`A` and `B` play a game in which they alternately call out positive integers less than or equal to `n`, according to the following rules. A goes first and always call out an odd number, `B` always calls out an even number each playerr 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 cal out a number, then which of the following is/are correct?

Options

A. For `n=6`, number of possible games is 8
B. For `n=6`, number of possible games is 10
C. For `n=10`, number of possible games is 55
D. For `n=8` number of possible games is 21

Answer

A, C, D

Explanation

`P_(n)=P_(n-1)+P_(n-2), P_(1)=1, P_(2)=1`
`P_(3)=1+1=2`
`P_(4)=2+1=3`
`P_(5)=5`
`P_(6)=8`
`P_(7)=13`
`P_(8)=21`
`P_(9)=34`
`P_(10)=55`