System of Equations
♘ + ♘ + ♜ = 11
♜ + ♜ + ♘ + ♘ = 12
At first glance, this may look complicated: two knights and one rook equal 11, while two rooks and two knights equal 12.
Notice that we can rewrite the second equation as:
From the first equation we already know that:
♘ + ♘ + ♜ = 11So we replace this sum in parentheses (two knights and a rook) with the number 11:
11 + ♜ = 12
From this we immediately see that ♜ = 1, because 11 + 1 = 12.
Substitute back into the first equation:
♘ + ♘ + 1 = 11 → ♘ + ♘ = 10 →
♘ = 5
Result: knight ♘ = 5, rook ♜ = 1.
If one equation contains only a single symbol, the situation is simpler:
♘ + ♘ + ♜ = 13
♜ + ♜ + ♜ = 9
From the second equation it’s clear that three rooks equal 9. That means one rook has the value 3. Substitute this into the first equation:
♘ + ♘ + 3 = 13
♘ + ♘ = 10
♘ = 5
