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## #1 2014-03-21 19:48:38

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### The counting frog.

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.
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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## #2 2014-03-22 00:51:13

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,460

### Re: The counting frog.

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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## #3 2014-03-22 03:23:02

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

Hi;

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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## #4 2014-03-22 04:03:15

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: The counting frog.

He eats the 17th one or the 18th?

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## #5 2014-03-22 04:08:22

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

This will help explain it:

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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## #6 2014-03-22 04:15:55

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,427
Website

### Re: The counting frog.

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

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## #7 2014-03-22 04:16:31

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: The counting frog.

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

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## #8 2014-03-22 04:20:58

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

Hi;

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

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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## #9 2014-03-22 04:41:48

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: The counting frog.

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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## #10 2014-03-22 04:47:21

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

Hi;

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

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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## #11 2014-03-22 04:48:39

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: The counting frog.

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

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## #12 2014-03-22 04:51:54

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

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

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.

Offline

## #13 2014-03-23 03:09:02

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,460

### Re: The counting frog.

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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## #14 2014-03-23 03:37:04

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

Hi;

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.

Offline

## #15 2014-03-23 04:16:45

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,427
Website

### Re: The counting frog.

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

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## #16 2014-03-23 04:21:29

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,460

### Re: The counting frog.

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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## #17 2014-03-23 04:44:06

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,427
Website

### Re: The counting frog.

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

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## #18 2014-03-23 05:28:56

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

Hi;

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.

Offline

## #19 2014-03-23 09:38:48

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,460

### Re: The counting frog.

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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## #20 2014-03-23 09:43:52

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,460

### Re: The counting frog.

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.

"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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## #21 2014-03-23 11:47:10

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,460

### Re: The counting frog.

Hi Bobby,

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

"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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## #22 2014-03-23 14:41:46

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

Hi;

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.

Offline

## #23 2014-03-23 22:54:24

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,460

### Re: The counting frog.

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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## #24 2014-03-24 02:05:46

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

### Re: The counting frog.

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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## #25 2014-03-24 03:38:24

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,123

### Re: The counting frog.

Hi gAr;

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.

Offline