12 Marbles Scale 3 Times

If the 2 groups weigh the same the heavier marble is in the 3rd group.

12 marbles scale 3 times. 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. So we need to begin the tedious task of mapping each result to an outcome. Click here for the answer. You have a balance scale.

If they balance then the different marble is in the group 9 10 11 12. They all weigh the same except one. 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. Once the group is determined split the marbles into 2 groups with 2 marbles each.

Your task is to identify the unusual marble and discard it. Either they balance or they don t. 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. 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 don t know if that one is heavier or lighter. Note that the unusual marble may be heavier or lighter than the others. 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. You have 12 marbles.

You are allowed to use the scales three times if you wish but no more. If they are equal then you know that the different ball is lighter and is 1 of the 3 not weighed. Split the marbles into 3 groups with 4 marbles each. The 12 marbles appear to be identical.

Pick 2 groups and use the scale to determine which group contains the heavier marble. So that the plan can be followed let us number the marbles from 1 to 12. In fact 11 of them are identical and one is of a different weight. If it does not tip to a side if it balances we know the unused group of 3 contains the heavy marble.

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. Keep the heavy group of 3 marbles and discard the rest. To do this put 3 marbles in each side 3 left 3 right 3 unused if the scale tips to a side we know that group of 3 has the heavy marble. There are two possibilities.