Given 12 coins such that exactly one of them is fake (lighter or heavier than the rest, but it is unknown whether the fake coin is heavier or lighter), and a two pan scale, devise a procedure to identify the fake coin and whether it is heavier or lighter by doing no more than 3 weighings.
Answers
Answered by
0
A. If they balance then you know the fake coin is one of the two from the previous lighter side that you didn't weigh, and you also know that the fake coin is lighter. So weigh one of those with a good coin. If those balance then you know the one you didn't weigh is the fake coin and you know it's lighter. If they don't balance, then the lighter one on the scale is the fake one.
`
B. If they don't balance, then the fake coin is either one of the ones on the PRESENT heavy side from the PREVIOUS heavy side and it's heavier, or you know that the fake coin is one from the PRESENT lighter side from the PREVIOUS lighter side and it's lighter. Now from the PRESENT heavy side, weigh one from the PREVIOUS heavy side with the other from the PREVIOUS heavy side. If they weigh the same, then the fake coin is the one from the PREVIOUS lighter side and it's lighter. Otherwise the heavier one from the PREVIOUS heavier side is the fake coin and it's heavier.
`
`
B. If they don't balance, then the fake coin is either one of the ones on the PRESENT heavy side from the PREVIOUS heavy side and it's heavier, or you know that the fake coin is one from the PRESENT lighter side from the PREVIOUS lighter side and it's lighter. Now from the PRESENT heavy side, weigh one from the PREVIOUS heavy side with the other from the PREVIOUS heavy side. If they weigh the same, then the fake coin is the one from the PREVIOUS lighter side and it's lighter. Otherwise the heavier one from the PREVIOUS heavier side is the fake coin and it's heavier.
`
Similar questions