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Message |
    
Tammynx
Moderator/Spanking Aficionado
Username: Tammynx
Post Number: 2224
Registered: 10-2005
| | Posted on Monday, July 02, 2007 - 03:32 pm: | 
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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?
Who can answer this WITHOUT cheating?? |
Fanny
Moderator/Spanking Aficionado
Username: Fanny
Post Number: 3287
Registered: 05-2005
| | Posted on Monday, July 02, 2007 - 07:30 pm: |
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Okay I know there has to be a mathematical equation for this, but hell if I know what it is.
I went for the frustrating long way of drawing this out on paper and was left with 10 open lockers.
Darn it, Tammy, I just spent an hour working on this. I hate when I get frustrated not being able to answer a riddle. I am the same way with magic tricks, if I can't figure them out, I get very frustrated.
Queen of Innocence
"Well behaved woman rarely make history"
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Petergrimm
New member
Username: Petergrimm
Post Number: 38
Registered: 05-2007
| | Posted on Monday, July 02, 2007 - 09:22 pm: |
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Fanny is correct there are ten lockers open, 1,4,9,16,25,36,49,64,81,and 100.
Basically find all factors of any number between 1 and 100 (including 1 and the number) Starting from CLOSED, the locker will toggle once for every factor as that number is reached. Since only perfect squares have an odd number of factors, only those will end up open.
Example 35 has factors 1,5,7,35 and ends up closed, while 36 has factors 1,2,3,4,6,9,12,18,36 and ends up open - see the six has no partner like the 3 and 12 are partners - so there are an odd number of factors hence it toggles open. This happens only for perfect squares.
OK Tammy, did Fanny "cheat" or did I? Her way is just as valid, though I am surprised she did not make any mistakes! |
Fanny
Moderator/Spanking Aficionado
Username: Fanny
Post Number: 3289
Registered: 05-2005
| | Posted on Tuesday, July 03, 2007 - 12:46 am: |
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Surprised, Peter? You would be amazed how many surprises I have up my sleeve! 
Based on the assumption that I did not cheat, then I guess you would be the one. 
Queen of Innocence
"Well behaved woman rarely make history"
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Tammynx
Moderator/Spanking Aficionado
Username: Tammynx
Post Number: 2227
Registered: 10-2005
| | Posted on Tuesday, July 03, 2007 - 10:54 am: |
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Well Perter is is MY riddle....I'll tell Fanny when she is correct....thank you very much! 
: 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:
closed-open-closed-open-closed-open-closed-open-closed
0 1 2 4 5 8 10 20 40
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):
closed-open-closed-open
0 1 5 25
Fanny you are one smart Lady!! |
Tammynx
Moderator/Spanking Aficionado
Username: Tammynx
Post Number: 2228
Registered: 10-2005
| | Posted on Tuesday, July 03, 2007 - 10:55 am: |
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Ohh I guess Fanny is right.... Peter you must have cheated!!
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