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[#26] 2 Min. Challenge : Integers

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Praetorian
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[#26] 2 Min. Challenge : Integers [#permalink] New post   19 Mar 2004, 06:02
1. Time yourself
2. Solve as fast as you can
3. Type your solution and mention your time , please
How many positive integers are there whos sum of digits is equal to its
squareroot.

a) 1
b) 2
c) 3
d) 4
e) 5



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Re: [#26] 2 Min. Challenge : Integers [#permalink] New post   Updated on: 19 Mar 2004, 07:01
My GUESS is B) 2
(Changed for 1 to 2)


Is there a mathametical way to solve this problem?

Time: > 2 mins.

Originally posted by kpadma on 19 Mar 2004, 06:11.
Last edited by kpadma on 19 Mar 2004, 07:01, edited 2 times in total.
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Re: [#26] 2 Min. Challenge : Integers [#permalink] New post   19 Mar 2004, 06:11
B) About 2 min.
It's more about a trial an error attempt.
I think there is only 1 and 81 which work
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Re: [#26] 2 Min. Challenge : Integers [#permalink] New post   19 Mar 2004, 07:59
took more than 2 mins.
B.

1 and 81 only.
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Re: [#26] 2 Min. Challenge : Integers [#permalink] New post   19 Mar 2004, 08:58
Hi,

I am not convinced with myself that these are the only 2 solutions of the infinite set of +ve integers.

If anybody finds a way to prove this, please pass it on.

Thanx.


While juggling with this, here is another ques. which got framed.....

How many positive integers are there whose sum of digits is equal to the sum of digits of its squareroot??
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Re: [#26] 2 Min. Challenge : Integers [#permalink] New post   19 Mar 2004, 09:15
Virtual wrote:
Hi,

I am not convinced with myself that these are the only 2 solutions of the infinite set of +ve integers.

If anybody finds a way to prove this, please pass it on.

Thanx.


While juggling with this, here is another ques. which got framed.....

How many positive integers are there whose sum of digits is equal to the sum of digits of its squareroot??


remember , you got to choose from the five choices above. mathematical proofs are good to know , but you got to cautious about that.
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Re: [#26] 2 Min. Challenge : Integers [#permalink] New post   19 Mar 2004, 09:42
Praet, so this means answer is 2? :)
I tried to solve using all square until 16 which I know by heart. I stopped there and realized there were only 2 solutions so far...
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Re: [#26] 2 Min. Challenge : Integers [#permalink] New post   Updated on: 19 Mar 2004, 10:02
Agreed, proof may not be a good option but how do we know that it may not be 3, 4 or 5 ???

What do i do with such a ques. in actual test ???

ps: BTW, I tried some large integers also and tried to get fix it based on max. 2 digit no., 3 digit no....... and so on.

but no success :(

Originally posted by Virtual on 19 Mar 2004, 09:59.
Last edited by Virtual on 19 Mar 2004, 10:02, edited 1 time in total.
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Re: [#26] 2 Min. Challenge : Integers [#permalink] New post   19 Mar 2004, 10:00
Paul wrote:
Praet, so this means answer is 2? :)
I tried to solve using all square until 16 which I know by heart. I stopped there and realized there were only 2 solutions so far...


yes, the answer is 2 numbers. i just made this problem a bit harder by including the option of 4 and 5 numbers.

getting problems correct under the time limit is the key.

good job guyz :)



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Re: [#26] 2 Min. Challenge : Integers [#permalink]
19 Mar 2004, 10:00
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