Suppose you are given 6 balls all of which look identical. You’re told that 4 of the balls all weigh the same, but there are 2 balls that have unequal weights. Additionally, these two balls together weigh the same as any two of the 4 balls having the same weight. Determine which two balls have different weights, and which one weighs less and which one weighs more, using a balance scale with the fewest number of weighings possible.
Hint given in book: First, calculate how many questions you have to answer about the possible relations between the weight of the balls, and use this to determine how many weighings with the balance scale are needed.
I believe the mathematical way of going about it would be taking log3 of (6 choose 2), but I'm not sure.