PSA: FiveThirtyEight are running the problem again [1], and this time have released the data from the previous battle so you can see the soldier distributions that everyone took last time [2]. Submissions are due this Friday.
This was a fun problem. I wish I spent a little more time on it. My solution and approach was pretty similar to the OP, code and write up here:
https://github.com/mattdodge/538-riddler-nation
The biggest takeaway I think is that you don't even need to beat the "winning solution", you need to beat more of the general population than that solution does.
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[1]: http://fivethirtyeight.com/features/the-battle-for-riddler-n...
[2]: https://github.com/fivethirtyeight/data/tree/master/riddler-...