mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

One two three

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.

Show answer & extension

Tags: colouring

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?

Show answer & extension

Tags: colouring

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?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020