Each day, a random integer will be picked between 0 and "1000. You will then have 10 guesses to guess the number. Each guess will be associated with a prime number, given in increasing order. For a guess associated with prime p, the game will tell you the p-adic distance between your guess and the target number. Good luck!

For a fixed prime p, define the p-adic norm of an integer x as p^-k, where x = np^k, with n not divisible by p. For example, for p = 3, the p-adic norm of 6 is 1/3, the p-adic norm of 9 is 1/9, and the p-adic norm of 11 is 1. The p-adic distance between two integers is the p-adic norm of the difference.

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