Clue to Puzzle #1: 12 Coins, Old Fashioned Balance
1. You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other.
The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more.
Note that the unusual marble may be heavier or lighter than the others. You are asked to both identify it and determine whether it is heavy or light.
The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more.
Note that the unusual marble may be heavier or lighter than the others. You are asked to both identify it and determine whether it is heavy or light.
A good starting point to this puzzle is to think about which weighings will lead to useful information. For example if you were to weigh one lot of six against the other lot of six....
...This would lead to no useful information as we already know what would happen, one side will go down and the other up, it would bring us no closer to identifying the faulty marble.
I'll assume you have numbered the marbles or can some how keep track of which ones are which.
Additionally we have a number of tools:
Not weighing or removing - Just because a marble is not on the balance doesn't mean we can't learn anything about it. Removing it or not weighing it can also be useful.
Swapping sides - Swapping all the marbles from one weighing to their opposite side would tell us nothing, but swapping some of them might. Especially if some are also removed.
Known good marbles - We may identify some marbles we know to be good. Sometimes comparing suspect marbles to those might be useful.
The answer is difficult, a complete solution for all 24 possible combinations is difficult to find. What might be useful is to say to yourself OK let's have marble number 9 as the odd one and say it's heavy, for example. Then think about what weighing you might perform, what the outcome would be and use the above tools to see if you can definitely identify it. Then try for a different marble.
Where next?
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