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How does one create a good problem?

'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'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Please define good.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Problem that I would be interested to solve

'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'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Then only you know what a good problem is...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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How do I make problems that the community wants to solve?

'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'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

I do not think you will have much problems with that.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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I kind of need to.

How do I create problems like the ones you post in exercises?

*Last edited by Agnishom (2016-07-07 02:39:04)*

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Did you notice that when I used to post a problem people tried to solve them. Why do you think that happened?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Because people enjoyed solving problems?

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Nope, because it was me asking them. My reputation.

You are well respected over there. If you ask people will respond.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Let me try asking the question from a different viewpoint

The problems you post in exercises are pretty good. How do you find inspiration to frame those problems?

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Kaboobly doo!

They are only interesting because I posed them.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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I think you have it the other way round. You mean

I posed them only because they are interesting.

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Hmmm, if you pose a problem it will be well received both here and there. That is because of your reputation and post counts.

But we can discuss some possible ways to make a problem interesting.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Could we please initiate that discussion?

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

I can only give my opinion, it has worked but you may come up with something far better.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Okay, but why not hear your opinion?

If I have seen further it is only by standing on the shoulders of giants

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

My intellectual shoulders are pretty narrow so I do not suggest standing on them.

Want to look a one of my problems and how it is structured?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Yes.

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

http://www.mathisfunforum.com/viewtopic.php?id=21958

That is typical and good.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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I agree. How did you find the inspiration for that problem?

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Hmmm, you look at a piece of math that is EM related. Then, you disguise it with a semi plausible story. Try to phrase it in such a way that the step by step logic problem solvers (math types) will be put inside a box, where they will stay.

The problem will be difficult for them because they use classical math and do not understand or approve of EM.

Make the problem entertaining by creating farcical people or situations. Make your point too. Do not get too carried away and all full of yourself with how you solved the problem...after all, if a human can solve it, it is trivial.

Be patient with the wrong answers and congratulate the right answers. And when someone improves on your way say thanks and really mean it.

Learn to think outside the box ( lateral thinking ) then problems will come to you naturally. Of course, this only demonstrates your own stupidity as you come to realize that there is so much about your favorite field that is unknown to you.

There is a problem in geometry in the other thread that the OP believes is super tough. It falls to EM methods rather easily and they give a piece of lateral thinking a chance and then the problem is trivial!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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I see.

How do I create CS problems specifically?

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

There are only certain intervals of time where your creativity, confidence and imagination will be riding high. During these periods things will happen naturally. To force the creative process is a mistake.

How a starship works...We are alive only because I knew something about these ships that he does not - Capt. James Tiberius Kirk.

Do you daydream alot?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Perhaps

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

I'm not crazy, my mother had me tested.

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