IL-GILLIS 2020 Problem 6

On a circle the numbers from 1 to 6 are written in order, as depicted in the picture. In each move, Lior picks a number $a$ on the circle whose neighbors are $b$ and $c$ and replaces it by the number $\frac{bc}{a}$ . Can Lior reach a state in which the product of the numbers on the circle is greater than $10^{100}$ in a) at most 100 movesb) at most 110 moves

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