GeekDad Puzzle of the Week – Right Triangle Numbers

Geek Culture


This past weekend, as Max was learning to stack cups quickly, he and I discussed triangle numbers. One way to describe the set of triangle numbers is the set of numbers that make complete rows when stacking cups or laying out bowling pins: 1, 3, 6, 10, 15, 21, etc.

The first 6 triangle numbers (Source: wikipedia)
The first 6 triangle numbers
(Source: wikipedia)

Pairs of consecutive triangle numbers have unusual properties: not only is the sum of any two consecutive triangle numbers always square, but it is also the case that the sum of the squares of two consecutive triangle numbers is always another triangle number! (Go ahead, try a few out… I’ll wait.)

So, do triangle numbers have anything to do with right triangles? That’s the crux of this week’s GeekDad Puzzle of the Week.

For your chance at this week’s fabulous prize answer this question: Are there any sets of three triangle numbers that could be the sides of a right triangle? If not, why not?

As always, please submit your responses to GeekDad Central, and any and all correct (or at least reasonably well-reasoned) answers will be entered into a random drawing for this week’s prize, a $50 Gift Certificate from the fine folks at ThinkGeek.

Good luck, and happy puzzling!

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