Nine gold coins
You have 9 gold coins. All 9 coins look exactly the same, but one coin is a fake and is either lighter or heavier than the other 8 coins. You have scales - balance type with 2 trays - but you have no measure weights.
What is the minimum number of measurements to find out the fake coin?
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1 solution
Let the nine coins are named as A1, A2, A3, B1, B2, B3, C1, C2, C3. (having 3 groups A, B and C each group has 3 coins)
From the table at max it is required 3 measurements to find out the fake coin either lighter or heavier with other coins.