Steven W. answered • 08/23/16
Tutor
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Hi Bonnie!
If you can put as many of the coins as you want on either side of the balance, you could determine the light coin in 3 weighings.
Start by splitting the coins four-and-four on either side, and see which side is lighter.
Does this give you an idea of how to narrow down to the light coin?
Just let me know if you would like to talk about it further, or if you have any other questions. I hope this gave you some ideas!
Steven W.
tutor
Okay. I cheated and went to the internet. :D It turns out that, if you know the odd one out is lighter, you can determine which one is lighter among three objects in one weighing. Just weigh two. If one of them is lighter, that is the one, and if they weigh the same, the unweighed coin is the lighter one.
So, to find the light one most efficiently, we break up our coins into three groups. So, for eight coins, that would be two stacks of three and a stack of two. Weigh the two stacks of three. If one of them is lighter, you take that one, and in one more step (as described above), you can determine the light coin.
If the two stacks of three are both equal, then the stack of two has the light one, and you just weigh one against the other.
Either way, you get two weighings Because these groupings of three are important, it turns out that the number of weighings is based on which power of 3 is the next one above your number of coins. If you have 3 or less, (where 31 is the next power above), it takes 1 weighing. If your number of objects is greater than three but less than or equal to 9 (32), it takes 2 weighings, and so on.
I'm never as clever as I like to think I am. :)
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08/25/16
Bonnie N.
08/25/16