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The Great Weights Puzzle

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

For the first weighing you need to put 4 weights on each tray.

Now look at each possible outcome of the first weighing and decide what you would do in each case.
You might like to first consider the case when the scales balance on the first weighing - what do you know about all the weights on the balance?

You might also like to think about the problem with fewer weights first, and use ideas you come up with there for the 12 weight problem.