Question

A and B play a game in which they alternate calling out positive integers less than or equal to n, according to the following rules:
•A goes first and always calls out an odd number.
•B always calls out an even number.
•Each player must call out a number which is greater than the previous number. (Except for A's first turn.)
•The game ends when one player cannot call out a number.

Some example games (for n = 8):
•1, 8
•3, 4, 5, 8
•1, 2, 3, 4, 5, 6, 7, 8

The length of a game is defined as the number of numbers called out. For example, the game 1, 8, above, has length 2.
a.

Answer 1

Good luck with that

Answer 2

a.How many different possible games are there?
b.How many different possible games of length k are there?

Answer 3

Fibonacci sequence