## An interesting Riddler puzzle this week

More of a thought experiment game than actual “Can be solved” puzzle from the Riddler.

In a distant, war-torn land, there are 10 castles. There are two warlords: you and your archenemy. Each castle has its own strategic value for a would-be conqueror. Specifically, the castles are worth 1, 2, 3, …, 9, and 10 victory points. You and your enemy each have 100 soldiers to distribute, any way you like, to fight at any of the 10 castles. Whoever sends more soldiers to a given castle conquers that castle and wins its victory points. If you each send the same number of troops, you split the points. You don’t know what distribution of forces your enemy has chosen until the battles begin. Whoever wins the most points wins the war.

They’re having a round robin tournament, but you can’t submit a mixed strategy. Just 10 numbers. An interesting question as to how many levels you want to go. I was briefly tempted to grab a genetic algorithm framework and try to evolve a good solution (against a population of other solutions and a few fixed and random-ish strategies), but then I decided to play other games instead. Still, I may think about it and submit an answer later on.

And they have a simpler, classic pick-a-low, problem:

Submit a whole number between 1 and 1,000,000,000. I’ll then take all those numbers and find the average submission. Whoever submits the number closest to ⅔ of the mean of all of the submitted numbers wins.

Now that one’s easy. I’m just going to submit one billion, because a) those things bore me and b) game theory geeks need to be reminded now and again that in the real world people are jerks.

IIRC Its been mathematically proven that the second problem does not have a solution.

peer sylvesterFebruary 5, 2017 at 3:16 am