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A pagoda function assigns a weight to each location in a move puzzle so that the total weight of occupied locations never increases under a legal move. Comparing the initial and desired totals can then prove that the desired position is unreachable.

In peg solitaire, a jump removes pegs at $a,b$ and adds one at $c$. Weights satisfying $w(c)\le w(a)+w(b)$ for every allowed jump make $P={\sum }_{\text{occupied }x}w(x)$ nonincreasing. If a target has larger $P$ than the initial board, no move sequence can reach it. Finding suitable weights is the creative step; failure of one chosen weight function does not prove reachability.