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 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025