100 doors
1,443.8K Views
There are 100 doors, all closed. In a nearby cage are 100 monkeys. The first monkey is let out, and runs along the doors opening every one. The second monkey is then let out, and runs along the doors closing the 2nd, 4th, 6th,… all the even-numbered doors. The third monkey is let out. He attends only to 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 monkeys have done their work in this way, what state are the doors in after the last pass, which doors are left open and which are closed ?
The doors that are left open are a the numbers that have a perfect square root : 4,9,16,25,36,49,64,81,100
Because they have odd number of dividers, and that means that the last monkey that can get to the door will open it.
Your Answer
More puzzles to try-
What is the logic behind these ?
3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »Defective stack of coins puzzle
There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »Which clock works best?
Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »(Advanced) Cheryl’s Birthday Puzzle
Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »Five greedy pirates and gold coin distribution Puzzle
Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »Magical flowers!!
A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »Tuesday, Thursday what are other two days staring with T?
Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »How could only 3 apples left
Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »How Many Eggs ?
A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »HARD MATHS – How much faster is one train from other Puzzle
Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »Most Analytical GOOGLE INTERVIEW Question Revealed
Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »Lateral thinking sequence Puzzle
Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »How did he know?
A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »Pizza Cost Math Brain Teaser
Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »Which letter replaces the question mark
Which letter replaces the question markRead More »Which room is safest puzzle
A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »Richie’s Number System
Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »Srabon wanted to pass
The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »Become Normal!!
Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »Sakib Knows The Number!
Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »
Accenture Interview PuzzlesAdobe Interview PuzzlesAge RiddleAkbar Birbal PuzzlesAlgorithm PuzzlesAlphabet riddleAmazon Interview PuzzlesAnalytical MathematicsAptitude PuzzleBank PuzzlesBetting PuzzlesBrain TeasersCalendar PuzzlesCards PuzzlesChess Board PuzzleChess PuzzlesChristmas Puzzlecipher PuzzleCivil Services PuzzleClock time puzzleCognizant Interview PuzzlesCoins PuzzleComputational PuzzleconundrumCoronavirus PuzzleCoupondunia Interview PuzzleCritical Thinking Puzzledata analyticsData Structure Interview QuestionsDecode PuzzleDetective PuzzlesDice PuzzleDictionary Riddlesdifficult riddleEasy Math puzzlesEasy puzzlesEinstein puzzleEnglish RiddleFamily Tree Puzzlefamous puzzleFill in the blanks riddlesFinding Killer RiddlesFlipkart interview puzzlesFunny RiddlesGeneral KnowledgeGeographical PuzzleGoogle Code Jam 2014Google Interview PuzzlesGRE PuzzleHard Puzzle
