Puzzle Corner #7

Puzzle Corner #7

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There are 100 doors and all closed. There are 100 magicians.

The first magician ways his wand, and opens every door. The second magician ways the wand closing the 2nd, 4th, 6th,…, all the even-numbered doors.

The third magician ways the wand on the 3rd, 6th, 9th,… doors (every third door, in other words), closing any that is open and opening any that is closed, and so on. After all 100 magician have done their work in this way, what state are the doors in after the last pass?

Send your correct answers latest by midnight of 15th March 2023 for lucky draw on 16th March 2023 for selecting the winner