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Topic: Imp Riddle (Read 2300 times) |
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Ela
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Imp Riddle
« on: Jul 18th, 2012, 11:10pm » |
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In a town of imps there are 1,000 residents.
At dusk, the first resident has turned the switch 'ON'
to 1,000 lamps, right after him came the second imp,
and turned off every second light. right after him the third imp
started to turn off every light that was on
and turning 'on' every light that was 'off' just if
it was a lump number that is divided by 3.
and so on for the forth.... fifth..... untill the last resident.
Q: After the last resident in imp Town , finish his duties, how many lamps stayed lighten ?
explain your answer.
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rmsgrey
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Re: Imp Riddle
« Reply #1 on: Jul 19th, 2012, 5:35am » |
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There's a version of this somewhere around here already - with a mad gaoler and 100 prison cells.
The answer is:
| hidden: | | The lamps whose number has an odd number of factors will be lit, ie those with numbers that are perfect squares |
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Ela
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Re: Imp Riddle
« Reply #2 on: Jul 19th, 2012, 6:17am » |
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that's close. but not the answer
i need an exact answer with a reason. 
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rmsgrey
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Re: Imp Riddle
« Reply #3 on: Jul 20th, 2012, 4:11am » |
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Okay: 31
Reason: because I said so!
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towr
wu::riddles Moderator
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Re: Imp Riddle
« Reply #4 on: Jul 20th, 2012, 8:46am » |
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I liked the first reason better 
Another reason:
Python Code:a = [];
for i in range(1000):
a.append(0);
for i in range (1, 1001):
for j in range (1, 1001):
if j % i == 0:
a[j-1] = 1 - a[j-1];
sum(a) |
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Which gives the same answer.
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| « Last Edit: Jul 20th, 2012, 8:47am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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0.999...
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Re: Imp Riddle
« Reply #5 on: Jul 20th, 2012, 7:22pm » |
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I got a different answer when I tried it on my string of 1000 "Christmas" lights.
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towr
wu::riddles Moderator
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Re: Imp Riddle
« Reply #6 on: Jul 21st, 2012, 1:52am » |
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Really? On the third round, how did you turn on the sixth light?
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0.999...
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Re: Imp Riddle
« Reply #7 on: Jul 21st, 2012, 5:35am » |
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By "it" I mean the version of the riddle that follows from me misreading the text.
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Ela
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Re: Imp Riddle
« Reply #8 on: Jul 22nd, 2012, 1:00am » |
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Thanks! 
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