Piece values as numbers

Give each piece its standard value: pawn $1$, knight $3$, bishop $3$, rook $5$, queen $9$. Now the pieces are numbers and positions become sums. Asking which pieces add up to a queen is solving for parts that total $9$. Three knights are one answer, $3 + 3 + 3 = 9$. It is not the only one: start from the largest piece that still fits under $9$, subtract it, and look for pieces that cover what is left.

The king has no value here because it cannot be traded. Treating a value as a variable lets you ask "what if": if the queen were worth $10$, which combinations still reach it? Arithmetic on the board is ordinary arithmetic with a story attached.