Counting Triangles

Probability Level 3

How many triangles are there in the completely connected pentagon as shown above?


The answer is 35.

Tan Chee Sen by Tan Chee Sen , 25, Malaysia

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1 solution

Guiseppi Butel
Jun 21, 2014

image image

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Initially, I had erred by counting duplicates of the Big 2's.

Guiseppi Butel - 6 years, 11 months ago

Can there be another way to solve this problem?

Asha Kumari - 6 years, 9 months ago

Refer to the above diagram, I first count (1,2,3) as 6 triangles, (3,5,7) as another 6, and so on. In the process, (3,7,9,6.1) is counted twice. So it's 6x5-5=25. Followed by the 4's and Big 2's, make it 35.

BK Lim - 6 years, 6 months ago

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