# Puzzles

## Archive

Show me a Random Puzzle**Most Recent Collections**

#### Sunday Afternoon Maths LIX

Turning SquaresElastic Numbers

Square Pairs

#### Sunday Afternoon Maths LVIII

Factorial PatternPlacing Plates

#### Advent Calendar 2016

#### Sunday Afternoon Maths LVII

Largest Odd FactorsList of All Puzzles

## Tags

time geometry 2d shapes 3d shapes numbers spheres trigonometry complex numbers algebra lines graphs coordinates odd numbers fractions differentiation calculus folding tube maps ellipses triangle numbers money bases triangles squares area square numbers chess probability circles averages speed sport multiples dates factors parabolas functions logic cards games people maths shape prime numbers irreducible numbers probabilty angles proportion dice integration sum to infinity dodecagons hexagons multiplication factorials coins shapes regular shapes colouring grids floors integers rugby crosswords percentages digits sums rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices symmetry planes volume number partitions ave pascal's triangle mean advent arrows## Triangles Between Squares

Prove that there are never more than two triangle numbers between two consecutive square numbers.

## Triangle Numbers

Source: ATM Mathematics Teaching 239

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