Line of primes

Probability 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 ∈ N . 2^m, m \in \mathbb{N} .

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


The answer is 4.

Alisa Meier by Alisa Meier , 24, Germany

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1 solution

Pop Wong
Jun 2, 2020
Prime Relabel the node (p-11) possible node to connect
11 0 2,8
13 2 0,6,18
17 6 2,8
19 8 0,6,12
23 12 8,20
29 18 2,20,26
31 20 12,18
37 26 18,30
41 30 26

From node-18 to node-2, there is no route to complete the ring 0-2-6-8, each node once, and then go to node 12.

So, 4 possible ways:

30-26-18-20-12-8-0-2-6 (and reverse the order) ; or 30-26-18-20-12-8-6-2-0 (and reverse the order)

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