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Team Fortress

You have all managed to raise yourselves an army of 50 soldiers and want to capture 10 castles. However, you know the other teams will as well. The castles are worth 1,2,...,10 points respectively. If you send more units to a specific castle than your opponent, you capture the castle and get the points.

All teams that send in an army will participate in a single elimination bracket. In each battle, the team with the most points wins and advances to the next round with the same army distribution, until only one remains to win. Once eight teams have arrived, the tournament will begin!

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Solution

This puzzle makes us think we are in a battle with the other puzzlehunt teams, and that should we just manage to win some rounds then we will be able to complete the puzzle. In fact this is a ruse! No matter what we seem to do, we never win against our wiley opponents. The opponent here is actually an AI, but if we look closely we can see a pattern to the play. Though each game may be different, after every puzzle reset the amount by which we lose follows a strict pattern - 7, 1, 8, 2, 8, 1, 8, 2, 8, 5 - and then it repeats. You may recognise this as the (rounded) first ten digits of the decimal expansion of e; more importantly though, you may notice that the digits sum to 50 and that they thus constitute a valid strategy in this game, and in fact it is the winning strategy!