A sequence $latex a_1,\ a_2,\ \ldots,\ a_n$ is called almost-increasing if $latex a_i\le a_{i+1}+8$ for all $latex i$. For example, the sequence

$latex 160,\ 170,\ 165,\ 180,\ 175$

is almost-increasing.

(a) How many different rearrangement of the sequence

$latex 140,\ 145,\ 150,\ 155,\ 160,\ 165,\ 170,\ 175,\ 180,\ 185$

is almost-increasing?

(b) How many different rearrangement of the sequence

$latex 155,\ 160,\ 164,\ 165,\ 170,\ 175,\ 180,\ 185,\ 190,\ 195,\ 200,\ 205,\ 210$

is almost-increasing?

Due to March 8, 2017