Sam Loyds Puzzling Scales Puzzle - Solution

To some people the idea of adding a b c to x y z, or multiplying letters together seems the height of absurdity, and they fail to grasp the simplicity of algebra.

In the first instance we see that a top and three cubes weigh equal to twelve marbles.

In the second equation a top alone equals a cube and eight marbles.

Now let us add three cubes to each side, as the addition of equal quantities to both sides of an equation does not change the balance.

By the addition of three cubes to the second pair of scales we have produced the identical values as shown by the first scales.

In the first case a top and three cubes = twelve marbles.

In the second illustration we have proved that a top and three cubes = four cubes and eight marbles, so a marble weighs as much as a cube.

It proves therefore that one cube and eight marbles, or nine marbles weighs equal to the top.