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## #1 2018-06-09 17:51:30

Amartyanil
Member
From: Universe
Registered: 2013-05-27
Posts: 76

### Letter-arranging

Hi;

Can anyone please provide a detailed solution for this problem?

All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other

Is there any program for solving this? If yes, please provide the code.

"Every place is the center of the universe. And every moment is the most important moment. And everything is the meaning of life." ~ Dan Harmon

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## #2 2018-06-09 19:38:49

bob bundy
Registered: 2010-06-20
Posts: 8,453

### Re: Letter-arranging

hi Amartyanil

First you could calculate the number of arrangements where there is no restriction.

Then imagine EA locked together as a single 'letter' and calculate how many ways you can arrange these five letters.  Do a similar thing with AE etc*.  Then subtract.

Bob

*You'll need to take care to avoid repeats caused by all three vowels together.

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #3 2018-06-20 05:25:24

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Letter-arranging

Is there any program for solving this? If yes, please provide the code.

bobbym used to be a pro at doing these with mathematica. But you can do that with any other language too, with some work.

'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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## #4 2018-07-02 15:40:09

Amartyanil
Member
From: Universe
Registered: 2013-05-27
Posts: 76

### Re: Letter-arranging

Can you please tell how the code will be looking?

"Every place is the center of the universe. And every moment is the most important moment. And everything is the meaning of life." ~ Dan Harmon

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## #5 2018-12-09 03:05:35

Amartyanil
Member
From: Universe
Registered: 2013-05-27
Posts: 76

### Re: Letter-arranging

?

Last edited by Amartyanil (2018-12-09 03:06:32)

"Every place is the center of the universe. And every moment is the most important moment. And everything is the meaning of life." ~ Dan Harmon

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## #6 2018-12-10 00:54:17

bob bundy
Registered: 2010-06-20
Posts: 8,453

### Re: Letter-arranging

hi Amartyanil

As there are 3 vowels (V) and 3 consonants (C) the 'structure' of a 'word' has to be:

VCVCVC or CVCVCV.

So I think there are 6 ways to assign actual vowels to the V positions (ie. 3 x 2 x 1) , and 6 ways to assign the consonants times 2 to allow for the two basic structures.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #7 2018-12-10 11:49:10

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,609

### Re: Letter-arranging

Hi Bob,

I like your strategy, but VCVCCV and VCCVCV are also valid arrangements because the constraint on adjacent letters only applies to vowels.

Those are the only other arrangements I could find.

"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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## #8 2018-12-10 19:57:27

bob bundy
Registered: 2010-06-20
Posts: 8,453

### Re: Letter-arranging

Hi Phrontister,

Great to hear from you.  That sound right.. Typical of me to leave out half the answers! I'll do my penance ... Listening to one hour of Brexit news should be sufficiently painful.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #9 2018-12-10 21:02:51

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,609

### Re: Letter-arranging

And there I was thinking that you were just testing me to see if I'd notice you'd only done half the job!

I feel your pain, having lasted just one minute of listening to the Brexit news that I woke up to this morning (yes, we down here sometimes hear about overseas goings-on too).

"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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## #10 2018-12-11 12:41:41

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,609

### Re: Letter-arranging

Here's a solution (I think) using the permutations formula.

Last edited by phrontister (2018-12-11 15:03:08)

"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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## #11 2018-12-15 21:09:56

bob bundy
Registered: 2010-06-20
Posts: 8,453

### Re: Letter-arranging

phrontister wrote:

And there I was thinking that you were just testing me to see if I'd notice you'd only done half the job!

Thanks!  That's excellent.  I shall use this excuse from now on.  I've modified my signature.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #12 2018-12-16 01:08:56

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,609

### Re: Letter-arranging

Thanks, Bob...I'll watch out for such!

Or are you playing 'Spot the Oxymoron'?

"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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