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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

**Naturalists in the everglades have observed the most amazing thing. A strange species of frog and fly are interacting. The flies travel in groups that are always 2014 in number. One naturalist believes that the flies group number is directly related to man's reckoning of time and next year they will travel in groups of 2015 etc. Anyway, when the flies land they do the most amazing thing. They all land on a circle equidistant from each other on the circumference!**

**The frog is no less amazing. He starts at one fly and eats him. He then counts 17 flies in a clockwise direction and eats that one. Then he counts off another 17 flies in a clockwise direction and eats that one. Round and round he goes with dazzling speed and viciousness consuming fly after fly. Always killing the 17th fly that is clockwise from him on the circle. The frog can only eat 2013 flies before he explodes. Which fly is not eaten?**

**A says) Impossible, many flies will be untouched by that stupid frog.**

**B says) A truly amazing creature that frog, must be from outer space. Oh yes, one fly does remain and he is at position...**

**C says) Hold on B, A is right. I do not think much of these alien frogs. I calculate almost half the frogs are safe because of modulo.**

**D says) Modulo, who is he?**

**E says) Yes, one fly escapes. Do you think he knew he was safe all along?**

**Does one fly escape and which one is he?**

**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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

**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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,532

He eats the 17th one or the 18th?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

This will help explain it:

**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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A floridan frog, it is, hmm?

'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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,532

There is a general solution to this in Knuth's Concrete Math, if I recall.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

You can post it but remember to hide the solution. Yes it is a Floridian frog.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,532

If on the second time around a fly has already been eaten does it count that as a spot it skips ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

It is always the 17th fly clockwise, spaces do not count.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,532

I don't see how I can solve that without writing some program, thanks.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Any solution will do. Just get the right answer is my motto.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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*Last edited by Agnishom (2014-03-23 04:17:54)*

'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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

*Last edited by phrontister (2014-03-23 04:46:50)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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Hi phrontister;

Please try to simulate the frog and get an answer first. A analytical solution can come later...

'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: 86,676

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Agnishom,

All three of my answers are based on a simulation, but there must be some error in logic or coding that I haven't spotted yet.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

*Last edited by phrontister (2014-03-23 11:51:03)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

*Last edited by gAr (2014-03-24 03:05:37)*

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi gAr;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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