You have 8 balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?

Solution below divided into hints:

Divide the balls into the following groups: (1,2,3), (4,5,6), and (7,8).

Weigh (1,2,3) against (4,5,6).

Either the two groups are equally heavy. (Case A) One of these groups is heavier than the other. (Case B)

**Case A** Weigh 7 against 8. Now you have identified the heavier ball in 2 weighing.

**Case B** Take the heavier group (assume it to be (1,2,3)), take any two balls and weigh them against each other. Either one of these is heavier else the third ball is.