Problem 2

You are given an ordered sequence of integers from to inclusive.

A new sequence is generated by taking the product of each two consecutive integers.

For example, in the generation of the second sequence, {1, 2, 3, 4, 5, 6, 7, 8} would become {2, 6, 12, 20, 30, 42, 56}.

This is repeated until there is only one integer left.

How many trailing zeros are there in the final integer? Can you find a closed mathematical expression for its value? (If you want, you can use a calculator to find it’s exact value).