12 Marbles Riddle

If they balance then the different marble is in the group 9 10 11 12.

12 marbles riddle. The one labeled both. You have a balancing scale you can use to find this marble and figure out if it weighs more or less than the others. For the first weighing let us put on the left pan marbles 1 2 3 4 and on the right pan marbles 5 6 7 8. You don t know if that one is heavier or lighter.

What is the minimum number of weighings required to do this. You have a balance scale. If 3 6 12 is heavy then either 6 is the odd heavy ball or 1 or 2 is the odd light ball. 12 marbles problem.

Split the marbles into 3 groups with 4 marbles each. How can you find the heavier marble by using a balance scale only thrice. One of the marbles is heavier in weight than the rest. There are two possibilities.

You have twelve marbles that are identical in size shape and color. If a black marble comes out you know that has to be the black marbles box so you put the black label on it. You have 12 marbles. Since you know that the box is labeled incorrectly it must have all black marbles or all white marbles.

So another perfectly valid solution to the 12 marbles puzzle might even be. In general if you have n weights at your disposal you can solve the puzzle up to 3 n marbles included. Weigh 7 vs 8 if they balance then 4 is the odd light ball or the heaviest of 7 vs 8 is the odd heavy ball. Either they balance or they don t.

So that the plan can be followed let us number the marbles from 1 to 12. 2v2 8 xy 1v1 0 z 3v3 2 xy 1v1 1 z 1v1 0 which requires only two weights in one third of the cases. That is a small dish hangs from each end of a rod that is balanced in the middle. The scales are of the old balance variety.

If 1 2 5 vs 3 6 12 balances then either 4 is the odd light ball or 7 or 8 is the odd heavy ball. You can perform up to a maximum of three weighings to find out which marble has the different weight and if it is heavier or lighter than the others. Eleven of the marbles are of equal weight but one is heavier or lighter. Pick 2 groups and use the scale to determine which group contains.