USAMO Guide Contests

A sequence

a_1, a_2, \ldots, a_8

is called skibidi if each

a_i

is an element of

\{1, 2, 3\}

and for every

i

a_i \neq a_{i+1}

. Let

N

be the number of skibidi sequences. A fair die with

N/48

faces where each face has a distinct integer from 1 to

N/48

, is rolled twice. What is the probability that the product of the two results is divisible by 6? Express your answer as

p/q

in lowest terms and find

p + q