mscroggs.co.uk
mscroggs.co.uk
blog     puzzles     academic     talks     contact     subscribe↓ ☰ ↓

subscribe

Puzzles

Square pairs

Source: Maths Jam
Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?
For which other numbers \(n\) is it possible to order the integers 1 to \(n\) in such a way?

Show answer

Tags: numbers, square numbers, sums
If you enjoyed this puzzle, check out Sunday Afternoon Maths LIX,
puzzles about sums, or a random puzzle.

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

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

Archive

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