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This puzzle is a variant of the Doctor's Dilemma.

There are two patients in a hospital (let's call them A and B), both of them need an operation by two different doctors (let's call them X and Y) -- so four different operations in total. However, just before the first operation, it is discovered that the hospital has only two surgeon gloves. Only one glove is needed for each operation.

Just like in the original puzzle, any of the surgeons may be infected with a rare flu, and the two patients may be affected as well. The virus that causes the flu transfers readily from flesh to flesh, or from flesh to any object which in turn can contaminate any flesh or object it touches. People avoid touching one another, or touching objects that may be contaminated. In particular, one can catch the flu:

  • if they wear a glove that has been previously used by another person.
  • if they are touched by (the exterior of) a glove that has been previously used to operate another person.
  • if they take a glove that has been previously used to operate another person, turn it inside-out and then wear it.

How can all the four operations can be performed using only two gloves and without the risk of anyone catching the flu from one another? For the sake of simplicity ignore the risk of contamination while preparing the gloves (put them on hands of doctors and turn them inside-out).

Just like the original puzzle, a vulgar version of this puzzle exists, involving rot13(pbaqbzf naq univat crargengvir frk).

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    $\begingroup$ as an aside, doing the intended solution with the "vulgar" version as it is specifically not advised to do that as it may have the opposite effect. $\endgroup$
    – htmlcoderexe
    Commented May 19, 2021 at 13:13
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    $\begingroup$ @htmlcoderexe I knew, but thank you for specifying that $\endgroup$
    – melfnt
    Commented May 19, 2021 at 13:28
  • $\begingroup$ "Just like in the original puzzle, any of the surgeons may be infected with a rare flu," Beginning a paragraph like that is confusing. Do I need to read the "original puzzle" before I can understand the problem statement in this one? Or is the problem statement self-contained? You already linked the Doctor's Dilemma at the beginning, so there is no need to repeat the reference if it can be avoided. $\endgroup$
    – Stef
    Commented Jan 14, 2022 at 13:00
  • $\begingroup$ @Stef the problem statement is self-contained. I repeated the reference to the original puzzle so that the ones that already knowi the original version can speed up their reading. $\endgroup$
    – melfnt
    Commented Jan 15, 2022 at 22:58

1 Answer 1

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Doctor X wears both gloves over each other and operates on patient A. Then, doctor X removes the outer glove and operates on patient B.

Doctor Y puts on the "outer" glove that doctor X removed after his first patient and operates on patient A. He then takes the second glove that doctor X used to operate on patient B and puts it over the glove he used to operate patient A, and operates patient B.

Turning any glove inside out after operating once makes this puzzle impossible.

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    $\begingroup$ How do they put on or take off gloves without touching them? $\endgroup$
    – Ian MacDonald
    Commented Apr 29, 2021 at 14:12
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    $\begingroup$ From the question: "For the sake of simplicity ignore the risk of contamination while preparing the gloves (put them on hands of doctors and turn them inside-out)". Otherwise I think it is impossible $\endgroup$
    – melfnt
    Commented Apr 29, 2021 at 17:53

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