12 Marbles Scale 3 Times

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.

12 marbles scale 3 times. Click here for the answer. Weigh 3 vs 4 if they balance then 8 is the odd light ball or the heaviest of 3 vs 4 is the. If it does not tip to a side if it balances we know the unused group of 3 contains the heavy marble. You have 12 marbles.

So that the plan can be followed let us number the marbles from 1 to 12. If they are equal then you know that the different ball is lighter and is 1 of the 3 not weighed. Pick 2 groups and use the scale to determine which group contains the heavier marble. If they balance then the different marble is in the group 9 10 11 12.

Once the group is determined split the marbles into 2 groups with 2 marbles each. Note that the unusual marble may be heavier or lighter than the others. So now in 2 tries we can find out which grp has the ball with the diffe weight then in another 1 try we can find out the different ball correct me if am wrong guys. Split the marbles into 3 groups with 4 marbles each.

The 12 marbles appear to be identical. Your task is to identify the unusual marble and discard it. If the 2 groups weigh the same the heavier marble is in the 3rd group. If 1 2 3 4 5 6 7 8 then either 1 2 3 4 contains a heavy ball or 5 6 7 8 contains a light ball so weigh 5 6 1 vs 7 2 12 with 3 possible outcomes.

There are two possibilities. So we need to begin the tedious task of mapping each result to an outcome. If 5 6 1 vs 7 2 12 balances then either 8 is the odd light ball or 3 or 4 is the odd heavy ball. In fact 11 of them are identical and one is of a different weight.

They all weigh the same except one. Next take 3 of the normal balls and 1 from the heavier group and weigh against the 1 ball from the lighter group plus the 3 balls you just replaced from the heavier group 2nd weighing. Lets split them into 4 grps of 3 each a 1 2 3 b 4 5 6 c 7 8 9 d 10 11 12 then weigh a against b and c vs d. Either they balance or they don t.

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. You have a balance scale. You are allowed to use the scales three times if you wish but no more. 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.