mscroggs.co.uk
mscroggs.co.uk
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.

subscribe

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?

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths LIV,
puzzles about multiples, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles

Tags

2d shapes triangles hexagons quadratics dates irreducible numbers shapes wordplay square roots perfect numbers differentiation odd numbers perimeter spheres volume lines proportion sum to infinity calculus division symmetry dodecagons rectangles cards ellipses scales factorials 3d shapes grids multiplication coordinates surds remainders ave crosswords folding tube maps arrows polygons shape geometry triangle numbers number crossnumbers fractions probabilty complex numbers functions people maths averages sums floors trigonometry parabolas taxicab geometry advent factors sequences routes angles books partitions square numbers balancing bases mean clocks time unit fractions palindromes cryptic crossnumbers squares cryptic clues indices cube numbers prime numbers graphs dice area planes logic christmas speed regular shapes means chalkdust crossnumber digits addition integers probability multiples coins algebra numbers games sport star numbers doubling integration chess percentages colouring chocolate rugby menace pascal's triangle circles money

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2019