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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
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
who provided the idea for this problem.