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# PS:quick way to solve ?

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PS:quick way to solve ? [#permalink]

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23 Apr 2008, 22:28
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I am looking for quick way to solve this problem , any suggestion ? I started picking different numbers which took me long time .

The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
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Re: PS:quick way to solve ? [#permalink]

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23 Apr 2008, 23:07
75 < 9² so, possible set is { 1² 2² 3² 4² 5² 6² 7² 8² } = {1 4 9 16 25 36 49 64 }
1 + 25 + 49 = 75, the answer is 1, 5, 7
i can't find faster way.
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Re: PS:quick way to solve ? [#permalink]

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24 Apr 2008, 09:32
Since 75 is divisible by 25 I took 5 as my first number and tried solving it...My answer was 1 5 and 7
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Re: PS:quick way to solve ? [#permalink]

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24 Apr 2008, 09:37
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since 8 ^2 is the largest subtract 64 from 75=11 can you get 11 as the sum of two squares No

thus moving on 7^2 =49 75-49=26 can 26 be expressed as sum of two squares yes
5^2+1^2

took close to 15 seconds.
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Senior Manager
Joined: 19 Apr 2008
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Re: PS:quick way to solve ? [#permalink]

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24 Apr 2008, 13:42
prasannar wrote:
since 8 ^2 is the largest subtract 64 from 75=11 can you get 11 as the sum of two squares No

thus moving on 7^2 =49 75-49=26 can 26 be expressed as sum of two squares yes
5^2+1^2

took close to 15 seconds.

That's a neat method ! thanks .

jcsekhar22 , thanks your method is quicky too .
Re: PS:quick way to solve ?   [#permalink] 24 Apr 2008, 13:42
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# PS:quick way to solve ?

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