Just count it

Probability Level 2

Find maximum numbers of triangles one can make from 10 matchsticks

not necessarily similar


The answer is 120.

Akash Singh by Akash singh , 21, India

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1 solution

The maximum number of triangles that can be made is equal to , ( 10 3 ) = 10 ! ( 10 − 3 ) ! × 3 ! = 10 × 9 × 8 3 × 2 = 120 \binom{10}{3} = \frac{10!}{(10-3)! \times 3!} = \frac{10 \times 9 \times 8}{3\times 2} = \boxed {120}

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And of course, can this configuration be achieved?

Calvin Lin Staff - 5 years, 10 months ago

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