On this network the following wealth distribution is feasible (4states)

• 1 has 5 coins
• 2 has 6 coins
• 3has 10 coins

The following is infeasible

• 1 has 12 coins
• 2 has 4 coins
• 3 has 5 coins

For humans trivial to see in small cases but the geometry solves this for any network