Tetrahedral Numbers

September 13, 2011

Before I started writing my own programming exercises, I enjoyed solving other programming exercises available on the internet, many of them mathematical in nature. Today’s exercise comes from http://open-cs.net/problems.php?id=18 and concerns triangular and tetrahedral numbers.

A triangular number tells the number of ways that balls can be stacked in a triangle. The first triangular number is 1, the second is 3 (a row of 1 plus a row of 2), the third triangular number is 6 (the first two rows plus a row of 3), the fourth triangular number is 10 (adding a row of 4), the fifth triangular number is 15 (think of the 15 balls on a pool table), and so on.

A tetrahedral number is the three-dimensional equivalent of a triangular number; think of cannonballs stacked in a three-sided pyramid. The top layer has one ball, the second layer has 3 balls (the second triangular number) so the second tetrahedral number is 1 + 3 = 4, the third layer has 6 balls giving a total of 10 balls in the tetrahedron, and so on.

Your task is to find the base of the tetrahedron that contains 169179692512835000 balls. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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