# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

## Tags

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

Today's number is the area of the largest dodecagon that it's possible to fit inside a circle with area \(\displaystyle\frac{172\pi}3\).

## Cube multiples

Source: Radio 4's Puzzle for Today (set by Daniel Griller)

Six different (strictly) positive integers are written on the faces of a cube. The sum of the numbers on any two adjacent faces is a multiple of 6.

What is the smallest possible sum of the six numbers?

## Polygraph

Draw a regular polygon. Connect all its vertices to every other vertex. For example, if you picked a pentagon or a hexagon, the result would look as follows:

Colour the regions of your shape so that no two regions which share an edge are the same colour. (Regions which only meet at one point can be the same colour.)

What is the least number of colours which this can be done with?