2019 CIME I Problems/Problem 9

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 $(a_ib_{ij(a_jb_{ij<0.$ (Error compiling LaTeX. Unknown error_msg)

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

2019 CIME I (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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2019 CIME I Problems/Problem 9

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