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max no of no 1-9 so that for any two adjacent, one is divided by the other

Source: Caucasus 2015 7.2

April 26, 2019
number theorydivisiblemaximum

Problem Statement

There are 99 cards with the numbers 1,2,3,4,5,6,7,81, 2, 3, 4, 5, 6, 7, 8 and 99. What is the largest number of these cards can be decomposed in a certain order in a row, so that in any two adjacent cards, one of the numbers is divided by the other?
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