Here is this week’s thinking challenge. This puzzle is from the book BrainMatics Logic Puzzles by Ivan Moscovich. Enjoy!
Ten hotel doors are numbered from 1 to 10; all are closed. The cleaning lady walks by and opens every door. Then a second cleaning lady walks by and closes all the even-numbered doors. Then the repairman walks by and changes the state of every door whose number is a multiple of three. Then another person changes the state of every door whose number is a multiple of four, and so on, until ten people have walked by.
Which doors will be open after the tenth person has walked by? Can you also guess as to which doors would be open at the end if there were 100 doors involved in the same procedure?
I will not be posting answers to the games and puzzles on my site. Email me if you think you have the answer. I really enjoy hearing from everyone who takes on these challenges!
Do you know of a great game or puzzle that you would be willing to share? Email me your suggestion and if I use it on my blog I will credit you for the submission. Thanks in advance for sending me your suggestions!
Puzzle Difficulty Rating: [ratings]