2020 CIME I Problems/Problem 15

Problem 15

Find the number of integer sequences $a_1, a_2, \ldots, a_6$ such that

(1) $0 \le a_1 < 6$ and $12 \le a_6 < 18$ ,

(2) $1 \le a_{k+1}-a_k < 6$ for all $1 \le k < 6$ , and

(3) there do not exist $1 \le i < j \le 6$ such that $a_j-a_i$ is divisible by $6$ .

$302$

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