# Zero a Million Puzzle

The Zero a Million Puzzle – How to win!!!

In the new TV game-show “Zero to a Million”, each player chooses a number in the range from 0 to 1,000,000. The mean of all the numbers is calculated and the mean is multiplied by 2/3. The person who chose the number closest to the result wins.

1. In order to maximize your odds of winning, which number would you choose?

2. If only integers were allowed, how would this affect your choice?

3. What would you choose if the prize equaled the winner’s number in dollars?

4. What would you choose if the range was from zero to infinity, but the prize was a fixed dollar amount?

a) if there are k people in total , the sum of all their choices is most likely to be N*k/2

so the remaining k-1 ppl sum is most likely to be N*(k-1)/2

we choose our number x st (N*(k-1) + x) * 2/(3*k) = x

thus x = (k-1)*N / (3*k – 2)

sounds reasonable ?