Divisibility + Mathematical Olympiad - practice problems
Number of problems found: 30
- 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 - Coloured numbers
Mussel wrote four different natural numbers with colored markers: red, blue, green, and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it div - 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. - 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? - Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - Three-digit 9601
Majka researched multi-digit numbers, in which odd and even numbers alternate regularly. Those who start with an odd number are called comics, and those who start with an even number are called cheerful. (For, number 32387 is comic, and number 4529 is hil - Matemakak 9432
The cookbook by Matěj Matemakak says: The greatest common divisor of flour weight and sugar weight is 15, the greatest common divisor of sugar weight and lemon peel weight is 6, the product of sugar weight and lemon peel weight is 1800, and the smallest c - Divisible 9331
The number X is the smallest natural number whose half is divisible by three, a third is divisible by four, a quarter is divisible by eleven, and its half gives a remainder of 5 when divided by seven. Find this number. - Determine 8611
Determine all natural numbers A and B pairs for which the sum of twice the least common multiple and three times the greatest common divisor of natural numbers A and B is equal to their product. - Solutions 8481
For which integers x is the ratio (x + 11) / (x + 7) an integer? Find all solutions. - Justification 8468
The natural number n has at least 73 two-digit divisors. Prove that one of them is the number 60. Also, give an example of the number n, which has exactly 73 double-digit divisors, including a proper justification. - Six-digit primes
Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they? - Year 2018
The product of the three positive numbers is 2018. What are the numbers? - Three-digit 7248
Find all three-digit numbers n with three different non-zero digits divisible by the sum of all three two-digit numbers we get when we delete one digit in the original number. - MO C–I–1 2018
An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Interested 7090
We call a natural number N bombastic if it contains no zero in its notation and if no smaller natural number has the same product of digits as the number N. Charles first became interested in bombastic prime numbers and claimed that there were not many of - 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 - Z9–I–4 MO 2017
Numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of the three was equal to the sum of the remaining two. The conductor said - Different 5402
Adélka had two numbers written on the paper. When she added their greatest common divisor and least common multiple, she was given four different numbers less than 100. She was amazed that if she divided the largest of these four numbers by the least, she - 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.
Do you have homework that you need help solving? Ask a question, and we will try to solve it.