mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Balanced sets

A set of points in the plane is called 'balanced' if for any two points \(A\) and \(B\) in the set, there is another point \(C\) in the set such that \(AC=BC\) (here \(AC\) is the distance between \(A\) and \(C\)).
For all \(n\geq3\), find a balanced set of \(n\) points.

Show answer

If you enjoyed this puzzle, check out Sunday Afternoon Maths XLIV,
puzzles about geometry, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024