MathDB

5)Players

A

and

B

play the following game: a player writes, in a board, a positive integer

n

, after this they delete a number in the board and write a new number where can be: i)The last number

p

, where the new number will be

p - 2^k

where

k

is greatest number such that

p\ge 2^k

ii) The last number

p

, where the new number will be

\frac{p}{2}

p

is even. The players play alternately, a player win(s) if the new number is equal to

0

and player

A

starts.
a)Which player has the winning strategy with

n = 40

?? b)Which player has the winning strategy with

n = 2012

Problem Statement