Question

The number of oranges in a tetrahedron with n layers is n/6(n+1)(n+2). A shopkeeper has 100 oranges. He wants to display them in a tetrahedron. Work out the largest number of layers he can have.

Answer 1

I'd go for approximation. Making the approximation that n, n + 1 and n + 2 are all about equal to n, then you can simplify your equation.

I can't tell if the (n + 1) and (n + 2) are in the numerator or denominator. Is this actually n(n+1)(n+2) / 6?

If so, solve n\^3/6 = 100, work out what n is (approximately) and then try that value of n to see how well it works.

Answer 2

You can just try increasing values of n, since that should exceed 100 before long. Note that you don't have to recalculate each time - to go from 2 * 3 * 4 / 6 to 3 * 4 * 5 / 6, you simply divide by 2 and multiply by 5.