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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

This is how I see the problem.

```
s = Permutations[{1, 2, 3, 4, 5, 6}, {6}];
s = DeleteCases[s, {___, 1, ___, 2, ___}];
s = DeleteCases[s, {___, 3, ___, 4, ___}];
s = DeleteCases[s, {___, 5, ___, 6, ___}];
Length[s]
```

**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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What value is that returning?

'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: 109,606

90 is the answer. 1,3,5 are students and 2,4,6 are guardians.

**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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**Arna****Member**- From: The Polar Plane
- Registered: 2014-07-23
- Posts: 1,668

ok list of answers

6

180

90

but they all differ from that answer!!

Nothing is impossible as the statement itself states I M POSSIBLE

In this realm of twisted reality,sanity is only illusion

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

It is just how I see the problem.

**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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That is very good!

Do you have a gf for this?

*Last edited by Agnishom (2014-10-23 00:00:01)*

'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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**Arna****Member**- From: The Polar Plane
- Registered: 2014-07-23
- Posts: 1,668

So the problem needs to be reported?

Nothing is impossible as the statement itself states I M POSSIBLE

In this realm of twisted reality,sanity is only illusion

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

What is very 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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**Arna****Member**- From: The Polar Plane
- Registered: 2014-07-23
- Posts: 1,668

Agnishom wrote:

Do you have any gf for this?

gf=Grammatical Framework??

Nothing is impossible as the statement itself states I M POSSIBLE

In this realm of twisted reality,sanity is only illusion

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

I have stopped working on the problem. There is another interpretation that would give a different answer. As you know I only work on clearly defined problems.

**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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

hi

I'm getting 54.

Like this:

(On paper I keep muddling Gs and Cs because of my writing so I'm using A for the guardians and C for the children.)

First interview must be a guardian, let's say Ax. 3 ways.

Hereafter I'll list the interview sequence:

Second interview

AxCx (3 x 1)

AxAy (3 x 2).

Third interview:

AxCxAy (3 x 1 x 2)

AxAyCx (3 x 2 x 1)

AxAyCy (3 x 2 x 1)

Fourth interview:

AxCxAyCy (3 x 1 x 2 x 1)

AxCxAyAz (3 x 1 x 2 x 1)

AxAyCxCy (3 x 2 x 1 x 1)

AxAyCxAz (3 x 2 x 1 x 1)

AxAyCyCx (3 x 2 x 1 x 1)

AxAyCyAz (3 x 2 x 1 x 1)

Fifth and sixth interview:

AxCxAyCyAzCz is forced (3 x 1 x 2 x 1 x 1 x 1 = 6)

AxCxAyAzCyCz (3 x 1 x 2 x 1 x 1 x 1 = 6)

AxCxAyAzCzCy (3 x 1 x 2 x 1 x 1 x 1= 6)

AxAyCxCyAzCz is forced (3 x 2 x 1 x 1 x 1 x 1 = 6)

AxAyCxAzCyCz (3 x 2 x 1 x 1 x 1 x 1 = 6)

AxAyCxAzCzCy (3 x 2 x 1 x 1 x 1 x 1 = 6)

AxAyCyCxAzCz is forced (3 x 2 x 1 x 1 x 1 x 1 =6)

AxAyCyAzCxCz (3 x 2 x 1 x 1 x 1 x 1 = 6)

AxAyCyAzCzCx (3 x 2 x 1 x 1 x 1 x 1 = 6)

Total = 9 x 6 = 54

Bob

*Last edited by bob bundy (2014-10-23 01:42:25)*

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

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Wasn't it a lot of hard work writing all of these down?

I will ask the problem poster to check his 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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

Yes, But it just goes to show my devotion to MIF.

Bob

ps. As it's only 54, I'm tempted to write out all the solutions. Then you'll have something to agree / disagree with.

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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi Bob;

Please write out all the solutions if you can.

**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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

I'm doing that now. But I've only got 48. Have to take a break and then have another look.

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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Okay, when you get it. Thanks for doing 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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'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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

Ok. Here's my solution set:

LATER EDIT: Due to carelessness, I missed a whole load of solutions. There should have been 36 more making the answer 90. See post 72 for the missing ones. My thanks to bobbym for helping me with this.

G1 C1 G2 C2 G3 C3

G1 C1 G2 G3 C2 C3

G1 C1 G2 G3 C3 C2

G1 C1 G3 C3 G2 C2

G1 C1 G3 G2 C2 C3

G1 C1 G3 G2 C3 C2

G1 G2 C1 C2 G3 C3

G1 G2 C1 G3 C1 C3

G1 G2 C1 G3 C3 C1

G1 G2 C2 C1 G3 C3

G1 G2 C2 G3 C1 C3

G1 G2 C2 G3 C3 C1

G1 G3 C1 C3 G2 C2

G1 G3 C3 G2 C1 C2

G1 G3 C3 G2 C2 C3

G1 G3 C1 C3 G2 C2

G1 G3 C3 G2 C1 C2

G1 G3 C3 G2 C2 C3

G2 C2 G1 C1 G3 C3

G2 C2 G1 G3 C1 C3

G2 C2 G1 G3 C3 C1

G2 C2 G3 C3 G1 C1

G2 C2 G3 G1 C1 C3

G2 C2 G3 G1 C3 C1

G2 G1 C2 C1 G3 C3

G2 G1 C2 G3 C1 C3

G2 G1 C2 G3 C3 C1

G2 G1 C1 C2 G3 C3

G2 G1 C1 G3 C2 C3

G2 G1 C1 G3 C3 C2

G2 G3 C2 C3 G1 C1

G2 G3 C2 G1 C1 C3

G2 G3 C2 G1 C3 C1

G2 G3 C3 C2 G1 C1

G2 G3 C3 G1 C1 C2

G2 G3 C3 G1 C2 C1

G3 C3 G1 C1 G2 C2

G3 C3 G1 G2 C1 C2

G3 C3 G1 G2 C2 C1

G3 C3 G2 C2 G1 C1

G3 C3 G2 G1 C1 C2

G3 C3 G2 G1 C2 C1

G3 G1 C3 C1 G2 C2

G3 G1 C3 G2 C1 C2

G3 G1 C3 G2 C2 C1

G3 G1 C1 C3 G2 C2

G3 G1 C1 G2 C2 C3

G3 G1 C1 G2 C3 C2

G3 G2 C3 C2 G1 C1

G3 G2 C3 G1 C1 C2

G3 G2 C3 G1 C2 C1

G3 G2 C2 C3 G1 C1

G3 G2 C2 G1 C1 C3

G3 G2 C2 G1 C3 C1

Bob

*Last edited by bob bundy (2014-10-23 19:41:27)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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How did you make that? By hand?

The correct answer is 90

'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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

I did do it by hand. If the 'correct' answer is 90, then please give one element that is missing from my set.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi Bob;

There are arrangements missing from your set.

G3 G2 G1 C3 C2 C1 and its permutations of the last 3 elements.

**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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

hi bobbym,

Thanks. I just missed them when trying to find all the possibilities. That adds 3 x 2 x 1 x 3! = 36 more and so I also now get 90.

Bob

G1 G2 G3 C1 C2 C3

G1 G3 G2 C1 C3 C2

G2 G1 G3 C2 C1 C3

G2 G3 G1 C2 C3 C1

G3 G1 G2 C3 C1 C2

G3 G2 G1 C3 C2 C1

G1 G2 G3 C1 C2 C3

G1 G3 G2 C1 C3 C2

G2 G1 G3 C2 C1 C3

G2 G3 G1 C2 C3 C1

G3 G1 G2 C3 C1 C2

G3 G2 G1 C3 C2 C1

G1 G2 G3 C1 C2 C3

G1 G3 G2 C1 C3 C2

G2 G1 G3 C2 C1 C3

G2 G3 G1 C2 C3 C1

G3 G1 G2 C3 C1 C2

G3 G2 G1 C3 C2 C1

G1 G3 G2 C1 C3 C2

G2 G1 G3 C2 C1 C3

G2 G3 G1 C2 C3 C1

G3 G1 G2 C3 C1 C2

G3 G2 G1 C3 C2 C1

G1 G3 G2 C1 C3 C2

G2 G1 G3 C2 C1 C3

G2 G3 G1 C2 C3 C1

G3 G1 G2 C3 C1 C2

G3 G2 G1 C3 C2 C1

G1 G3 G2 C1 C3 C2

G2 G1 G3 C2 C1 C3

G2 G3 G1 C2 C3 C1

G3 G1 G2 C3 C1 C2

G3 G2 G1 C3 C2 C1

*Last edited by bob bundy (2014-10-23 19:39:10)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Calvin wrote:

'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: 109,606

They have now marked my original answer correct and upgraded the value of the question to 100 pts.

**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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**danaj****Member**- Registered: 2014-03-03
- Posts: 29

I did it this way, which is longer but lets one see all the results. Perl:

```
use ntheory qw/:all/;
my @I = qw(A a B b C c); # lower case = child, upper case = guardian
forperm {
my $s = "@I[@_]"; # the permuted string
say $s unless $s =~ /a.*A|b.*B|c.*C/; # print unless child precedes its guardian
} 6;
```

which prints out the 90 cases as: "A a B b C c" , "A a B C b c", "A a B C c b", etc. There are lots of ways to structure the restriction (e.g. a hash of positions, then do position comparisons).

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