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

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

Archive

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