# Why would someone ever do that?

**Discrete Mathematics**Level 4

Let *a* be the sum of the number of towers of every possible sequence that could have been made by me, and let *b* be the number of blocks that I used to build each tower of all the possible sequences that was shown to my brother. What is the value of *a + b*?

**Notes and Assumptions**

A sequence of towers is a sequence of a certain number of towers with the same number of wooden blocks. Every sequence made by me had a total number of 504 blocks, in other words, I used all the wooden blocks in every sequence.

Consider that the space which I used to build the towers is infinite.