Puzzles
Weigh any whole number from 1 to 40 pounds using only four weights on a balance scale
You have a two-pan balance scale and may place weights on either side. What is the smallest set of four whole-number weights that lets you balance any integer weight from 1 to 40 against them?
Reveal the answer
1, 3, 9 and 27 pounds — powers of three. Because weights can go on either pan, each weight can subtract as well as add, letting four weights represent any value from -40 to 40. Claude Gaspard Bachet de Méziriac published the puzzle in 1612, generalizing what's now called a 'balanced ternary' system, later used in some early computers.