Shamgar saved Israel by striking down 600 Philistines with an oxgoad.

Assume the Philistine army were marching downhill in symmetry as follows:

__In The Leading Rows__

* one soldier in the first row

* two soldiers in the second row

* each row having one extra soldier until row n

__The Main Block__

* x rows of n + 1 soldiers

__The Trailing Rows__

* the leading rows in reverse: n soldiers in the first row, n - 1 in the next, down to a final row of 1 (the soldier whom Shamgar strikes directly with his goad)

Thus, Shamgar struck the last man, who toppled the next row, who toppled the next row etc in a domino effect.

What numbers of leading/trailing rows are possible?

I'll give a couple of example possibilities:

1. zero: the main block would be 600 rows of 1 soldier

2. one: the main block would be 299 rows of 2 soldiers

3. two: the main block would be 198 rows of 3 soldiers

**Edited by BMAD, 23 April 2014 - 03:36 PM.**