Problem 2: A square medieval castle on a square island is under siege. All around the castle there is a square moat 10 meters wide. Unfortunately, a group of  raiders have brought footbridges that are only 9.5 meters long. The invaders do not want to fail in their assault.  How can they use their footbridges to invade the castle?

Solution:

Puzzles : That crooked your mind.

Problem 1: You have 100 doors in a row that are all initially closed. you make 100 passes by the doors starting with the first door every time. the first time through you visit every door and toggle the door (if the door is closed, you open it, if its open, you close it). the second time you only visit every 2nd door (door #2, #4, #6). the third time, every 3rd door (door #3, #6, #9), etc, until you only visit the 100th door.

for example, after the first pass every door is open. on the second pass you only visit the even doors (2,4,6,8...) so now the even doors are closed and the odd ones are opened. the third time through you will close door 3 (opened from the first pass), open door 6 (closed from the second pass), etc..

question: what state are the doors in after the last pass? which are open which are closed?

Solution: