Clue to Puzzle #1: 12 Coins, Old Fashioned Balance
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.
My suggestion for your first weighing would be 1,2,3,4 vs 5,6,7,8. Of course this suggestion is not unique any four against any four would be equally valid.
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