NRICH: Triangle Numbers

Take a look at the multiplication square. 

In the multiplication square below, the first eleven triangle numbers 1361015212836455566 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.

Multiplication square

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.

Age 11 to 14

Math Topics
Algebra & Pre-Algebra, Patterning & Sequencing
Middle School, High School, Educator
6th Grade, 7th Grade, 8th Grade, 9th Grade

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NRICH (University of Cambridge)

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