Mario has to meet the Princess at the opposite node of the network, as shown above. The digit on each node indicates the number of coins he collects upon arriving at the node. He can visit each node only once.

For example, if Mario follows the red arrow trail illustrated below, he will obtain \(1+6+3+4=14\) coins before reaching the Princess.

To prove his love, the Princess demands that Mario collect exactly 17 coins (as that is her favorite number). Can Mario accomplish this task?

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