You are given twelve identical-looking balls and a two-sided scale. One of the balls is of a different weight, although you don’t know whether it’s lighter or heavier. How can you use just three weighings of the scale to determine not only what the different ball is, but also whether it’s lighter or heavier?
What is the weight of the 9 balls?
9 Balls Puzzle :- You have given a two-arm balance scale and 9 identical looking balls. One of the ball is of different weight (heavier/lighter) than rest of the 8 balls, which all are of equal weight.
What happens if you have 7 balls on one side of the scale?
If you have seven balls on one side and one on the other, of course the scale is going to tip to the side with seven balls (unless your odd ball out is ridiculously heavy, but let’s not entertain that scenario). So we need to invert a few of these configurations so that we’re putting four on each side for each weighing.
How to find out if a ball is heavier than a B?
Now weigh them against each other to find out the set containing different weight (heavier/lighter) ball and whether the ball is heavier or lighter. First weigh :- Weigh A {3 balls} vs. B {3 balls}, Now either the scale will balance or the scale will not balance and one side will be heavier.
Which is the heavy ball 7 or 12?
If 7,2,12 is heavy then either 2 is the odd heavy ball or 5 or 6 is the odd light ball. Weigh 5 vs 6, if balanced then 2 is the odd heavy ball, or the lightest of 5 vs 6 is the odd light ball. If 7,2,12 is light then either 7 is light or 1 is heavy.
What are the outcomes of weighing 12 balls?
With each weighing, the scale can either tip to the left, tip to the right, or stay balanced. This gives you a total of 3 3 = 27 possible outcomes, and in this case you need to discern 24 results from them (one of 12 balls is either light or heavy, which is 12 × 2 = 24). So, we need to begin the tedious task of mapping each result to an outcome.
Which is heavier, 3 or 6 identical balls?
Weigh {1} and {2}. If they balance, 6 is fake (lighter). If they don’t balance then whichever one is heavier is fake (heavier). If {3,6,9} is heavier, then either 3 is heavy or 5 is light. Weigh {5} and {9}. They won’t balance. If {5} is lighter, 5 is fake (lighter). If they balance, 3 is fake (heavier).
