Let $\text{N}$ denote the number of strictly increasing sequences of positive integers $a_1,a_2,\cdots, a_{19}$ satisfying the following two rules $:$

$a_1=1$ and $a_{19}=361,$
for any $i \neq j,$ if $b_{ij}$ is the $(i \cdot j)^{\text{th}}$ number not in the sequence $,$ then $(a_i-b_{ij})(a_j-b_{ij})<0.$

Find the largest positive integer $k$ such that $2^k$ divides $\text{N}.$

Solution 1

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2019 CIME I (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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2019 CIME I Problems/Problem 9

Solution 1

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