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03-27-2008, 03:24 PM
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#1 (permalink) |
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Forum Sugar Momma!!!
 
Join Date: Oct 2007
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Question for March 27, 2008
Suppose you're in a hallway lined with 100 closed lockers.
You begin by opening every locker. Then you close every second locker. Then you go to every third locker and open it (if it's closed) or close it (if it's open). Let's call this action toggling a locker. Continue toggling every nth locker on pass number n. After 100 passes, where you toggle only locker #100, how many lockers are open? 3,000 credits for the correct answer!!!!! PM me your answer.
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03-27-2008, 04:06 PM
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#2 (permalink) | |
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UK Moderator
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Re: Question for March 27, 2008
Quote:
No I don't know the answer. NELLY
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03-28-2008, 04:51 PM
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#3 (permalink) |
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Forum Sugar Momma!!!
Join Date: Oct 2007
Location: Redlands CA
Bike: 2007 Ninja 250
Posts: 4,209
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Answer for March 27
Answer: 10 lockers are left open:
Lockers #1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Each of these numbers are perfect squares. This problem is based on the factors of the locker number. Each locker is toggled by each factor; for example, locker #40 is toggled on pass number 1, 2, 4, 5, 8, 10, 20, and 40. That's eight toggles: open-closed-open-closed-open-closed-open-closed. The only way a locker could be left open is if it is toggled an odd number of times. The only numbers with an odd number of factors are the perfect squares. Thus, the perfect squares are left open. For example, locker #25 is toggled on pass number 1, 5, and 25 (three toggles): open-closed-open. Zebratounge, reiobard and grommit got the correct answer!!!!
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My Gallery Custom Painted Metal Signs "You gotta listen to the way people talk. You don't say "affirmative," or some sh*t like that. You say "no problemo." And if someone comes on to you with an attitude you say "eat me." And if you want to shine them on it's "hasta la vista, baby." |
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