MathDB

An integer is given

N> 1

. Arne and Britt play the following game: (1) Arne says a positive integer

A

. (2) Britt says an integer

B> 1

that is either a divisor of

A

or a multiple of

A

. (

A

itself is a possibility.) (3) Arne says a new number

A

that is either

B - 1, B

B + 1

. The game continues by repeating steps 2 and 3. Britt wins if she is okay with being told the number

N

before the

50

th has been said. Otherwise, Arne wins. a) Show that Arne has a winning strategy if

N = 10

. b) Show that Britt has a winning strategy if

N = 24

. c) For which

N

does Britt have a winning strategy?

Problem Statement