The Counterfeit Coin Problem (version 1&2)?
3 versions to counterfeit coin problems. I need an explanation to no.1&2. I can’t seem to understand my research.
Version 1:
You are given 8 coins, one of them is fake coin, which is lighter than the others. By using only the balance weighing scale at most twice, explain the steps to identify the fake coin.
Version 2:
Something similar to Version 1 but it’s 9 coins instead of 8. One of them is fake, and it is heavier than the others. And again, by using only the balance weighing scale at most twice, explain the steps to identify the fake coin.
Hope that someone can explain these to me. Thanks.
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OK, version 1: You put 3 coins on each side of a balance, leaving the other 2 aside. If they balance, you know that it’s one of the other 2, so you’d put the other 2 into the balance, and the lighter one is counterfeit. If they don’t balance, you take the lighter group of 3, putting 1 into each side of the scale-if they balance, you know it’s the third; if they don’t balance, you know the lighter one is counterfeit.
Version 2: Same thing, except you leave 3 aside, and if the 3 you put on there balance, you put 2 of the 3 left aside on your scales-if they balance, you know it’s the 3rd one left over.
You might get 8 objects, you don’t need a scale, but put them in little piles to run through all the above, so you can better visualize all this.
For version 1, I think the only way to do it would be to take the 8 coins and split them into 2 grouns of 4. Weight each group against each other, and see which is heavier. The heavier group are the real coins, so get rid of them. Of the 4 remaining coins, split then into groups of 2. The heavier 2 are dis-carded as well. That leaves you 2 coins. I’m not sure what can be done at this point, except maybe the weight is significant enough to determine by hand? If you could weight it a 3rd time, you would know for sure. At least this answer brings you down to 2 out of 8.
For 9 coins, seperate them into piles of 4,4,&1. Weight the 4 against each other (If they are the same, then the leftover coin is the counterfeit.) Follow the same procedure as above.
I’m guessing the actual solution has something to do with numbering the coins 1-8 or 1-9 and then weighing them twice in some fashion to dicover the fake.
Good luck!