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 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025