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


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


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


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


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