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30 votes
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Find the heaviest and the second heaviest coins

fljx's user avatar
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19 votes
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Determine whether the counterfeit coin is heavier or lighter in two weighings on a standard balance

NoeS's user avatar
  • 279
17 votes
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Minimum number of turns

Oo, I've got this one; these come up a lot while organising board game tournaments. a) what is the minimum number of turns needed to determine the heaviest box? b) what is the min number of turns ...
Bass's user avatar
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13 votes

Determine whether the counterfeit coin is heavier or lighter in two weighings on a standard balance

Goldstein's user avatar
  • 291
8 votes

Seven genuine and two fake coins

Here is a method. Let's name the coins ABC DEF GHI.
Florian F's user avatar
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7 votes
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Minimum K for detecting fake pearls in one weighing

As others have shown, it suffices to find a $10$-set whose $2^{10}$ subsets have distinct sums, and we want to minimize the maximum element of this $10$-set. An upper bound from https://oeis.org/...
RobPratt's user avatar
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5 votes

Determine whether the counterfeit coin is heavier or lighter in two weighings on a standard balance

Here's a complete set of solutions for arbitrarily many coins to a more restrictive version of the problem, where the second weighing is not allowed to depend on the result of the first. This gives ...
benrg's user avatar
  • 151
5 votes
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How many solutions to the twelve coins problem are there?

I have an answer to the non-adaptive version of the problem, that is, the version where one must declare ahead of time all three weighings one will perform, and their algorithm is not allowed to ...
Feryll's user avatar
  • 2,389
5 votes

Minimum K for detecting fake pearls in one weighing

Instead of $K=512$, I suppose that already is enough (and perhaps the best possible choice). I make use of a special property of the set With positive integers $a$ and $b$ specified below, set If $...
Hagen von Eitzen's user avatar
5 votes
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Designing a four-pan scale

Here is my solution. I do not know if this is optimal or not. Here is the method. Proof of Lemma:
Mike Earnest's user avatar
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4 votes
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14 coins problem but you can't understand the scale

If each coin is given by a different lower-case letter, you could use these tests: More coins can't be done because: Comments:
tehtmi's user avatar
  • 3,326
3 votes

Minimum K for detecting fake pearls in one weighing

To add to what @HaganvonEitzen said in their answer, I have found a slightly smaller set that is solved in the same way. I have no clue if this is the minimum however.
not_not_Alex's user avatar
3 votes

Minimum K for detecting fake pearls in one weighing

I think you need at least pearls per box. You grab and put these all together on the scale to get some weight x. You have a total of pearls and now compute
quarague's user avatar
  • 1,863
3 votes
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Centridipity problem

In the frame of the car, there are two forces: gravity pointing down, and centrifugal pointing to the right. In effect, we can analyze physics in the frame of the car by pretending like there is an ...
DanDan面's user avatar
  • 1,044
3 votes

Finding the median mass: is there a general solution for 2n + 1 objects?

Short answer to the question in the title: No. A bit longer answer: We, as the humanity, don't know if an optimal general method exists, and certainly not what it might be. Even longer answer still: ...
Bass's user avatar
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2 votes

12 coins problem but you can't understand the scale

ralphmerridew's user avatar
1 vote

Find the heaviest and the second heaviest coins

Assuming you can fit more than 1 coin on each side: Split the 32 in two groups (of 16) and determine heaviest side Take heaviest side, split in two groups (8) and determine heaviest side Repeat (4), ...
user88468's user avatar
1 vote

Minimum K for detecting fake pearls in one weighing

An easily found decent? upper bound
Retudin's user avatar
  • 9,238

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