[bonanova]

Here's a simple game between two players.

Player A picks an integer p of at least four digits, like 1739.

Player B picks an integer n of no more than two digits, like 23.

Play proceeds as follows.

Player A says a number from 1 to n, inclusive, like 16.

Player B adds to it a number from 1 to n, inclusive, like 9, and says 25.

Players alternate turns, adding to the running total numbers from 1 to n, inclusive.

The player who says the number p, in this case 1739, wins the game.

You can be Player A or B.

Which do you choose, and what is your strategy?

[superprismatic]

I would like to be player A. For p, I would choose a prime number of at

least four digits. Now, because my number is prime, it is not divisible

by n+1. Let k=p modulo (n+1). k is non-zero. Then, I will choose k

as my first pick. Whatever number B chooses will make the running total

modulo (n+1) different from k. In subsequent moves, I will always be able

to bring the running total modulo (n+1) back to k, eventually getting to p

for the win.

Edited January 31, 2011 by superprismatic

[bonanova]

If the incremental numbers are of a single digit the strategy simplifies greatly.

As does finding the solution.

Good job.