View source for 2019 CIME I Problems/Problem 9

Let <math>\text{N}</math> denote the number of strictly increasing sequences of positive integers <math>a_1,a_2,\cdots, a_{19}</math> satisfying the following two rules<math>:</math>
* <math>a_1=1</math> and <math>a_{19}=361,</math>
* for any <math>i \neq j,</math> if <math>b_{ij}</math> is the <math>(i \cdot j)^{\text{th}}</math> number not in the sequence<math>,</math> then <math>(a_ib_{ij(a_jb_{ij<0.</math>
Find the largest positive integer <math>k</math> such that <math>2^k</math> divides <math>\text{N}.</math>

==See also==
{{CIME box|year=2019|n=I|num-b=8|num-a=10}}

[[Category:Intermediate Combinatorics Problems]]
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