The sum of $9$ positive natural numbers, not necessarily distinct, is $100$. If placed appropriately on the vertices of the following graph, two of them will be joined by an edge if and only if they have a common divisor greater than $1$ (that is, they are not relatively prime).
What, in non-decreasing order, are those $9$ numbers? The answer is unique.
1 2 2 3
counts as ascending, but it's certainly non-decreasing. $\endgroup$