← Your path
The hundred-door corridor
Your goal
List every door left open after pass 100 and find a rule explaining the result.
▤ Your first notebook · Statement, rules and controls
The challenge
A corridor has one hundred closed doors, numbered 1 to 100. You walk through it one hundred times. On each pass you toggle certain doors: closed doors open, and open doors close.
- On pass 1, toggle every door. On pass 2, toggle doors 2, 4, 6… On pass 3, doors 3, 6, 9…
- Continue through pass 100: each pass toggles the multiples of its number.
How to play
Enter the open door numbers separated by commas and press “Check the list”. You can write your reasoning and explore the first ten passes. We check the list; you compare your own argument with the solution.
Hints are optional. Reading an explanation does not complete the level: test your strategy on the board.
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