# 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

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