Challenge Level

In 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?

Can you predict the positions of the next triangle numbers?

Check to see if you're right.

Thank you to Paul Stephenson from The Magic Mathworks Travelling Circus who provided the idea for this problem.