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 Post subject: Combinatorics?Posted: Fri Dec 04, 2009 1:11 pm

Joined: Sat May 16, 2009 8:27 pm
Posts: 209
Is this the part of pure maths that would help me get my head round combination questions?
Eg 10 seats at table. How many diff seating arrangements. Sandwiches, fillings and garnish etc
Sorry to say I end up drawing and work from there.
Any web pages to be recommended for this please?

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 Post subject: Re: Combinatorics?Posted: Fri Dec 04, 2009 1:22 pm

Joined: Fri Mar 20, 2009 7:34 pm
Posts: 37
rachag wrote:
Is this the part of pure maths that would help me get my head round combination questions?

Yes.
Quote:
Sorry to say I end up drawing and work from there.

Drawing things is almost always a good way to approach a problem in maths.

Quote:
Any web pages to be recommended for this please?

What level of combinatorics do you want to learn ? Enough for 11 plus ? A level ?

If you know nothing at the moment, you would probably beneift from getting a GCSE/ O level standard text, and working through the problems in that first.

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 Post subject: Re: Combinatorics?Posted: Fri Dec 04, 2009 2:23 pm

Joined: Thu Jan 03, 2008 8:26 am
Posts: 1326
Location: Watford, Herts
rachag wrote:
Is this the part of pure maths that would help me get my head round combination questions?
Eg 10 seats at table. How many diff seating arrangements. Sandwiches, fillings and garnish etc
Sorry to say I end up drawing and work from there.
Any web pages to be recommended for this please?

Combinatorics is a broad field. The part you want is permutations and combinations: a Google search on that phrase will give you several introductory presentations. Don't be put off: it's not really that hard. And as wiltsman says, trying out examples on paper is an excellent way to attack maths problems.

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 Post subject: Posted: Fri Dec 04, 2009 3:45 pm

Joined: Sat May 16, 2009 8:27 pm
Posts: 209
Thanks
I wanted to know enough to be able to show a sensible methodical approach to DD for selective school age 11 long answers.
I find the ones about A only sits on B's right, or A only sits opposite B difficult to get my head round.
So, I will go through GCSE maths books and perhaps refine my searches on the internet to basic combinatorics. The web pages I looked at really did not enlighten me at all - way too advanced.

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 Post subject: Posted: Fri Dec 04, 2009 7:52 pm

Joined: Fri Mar 20, 2009 7:34 pm
Posts: 37
rachag wrote:
I find the ones about A only sits on B's right, or A only sits opposite B difficult to get my head round.

Do you have a specific example ?

Quote:
So, I will go through GCSE maths books and perhaps refine my searches on the internet to basic combinatorics. The web pages I looked at really did not enlighten me at all - way too advanced.

Do a search on "combinations and permutations".

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 Post subject: Posted: Fri Dec 04, 2009 10:51 pm

Joined: Sat May 16, 2009 8:27 pm
Posts: 209
Sorry, unable to find paper but from memory . . .
Albert Bertha Charlie and Dan go out to dinner. Albert must sit facing south to have a sea view and Bertha and Charlie always sit next to each other.
How many seating combinations are there?
After a few days, Charlie agrees to do without the sea view. How many further seating combinations are there?
If Bertha and Charlie can sit apart from each other, how many seating arrangements are possible?
Such possibilties can also fit with sandwiches and garnishes etc
May not be that onerous to work out by simply repeated table plans, and perhaps this OK in answer as long as done in orderly fashion but I would like to know on a personal level how to approach it from a mathematical view point

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 Post subject: Posted: Sat Dec 05, 2009 8:29 pm

Joined: Fri Mar 20, 2009 7:34 pm
Posts: 37
rachag wrote:
Sorry, unable to find paper but from memory . . .
Albert Bertha Charlie and Dan go out to dinner. Albert must sit facing south to have a sea view and Bertha and Charlie always sit next to each other.
How many seating combinations are there?

There's not enough info to answer the question.

How many seats are there ?
Does it matter in which direction B, C, D face ?

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 Post subject: Posted: Sat Dec 05, 2009 10:09 pm

Joined: Sat May 16, 2009 8:27 pm
Posts: 209
Only 4 seats and a square table.
Doesn't matter which way the others face.

Next time I go through this process with DD 2 I shall keep a separate file of difficult questions (for me), questions she finds difficult in topic order etc etc...

Honestly, both myself and OH have A grades at A level maths and can still spend 20 mins arguing about how to do part f on question 15 of a 75 min paper! Some of these questions are really mind boggling. I suppose the children need to learn when to cut their losses and how to show they make logical progress even if they don't get the answer.

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 Post subject: Posted: Sun Dec 06, 2009 8:35 pm

Joined: Fri Mar 20, 2009 7:34 pm
Posts: 37
rachag wrote:
Only 4 seats and a square table.
Doesn't matter which way the others face.

You can merely enumerate all the possibilities here; there's no need for combs and perms.

Label the seats 1 2 3 4. Let seat 1 be south facing. A must sit here, so we can forget about this seat from now on. For seats 2 3 4 we have the following perms:

1234
ABCD
ACBD

Those 4 are the only ones which satisfy the requirements (since any other separates B and C eg ABDC)

Quote:
Honestly, both myself and OH have A grades at A level maths and can still spend 20 mins arguing about how to do part f on question 15 of a 75 min paper! Some of these questions are really mind boggling. I suppose the children need to learn when to cut their losses and how to show they make logical progress even if they don't get the answer.

I would be amazed if any 11 plus paper required the kids to be able to compute combs and perms. I suspect all of the questions are worded like the one above, so that they can be done by inspection with a little thought.

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