# Puzzles

## Combining multiples

In each of these questions, positive integers should be taken to include 0.

1. What is the largest number that cannot be written in the form \(3a+5b\), where \(a\) and \(b\) are positive integers?

2. What is the largest number that cannot be written in the form \(3a+7b\), where \(a\) and \(b\) are positive integers?

3. What is the largest number that cannot be written in the form \(10a+11b\), where \(a\) and \(b\) are positive integers?

4. Given \(n\) and \(m\), what is the largest number that cannot be written in the form \(na+mb\), where \(a\) and \(b\) are positive integers?

If you enjoyed this puzzle, check out Sunday Afternoon Maths LIV,

puzzles about factors, or a random puzzle.

puzzles about factors, or a random puzzle.