Hilbert's Dormitories

Calculus Level 1

In Hilbert's Dormitories, there are an infinite number of rooms labelled numerically: 1, 2, 3, .... The current accommodation is rather strange:

  • Every room labelled with a perfect square (like rooms 1, 4, 9, 16, ...) has 2 occupants: a boy and a girl.
  • Every other room has just one occupant: a boy.

Hilbert, the superintendent, doesn't like this setting and wants every room to have exactly 2 occupants: a girl and a boy. Can he possibly do this, given an infinite amount of time?

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