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Shamgar vs the Phillistines

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Posted 23 April 2014 - 03:33 PM

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.

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#2 Rob_G


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Posted 23 April 2014 - 07:58 PM

Spoiler for The rest

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#3 m00li


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Posted 24 April 2014 - 02:21 AM

Spoiler for Solution

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