Three Level Scales
Read the puzzle
Three scales balance. Scale 1: one triangle equals one square plus one circle. Scale 2: two squares equal one triangle plus one circle. Scale 3: two triangles equal three squares. Same shapes weigh the same. A fourth scale holds one triangle and one square on the left and an empty pan with a question mark on the right. How many circles balance the last scale?
How many circles balance the last scale?
5 CIRCLES
Square = 2 circles, triangle = 3 circles.
How to solve it
Turn the scales into equations: T = S + C, 2S = T + C and 2T = 3S.
Put the first into the second: 2S = S + C + C, so S = 2C; a square weighs 2 circles. Then T = 2C + C = 3C. Check with the third scale: 2T = 6C and 3S = 6C, so it balances.
The last pan holds T + S = 3C + 2C = 5 circles.
A common slip is answering 2 or 3, the weight of just one of the shapes. The answer is 5 circles.
Learn the method: Three Level Scales Riddle: How Many Circles Balance the Last?
