How can two doctors operate two patients with only two pairs of latex gloves?!

A picture of a doctor wearing latex gloves.
Photo by Jafar Ahmed on Unsplash.

Problem statement

Alice and Bob are a bit sick, and they need to undergo surgery. Both of them need something done to their stomach and their heart.

Unfortunately, the hospital is severely underfunded and only has two pairs of latex gloves at their disposal.

How can Charles and Diana (respectively the stomach and heart surgeons) operate, knowing that

  • the gloves that touch one doctor's skin cannot touch the other doctor's skin; and
  • the gloves that touch one patient's blood cannot touch the other patient's blood?

Sadly, washing the gloves is out of the question, because the hospital has no means of properly sanitising the gloves!

Give it some thought!

If you need any clarification whatsoever, feel free to ask in the comment section below.

My uncle told me this puzzle a long time ago! I had a blast solving it!

Solvers

Congratulations to the ones that solved this problem correctly and, in particular, to the ones who sent me their correct solutions:

  • Pedro G., Portugal;
  • Francisco M., Mexico;
  • I+T, USA;
  • David H., Taiwan;
  • Chukwudi, Nigeria/UK;
  • Oliver S., Germany;
  • Matthias W., Germany;

Join the list of solvers by emailing me your solution!

Solution

The solution for this is as follows:

Let the gloves be numbered 1 and 2.

  • Charles wears both gloves, 2 on top of 1, to operate Alice.
  • Charles removes gloves 2 and uses gloves 1 to operate Bob.

At this point, gloves 1 touched Charles' skin and Bob's blood, while gloves 2 only touched Alice's blood but no one's skin.

  • Diana puts gloves 2 on, and operates Alice;
  • Diana puts gloves 1 on top of 2, and operates Bob.

There you have it! This is the way to go. Not very hygienic, but works from the logic point of view, doesn't it?

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