mscroggs.co.uk
mscroggs.co.uk

subscribe

Advent calendar 2024

23 December

In a grid of squares, each square is friendly with itself and friendly with every square that is horizontally, vertically, or diagonally adjacent to it (and is not friendly with any other squares). In a 5×5 grid, it is possible to colour 8 squares so that every square is friendly with at least two coloured squares:
It it not possible to do this by colouring fewer than 8 squares.
What is the fewest number of squares that need to be coloured in a 23×23 grid so that every square is friendly with at least two coloured squares?

Show answer

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026