riddler-castles/castle-solutions: 1309
Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub · About: simonw/fivethirtyeight-datasette
rowid | Castle 1 | Castle 2 | Castle 3 | Castle 4 | Castle 5 | Castle 6 | Castle 7 | Castle 8 | Castle 9 | Castle 10 | Why did you choose your troop deployment? |
---|---|---|---|---|---|---|---|---|---|---|---|
1309 | 0 | 0 | 0 | 0 | 0 | 24 | 24 | 24 | 24 | 4 | There are a total of 55 points in play here. Assuming no drawn battles, I need to get 28 points (at least) to win. There are 4.2634215e+12 number of solutions to x1 + x2 + ... + x10 = 100. Before I saw this number, I thought for a minute about brute forcing it by finding all solutions and doing a one-vs-one across them all to find the winner. So, I ended up brute-force searching over all solutions of x1+x2+x3+x4 = 20 to get best candidate (0, 5, 5, 10). I ran again for x1+x2+x3+x4=24 to get best candidate (0, 6, 6, 12) and for x1+x2+x3+x4+x5=20 to get best candidate (0, 2, 4, 6, 8). Extrapolating it for the problem of 10 castles with 100 soldiers, I get (1, 3, 5, 7, 9, 11, 13, 15, 17, 19). This (I think/hope/believe) wins on average against the set of all possible solutions but my concern is that I lose against a top-heavy strategy (10, 0, 0, 0, 0, 0, 0, 20, 30, 40) and a bottom-heavy strategy (8, 10, 12, 14, 16, 18, 22, 0, 0 ,0). I ended up going with a middle-heavy strategy giving up on 25 points for castles 1-5+10. |