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 money, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024