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namrata
April 6th, 2003, 04:49 PM
get set gooooooooooooooo.......

there are 1000 doors( all numbered from 1 to 1000). there are 1000 servants(also numbered)
servant 1 is standing before door no.1, servant 2 before door 2 and so on....
Servant 1 is ordered to open all the doors which are multiple of his own number( i.e he will open all the doors from 1 to 1000) now servant 2 is ordered to just do opposite(i.e if open then close it and if closed then open) to the doors of his multiples(i.e. he will close the doors numbered 2, 4, 6.....). then servant 3 will also do the opposite to the doors of his multiples(3,6,9...). Puzzled???
Question is: when all the 1000 servants will execute their duty how many doors will be open and how many will be closed?
have a good day!!!

smalik
April 6th, 2003, 08:53 PM
[whatever the answer will be, But take it sure
you ll find 1000 times read your topic( mentioned under your post) n very few replies!!
good question, working out

navingulia
April 6th, 2003, 11:13 PM
500 open 500 closed

birbal
April 7th, 2003, 12:34 AM
Lot of people get distracted by the number 1000 here. To solve such problems, one has to assume there are N servants and N doors. As N increases from 1 to infinity, see what happens.

It is a very simple series, and you see only a few doors remain open in the end. I will leave the series formulation to you, but you are looking at a series 3, 8, 15, 24, 35, .... The 31 st term is 981 and 32nd term is 1044.

Birbal Singh

akdalal
April 7th, 2003, 10:15 AM
The answer is simple, which is

p-(n-1)

where p = no of doors
n = no of servants

1000-(1000-1)
1000-999
1

Cheers!!!

shekhar_nehra
April 9th, 2003, 11:47 PM
Namrata ji ,
The answer is 31 doors are open and 969 closed.

yvsgaawar
April 10th, 2003, 02:51 AM
Shekhar Nehra (Apr 09, 2003 02:17 p.m.):
Namrata ji ,
The answer is 31 doors are open and 969 closed.



Mine is matching with Sekhar Nehra's 31/969.

satyeshwar
April 10th, 2003, 11:19 AM
Mera answer bhi 31/969 hi aaya hai. And I wrote a program to solve this.

namrata
April 10th, 2003, 03:02 PM
May be the answer 31/969 is correct as i myself dont know the correct answer a freind of mine asked me and even she did not knowthe correct ansewr so i thought of asking all u people

rsdalal
April 10th, 2003, 05:51 PM
Door # 1 is Opened
Door # 4 is Opened
Door # 9 is Opened
Door # 16 is Opened
Door # 25 is Opened
Door # 36 is Opened
Door # 49 is Opened
Door # 64 is Opened
Door # 81 is Opened
Door # 100 is Opened
Door # 121 is Opened
Door # 144 is Opened
Door # 169 is Opened
Door # 196 is Opened
Door # 225 is Opened
Door # 256 is Opened
Door # 289 is Opened
Door # 324 is Opened
Door # 361 is Opened
Door # 400 is Opened
Door # 441 is Opened
Door # 484 is Opened
Door # 529 is Opened
Door # 576 is Opened
Door # 625 is Opened
Door # 676 is Opened
Door # 729 is Opened
Door # 784 is Opened
Door # 841 is Opened
Door # 900 is Opened
Door # 961 is Opened
closed =969 Opned = 31

Narmata ji may be you should have put a condition that no program etc to use.

rsdalal
April 10th, 2003, 05:56 PM
Pattern is perfect squares
1*1 = 1
2*2 = 4
3*3 = 9
4*4 = 16
and so on

sonal
April 10th, 2003, 06:14 PM
[

navingulia
April 10th, 2003, 10:58 PM
waah bhai, kyaa baat hai. ib tai meri bhi samajh mai aa gayaa. jiske even number of factors hain wo waise ka waisa aur jiske odd number of factor sai wo ulta hoga.

shekhar_nehra
April 10th, 2003, 11:47 PM
Namrata ji,
31/969 answer is correct.
Ranvir ji has provided an excellent and simple solution to the problem.With verification by Satyeshwar bahi's program .
Now I hope you can explain it to your friend as well.

Cheers!

namrata
April 11th, 2003, 12:51 AM
Thankyou everyone for the answer .
But please dont call me ji from next time .