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## 'Triangle Numbers' printed from http://nrich.maths.org/

Take a look at the multiplication square below.

The first eleven triangle numbers $1$, $3$, $6$, $10$, $15$, $21$,
$28$, $36$, $45$, $55$, $66$ have been identified.

Can you see
a pattern?

Does the pattern continue?

If so, can you explain why triangle numbers take up these positions
in a multiplication square?

Thank you to Paul Stephenson from

The Magic Mathworks
Travelling Circus who provided the idea for this problem.