Skip to main content
LogoNumerus System
Back to Logic Problems

100 Doors Problem

Mediumlogic

This Medium puzzle in the “logic” category rewards careful reading and step-by-step reasoning. Use the hint if you are stuck, then compare your approach with the explained answer.

There are 100 closed doors in a hallway.

You make 100 passes:

  • On pass 1, you toggle every door
  • On pass 2, you toggle every 2nd door
  • On pass 3, you toggle every 3rd door
  • And so on, until pass 100, when you toggle only door 100

A toggle means:

  • If the door is closed, it becomes open
  • If it is open, it becomes closed

Which doors are open at the end?

Preparing…