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**golchhamohit****Member**- Registered: 2013-06-05
- Posts: 10

Hi,

I came up with an interesting puzzle to solve.here it is.

Can you find four numbers such that sum of every two ans sum of every four may be perfect squares.??

Inspite of knowing the answers,I am not able to get how??

Help me out.

Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

Are there any more restrictions on the numbers?

Must the four numbers be all different? Must they be integers. Positive? Can any be 0 if they are not all positive? Are they less than some constant?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**golchhamohit****Member**- Registered: 2013-06-05
- Posts: 10

Hi bobbym,

Apologies for not making question clear.And the constraints are,

1. 4 numbers are distinct.

2. All 4 nos are strictly positive.(so not 0)

3. There are many solutions to this problem,but goal is to find smallest set of 4 such numbers.

I could not understand your last question..less than some constant..can you please elaborate?

Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Are the numbers less than say 10?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**golchhamohit****Member**- Registered: 2013-06-05
- Posts: 10

Hi bobbym,

The numbers are not less than 10 infact not even less than 100.

One more clue.there is only one number below 1000 of the four.

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How large is the solution? Hopefully each of the numbers are at least within 9999.

I want to bruteforce it

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**golchhamohit****Member**- Registered: 2013-06-05
- Posts: 10

Hi Agnishom,

3 numbers are within 9999 and one above that. how will u bruteforce easily without programs. I need to know that logic.

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I don't think there is a straightforward 'logic' to that.

Even if I do not bruteforce, I will have to use a computer.

bobbym could enlighten more

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

You are going to get an undetermined set of equations that will be very difficult to solve. Looks like a computer is the best way but the only logic will be the program itself.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**golchhamohit****Member**- Registered: 2013-06-05
- Posts: 10

And I dont get any other logic other than naive solution which is brute force as mentioned by Agnishom.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

You want every pair of numbers to be a square also. Am I getting that right?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**golchhamohit****Member**- Registered: 2013-06-05
- Posts: 10

yes..absolutely right.

The four numbers are 386,2114,3970,10430.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Okay, thanks for that solution there.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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So, how about programming it? Could you give me an idea?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Four loops of course is the most simplistic idea. Remember how to pseudocode?

I am trying to be just a bit cleverer than that. Not too much cleverer, I might hurt myself.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Four nested loops?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Yes, for each variable. Use the constraints he gave above.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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But whats going to be the upperbound of the loops. Are you asking me to cycle through the values?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi Agnishom;

3 numbers are within 9999

The numbers are not less than 10 infact not even less than 100.

One more clue.there is only one number below 1000 of the four.

3 numbers are less than 10000 and one number is less than 1000. Also the numbers are distinct.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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