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So, being inundated with the "How many triangles?" questions on Facebook, I noticed this one which is actually more difficult than I expect the question author intended:

http://creative.ak.facebook.com/ads3/flyers/36/28/6002237517496_1_992e4bd8.jpg [Broken]

Assuming you have 21 dots evenly distributed in an equilateral triangular pattern (like bowling pins), how many distinct triangles can be formed by connecting the dots?

Of course, I'll bet they expect people to interpret "

And on that note, how many are possible with 3 dots, 6 dots, 10 dots, and 15 dots? Is there a nice formula for progression as the number of available dots increases?

DaveE

http://creative.ak.facebook.com/ads3/flyers/36/28/6002237517496_1_992e4bd8.jpg [Broken]

Assuming you have 21 dots evenly distributed in an equilateral triangular pattern (like bowling pins), how many distinct triangles can be formed by connecting the dots?

Of course, I'll bet they expect people to interpret "

*equilateral*triangles" rather than simply "triangles", but it does make for a more interesting challenge.And on that note, how many are possible with 3 dots, 6 dots, 10 dots, and 15 dots? Is there a nice formula for progression as the number of available dots increases?

DaveE

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