mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

The taxman

In a very strange country, the tax system works as follows.
£1, £2, £3 up to £12 are available.
You pick an amount. You keep this amount, but the taxman takes any factors of it. You cannot pick any amount without a factor.
This continues until you can take no more money. The taxman gets any remaining money.
For example, you might play as follows:
In this example, you end with £22 and the taxman ends with £56.
Is it possible to get more money than the taxman? What is the most you can get?

Show answer & extension

Tags: numbers, money
If you enjoyed this puzzle, check out Sunday Afternoon Maths XLII,
puzzles about numbers, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

mean neighbours range determinants perfect numbers perimeter powers pentagons consecutive numbers proportion christmas irreducible numbers quadratics ellipses partitions probabilty floors crossnumbers multiples dice star numbers multiplication chocolate time prime factors ave geometric mean factors unit fractions chalkdust crossnumber cubics quadrilaterals spheres numbers area dates elections triangle numbers albgebra polygons wordplay balancing polynomials clocks integers sport rugby folding tube maps doubling colouring routes cube numbers hexagons tangents geometric means chess sum to infinity products advent integration graphs addition 2d shapes calculus digital products sequences triangles taxicab geometry games circles prime numbers menace factorials matrices logic functions expansions parabolas cryptic crossnumbers dominos symmetry averages books bases sets lines medians rectangles money binary axes trigonometry volume square grids differentiation squares sums means surds consecutive integers cards angles crosswords arrows speed tournaments combinatorics number lists even numbers geometry indices cryptic clues digital clocks division percentages gerrymandering pascal's triangle planes scales probability coordinates tiling 3d shapes fractions shape regular shapes digits square numbers algebra palindromes xor decahedra coins multiplaction squares dodecagons people maths the only crossnumber shapes grids odd numbers remainders complex numbers square roots median

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026