The fake gold coin
✓ With solution
Eight gold coins, one of them fake and heavier. How many weighings to find it?
A merchant has eight gold coins that look exactly alike, but one is fake and slightly heavier than the rest. He has only a two-pan balance, with no weights.
What is the smallest number of weighings that guarantees he finds the fake coin?
- AOne
- BTwo
- CThree
- DFour
Show the answer
Answer: B) Two. Two is enough. Put 3 coins on each pan and keep 2 aside. If the pans balance, the fake is one of the 2 set aside: weigh them, and the heavier is fake. If one pan drops, the fake is among its 3 coins: put one on each pan; if they balance, the third is fake, otherwise it's the heavier one. One weighing can't do it: a weighing has only three outcomes (left, right, balance), but there are eight possibilities.
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