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# Puzzles

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## Triangles Between Squares

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

## Triangle Numbers

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