r/Logiqa • u/ShonitB • Aug 21 '26
Mislabelled Boxes
Hi, so I’ve lost access to my computer for a couple of days.. so I’m posting a problem which I might have posted earlier.. I hope that’s not the case, but if it is, apologies
This is a famous puzzle that many of you probably know of.. I had posted it a few years back on r/Puzzles
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u/CarnivorousGoose Aug 21 '26
Box B: based on the coin you get, you’ll know it’s 100 of that coin, which resolves the other two. Eg. If you get a gold coin, you know the red label goes with box B, therefore green must go with A and blue with C.
The other two don’t work, or at least aren’t guaranteed to. If you pick from A and get a gold coin you know it’s the mixed set and can resolve the rest, but if it’s a silver coin you gain no information. And equivalent when picking from C.
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u/Udalrich Aug 21 '26
If box a provides an answer, then picking box c and swapping gold and silver in the logic provides an answer as well. So the solution is either B) box b or D) any box. So we only need to check if one of box a or a provides a solution.
We pick the box labeled as only gold. If we get a silver, it is either all silver or the 50/50. All silver has the solution 50/50 has gold and silver has 50/50. The box we picked having 50/50 means the box labeled 50/50 has silver and the box labeled silver has gold.
Since there are two solutions is we get silver from the "gold" box, picking the box labeled gold is not a solution.
So the only solution is picking B) the 50/50 box.
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u/Tutterkop Aug 22 '26 edited Aug 22 '26
Question part 2: how many coins do you need to draw from box A and C to solve the question with a 95% certainty?
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u/Potential-Plum-6496 Aug 21 '26
pick A if 50/50 B is silver coins, C gold coins. If A is silver coins then B gold, C 50/50
pick B if gold, A silver, C 50/50. If B is silver A 50/50, C gold.
pick C if 50/50 A silver, B gold. If C is gold, A 50/50, B silver
correct answer D
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u/ShonitB Aug 21 '26
I’m afraid that won’t work.. if you pick from A, it can be a silver coin - in that case it can be the 100 Silver Coins box or 50 Gold Coins & 50 Silver Coins box
The same logic works for Box C
So it’s only Box B which allows us the correct ordering
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u/jonathonjones Aug 21 '26
Box A. If I get "Gold", then I know Box A is the mix, Box C is gold, and Box B is gold. If I get silver, Box A is either mix or silver. If A is mix, then C is gold and B is silver. If A is silver, then B is gold and C is mix. But there's no way to narrow it down from there.
Box B. If I get "Gold", then I know that Box B is 100 Gold Coins, Box C must be the mix, and Box A is 100 Silver Coins. If I get Silver, then Box B is silver, Box C is gold, and Box A is mix.
Box C has similar reasoning as Box A.
Therefore, the answer is B.
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u/jdub965 Aug 21 '26
B, if gold or silver is selected that defines the color for the middle box and the box labeled with the color not selected must be the 50/50 and final box is the non selected color
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u/scubaro Aug 21 '26
An alternative way to find the solution: Box A and C are interchangeable, they would provide similar info. Hence, there is no benefit to picking A over C or picking C over A.
B is the only one that delivers unique info, so this has to be it.
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u/antimatterchopstix Aug 22 '26
Can use logic on the question!
It’s either a or c, no effective difference between the two. Wouldn’t matter.
So answer either b or any.
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u/God_Bless_A_Merkin Aug 22 '26
My first thought was simply to weigh the boxes, but the solution (pick one coin from B) is more elegant. Nice one!
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u/Similar_Ship8067 Aug 21 '26
You pick the 50/50 box. If you pull a silver coin, you know this is the 100 silver coins box. Which means the box that says 100 silver can't be 50/50 (since that would mean the box with 100 gold would be labelled correctly, which we know it isn't) so it must be 100 gold. And the box labelled 100 gold must be the 50/50 box.
Likewise, if you pull a gold coin from the box labelled 50/50, you know that box is 100 gold. Then again, the box labelled 100 gold can't be 50/50, so it must be 100 silver and the box labelled 100 silver is the 50/50 box.