19. Fero chose three cards. He added the numbers written on them and found that their sum was 1 more than the sum of the numbers on the remaining cards. Which cards could have been left on the - Double-digit 5411
Anička and Blanka each wrote one double-digit number, which started with a seven. The girls chose different numbers. Then each inserted a zero between the two digits, giving them a three-digit number. Everyone subtracted their original two-digit number fr - Dance ensembles
Four dance ensembles were dancing at the festival. None had less than ten and more than 20 members. All dancers from some of the two ensembles were represented in each dance. First, 31 participants were on the stage, then 32, 34, 35, 37, and 38. How many - Restriction 7442
The figure shows two rows of hexagonal boxes that continue to the right without restriction. Fill in one field with one positive integer so that the product of the numbers in any three adjacent fields is 2018. Determine the number that will be in the top
- Three-digit unknown int
Viera compiled different three-digit numbers from three given digits. When she added up all these numbers, she published 1221. What numbers did Vierka use? Identify five options - Subtract 10001
For five whole numbers, if we add one to the first, multiply the second by the second, subtract three from the third, multiply the fourth by four, and divide the fifth by five, we get the same result each time. Find all five of the numbers that add up to - Clubhouse
There were only chairs and tables in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs - Characteristics 65294
Kuba wrote down a four-digit number, two evens, and two odds. If he crossed out both even digits in that number, he would get a number four times smaller than if he crossed out both odd digits in the same number. What is the most significant number with t - Originally 5427
There were red and green candies in the tin. Čenek ate 2/5 of all the red candies, and Zuzka ate 3/5 of all the green candies. Now, the red candies make up 3/8 of all the candies in the can. How many candies were originally in the can?
- -------------- 7311
In the following addition example, the same letters represent the same digits, and the different letters represent different digits: RATAM RAD -------------- ULOHY Replace the letters with numbers so that the example is correct. Find two different replace - Characteristics 2104
Betka thought of a natural number with different digits and wrote it on the board. Podeň wrote the digits of the original number on the back and thus got a new number. By adding these two numbers, he got a number with the same number of digits as the inte - Double-digit 80970
Eva thought of two natural numbers. She first added these correctly, then subtracted them correctly. In both cases, she got a double-digit result. The product of the resulting two-digit numbers was 645. Which numbers did Eva think of? Please, what is this - Twos
Vojta started writing the number this year, 2019202020192020, into the workbook. And so he kept going. When he wrote 2020 digits, he no longer enjoyed it. How many twos did he write? - Three-digit 5312
Find the smallest four-digit number abcd such that the difference (ab)²− (cd)² is a three-digit number written in three identical digits.
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