# Line of primes

Discrete Mathematics Level 4

Hugo has written the 9 smallest primes with 2 digits down on 9 cards.

Now he places the 9 cards in a line, so that the difference of the numbers written on neighbored cards is always divisible by $$2^m, m \in \mathbb{N} .$$

In how many ways can Hugo arrange his deck, so that his deck suffices the property given above?

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