# Puzzles

## Archive

Show me a Random Puzzle**Most Recent Collections**

#### Sunday Afternoon Maths LIX

Turning SquaresElastic Numbers

Square Pairs

#### Sunday Afternoon Maths LVIII

Factorial PatternPlacing Plates

#### Advent Calendar 2016

#### Sunday Afternoon Maths LVII

Largest Odd FactorsList of All Puzzles

## Tags

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

Source: Futility Closet

Each point on a straight line is either red or blue. Show that it’s always possible to find three points of the same color in which one is the midpoint of the other two.

## Coloured Pins

A bowling alley has a mixture of red and blue pins. Ten of these pins are randomly chosen and arranged in a triangle.

Will there always be three pins of the same colour which lie on the vertices of an equilateral triangle?

## 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?