If you have sticks which measure 1, 2, 3, 4, 5, 6, 7, 8 and 9 cm (one of each). How many different triangles can you make using three of the sticks?

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If you have sticks which measure 1, 2, 3, 4, 5, 6, 7, 8 and 9 cm (one of each). How many different triangles can you make using three of the sticks?

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Yes there are two formulas.

One is for when there are an even numbers of sticks and

the other is for when there are an odd number of sticks.

If you have sticks of lengths 1,2,3,...,n inches

The formula for when n is even is n(n-2)(2n-5)/24

The formula for when n is odd is (n-1)(n-3)(2n-1)/24

The case above is when there are 9 sticks. Since 9 is odd,

we use the formula, (n-1)(n-3)(2n-1)/24

(n-1)(n-3)(2n-1)/24 = (9-1)*(9-3)*((2*9)-1) /24

=(8*6*17)/24

=34

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