riddler-pick-lowest/low_numbers: 3116
Data source: https://github.com/fivethirtyeight/data/blob/master/riddler-pick-lowest/low_numbers.csv
rowid | Your Number | Show Your Work |
---|---|---|
3116 | 193 | Assuming 1500 entries, assuming a Zipf distribution, the number choosing 1 would be 1500/7.89 ~ 190. The Zipf distribution is: n, n/2, n/3, n/4, n/5, n/6, ... (i.e the harmonic series). The 7.89 is the sum of the harmonic series out to 1500. So the expected value of the number choosing a particular interger drops to 1 at about 190. So the lowest unused number is probably around there. If we think of this as an n person zero sum game, then it depends on whether n is even or odd. If n is odd (= 2*k + ), then any alliance of k + 1 players can force a win by choosing all the numbers from 1 to k + 1. At least 1 of them must be unique. If n is even (= 2*k), then any alliance of k players can force a tie by choosing all the numbers from 1 to k. At least 1 of them must be unique, unless the other k players also choose all the numbers from 1 to k. |