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 sums, 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

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

Archive

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