   # If you have sticks of length 1, 2, 3, 4, 5, 6, 7, 8 and 9 cm. How many different triangles con you make using 3 sticks?

141 views

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? posted Sep 6, 2017

34 is the answer answer Sep 20, 2017

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 answer Nov 2, 2017

Similar Puzzles
+1 vote

If you have 7 sticks of length 1, 2, 3, 4, 5, 6, and 7cm. Is it possible to make two lines of the same length with them? Can you make four lines of the same length?