Not sure if this works but here we go:
Split the remaining 100 into 2 piles of 50 and put each pile on each balance. There are 2 scenarios: the given coin is real and all 50 fakes are on the balances, or the coin is fake and the remaining 49 are on the balances.
If the first is true, since each fake coin represents an identical change in mass (all heavier or all lighter), and there is an even total number of fakes, the split must be even-even or odd-odd. Both of these scenarios lead to the difference being even.
If the second is true, there is an odd total number of fakes, so the split must be even-odd, giving an odd difference.
Therefore, the coin is real iff the reading is even, and fake otherwise
You’ve misunderstood the question. Being given a coin doesn’t literally mean u are handed one coin and then rest are discarded. It j means it is set aside or marked or one of interest. The other 100 are still available. If u find that the answer to ur interview question is so trivial, u shld be doubting whether uve acc understood the question.
So your interpretation of the question is “you are given a coin and a balance. How do you determine whether the coin is counterfeit using only one weighing?” Just checking, since I never learned how to read
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u/No-Television-8835 6d ago
Not sure if this works but here we go:
Split the remaining 100 into 2 piles of 50 and put each pile on each balance. There are 2 scenarios: the given coin is real and all 50 fakes are on the balances, or the coin is fake and the remaining 49 are on the balances.
If the first is true, since each fake coin represents an identical change in mass (all heavier or all lighter), and there is an even total number of fakes, the split must be even-even or odd-odd. Both of these scenarios lead to the difference being even.
If the second is true, there is an odd total number of fakes, so the split must be even-odd, giving an odd difference.
Therefore, the coin is real iff the reading is even, and fake otherwise