2024 IOQM Problems
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
Problem 1
The smallest positive integer that does not divide is:
Problem 2
The number of four-digit odd numbers having digits , each occuring exactly once, is:
Problem 3
The number obtained by taking the last two digits of in the same order is:
Problem 4
Problem 5
Problem 6
Find the number of triples of real numbers such that .
Problem 7
Determine the sum of all possible surface areas of a cube two of whose vertices are and .
Problem 8
Let be the smallest integer such that the sum of digits of is divisible by as well as the sum of digits of is divisible by . What are the first two digits of in the same order?
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Three positive integers with satisfy the folowing equations: . Find the value of .