Gold and Nickel

You have 15 identical coins – 2 of them made of pure gold and the other 13 made of nickel (covered with thin gold layer to mislead you). You also have a gold detector, with which you can detect if in any group of coins, there is at least one gold coin or not. How can you find the pure gold coins with only 7 uses of the detector?

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hyltonic
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hyltonic

Solved. 1. As previously commented, separate coins into groups of 3. Scan to narrow down your coins to 6, being sure not to mix up each group of coins. Rearrange each group of 3 into two columns and three rows as you can see columns (1 & 2) and rows (A, B & C), G is Gold, N is Not Gold: 1 2 A: G N B: N G C: N N 2. Now, scan each ROW. Sort out the row that doesn’t have gold: 1 2 A: G N B: N G 3. Then, in either row, swap the… Read more »

Puzzled
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Puzzled
Puzzled
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Puzzled

This solution doesn’t appear to be guaranteed, at least as far as I can see. What if you arrange the six, and both gold coins are in column A. Then you scan 2x, eliminating Col B. But the switch and last scan will only leave you with one gold coin. It appears to me to take 8 scans to guarantee the 2 gold coins.
Or am I wrong?

Harry
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Harry

You cannot find the gold coins with 100% accuracy with this method. You can use logical deduction to reduce the amount of scans you are doing (like the first step, there is no need to scan the last pile of 3 in any case whatsoever) but then your method gets rather case specific and would not work for all the arrangements. I do not have the answer to this either, I just don’t believe this is solved yet.

Allen
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Allen

I’ve ALMOST got it. If you divide them into five groups of 3, you only have to scan four of those groups maximum to narrow it down to 6 coins. If none of the four groups has any gold coins, then you can easily solve which two of the remaining three coins are gold with 2 more scans. If two of the four have gold coins, scan 2 out of 3 from each group. If neither have gold, you’ve found your coins, and if only one has gold, you’ll find your last coin with one more scan. If both have… Read more »

Puzzled
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Puzzled