mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Triangle numbers

Let \(T_n\) be the \(n^\mathrm{th}\) triangle number. Find \(n\) such that: $$T_n+T_{n+1}+T_{n+2}+T_{n+3}=T_{n+4}+T_{n+5}$$

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths VI,
puzzles about numbers, 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

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

Archive

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