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#1 2014-09-02 00:41:54

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
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Grandma's Crockery Obsession

I borrowed this problem from issue 62 of Eureka.

We are given 16 teacups, four each in each of four colours, and, similarly, 16 saucers. Arrange the cups on top of the saucers in a 4 by 4 square grid so that:

    in each row and column, there is one cup of each colour;

    in each row and column, there is one saucer of each colour;

    (Orthogonality Condition) no cup-saucer colour combination is repeated. (To be clear, this means that, for example, red-on-green and green-on-red are both allowed.)

In how many ways can you arrange the teacups?

Last edited by Agnishom (2014-09-02 01:11:54)


'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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#2 2014-09-02 00:57:04

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

Re: Grandma's Crockery Obsession

That is a B problem and only worth 100?


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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#3 2014-09-02 01:04:39

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

Did you not notice the author's name?


'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 2014-09-02 01:07:00

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

Re: Grandma's Crockery Obsession

Yes, I suppose I did. That will make the problem much easier to solve...


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

#5 2014-09-02 01:08:57

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

How?

The problem rating will go up. The Brilliant stuff needs some time before they can rate a 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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#6 2014-09-02 01:12:07

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

Re: Grandma's Crockery Obsession

I know about their ratings and I am plenty mad over them too.

How?

Hahahhohohoohahahh that 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.

Offline

#7 2014-09-02 01:14:46

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

The fact that I shared the problem on Brilliant is not important.

I still do not see how that helps you to solve it? Have you solved it already?


'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.

Offline

#8 2014-09-02 01:18:53

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

Re: Grandma's Crockery Obsession

Everything is important - Michael Corleone

I still do not see how that helps you to solve it?

I will just ask you.

Have you solved it already?

Give me a place to sit and an M that is fast enough, a back brace and I can solve any 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.

Offline

#9 2014-09-02 01:33:46

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

Who is Michael Corleone? Is he real?

You cannot imagine an arbitarily fast M


'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.

Offline

#10 2014-09-02 01:38:54

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

Re: Grandma's Crockery Obsession

Yes, he is sort of real:

235px-Michaelcoreleone.jpg

And yes, I have already solved that problem once before.

The first time I saw a solution to your problem was in a Martin Gardner book. He used the face cards instead of teacups.


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

#11 2014-09-02 02:12:42

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

Please post your solution


'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.

Offline

#12 2014-09-02 02:17:29

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

Re: Grandma's Crockery Obsession

Post it as soon as I 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.

Offline

#13 2014-09-04 02:09:19

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

I tricked the guys to get an 175 points rating.


'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.

Offline

#14 2014-09-04 02:12:40

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

Re: Grandma's Crockery Obsession

Do rotations and reflections count or not?


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 2014-09-04 02:20:53

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

Yes, they do


'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.

Offline

#16 2014-09-04 02:47:29

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

Re: Grandma's Crockery Obsession

There are 3 MOLS of order 4 but I do not know if that is the correct number with rotations and reflections considered.


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

#17 2014-09-04 02:54:11

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

Do you have Eureka 62?


'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.

Offline

#18 2014-09-04 02:56:31

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

Re: Grandma's Crockery Obsession

I do not even know what it 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.

Offline

#19 2014-09-04 14:10:07

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,773
Website

Re: Grandma's Crockery Obsession

image.jpg
image.jpg
image.jpg
image.jpg
image.jpg

Last edited by Agnishom (2014-09-04 14:19:43)


'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.

Offline

#20 2014-09-04 16:35:41

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

Re: Grandma's Crockery Obsession

My program still ain't ready yet.


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

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