Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

#1 2015-01-17 17:31:18

ElainaVW
Member
Registered: 2013-04-29
Posts: 580

Restricted partitions

s = {12, 7, 10, 9, 7, 13, 11, 9, 8, 13, 10, 10, 8, 11, 11, 9, 7, 11, 9, 12}

How many combinations can be made, when 6 numbers are picked from s without replacement and the total of all 6 is less than or equal to 60?

Only combinatorial solutions will count.

Offline

#2 2015-01-22 18:48:57

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

Re: Restricted partitions

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

#3 2015-02-12 17:28:02

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Restricted partitions

Hi;

I don't understand the question, but would like to try to.

Maybe if I can get you to help me with this smaller example (in which group totals are ignored):

s={12, 7, 10, 9, 7}, and 4 numbers are picked from s without replacement.

What does "without replacement" mean?

Ignoring "without replacement", I think that there are 5 combinations here, namely:
{12,7,10,9}, {12,7,10,7}, {12,7,9,7}, {12,10,9,7} and {7,10,9,7}

Which of these are valid?

Thanks.

Last edited by phrontister (2015-02-12 17:29:41)

"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

Offline

#4 2015-02-12 18:05:30

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

Re: Restricted partitions

Hi;

What does "without replacement" mean?

When you pick objects from a big collection of objects you can do it in 2 different ways. One is with replacement, which means you put the one you just picked back into the main collection so it might be picked again. The other way is without replacement, which means the object is removed from the main collection and can not be picked again.

If you are clear on the replacement stuff can you now explain what problem you are trying 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 2015-02-12 18:40:56

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Restricted partitions

I see.

That means each time a number is removed the number of options from which to choose reduces by one, so that the last number chosen is from a group of 15 numbers.

I think the task is to find the number of different chosen groups there would be that sum to less than 61.

Hmmmm. I think that's beyond me.

Last edited by phrontister (2015-02-12 18:47:55)

"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

Offline

#6 2015-02-12 18:48:24

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

Re: Restricted partitions

It might be but it is not beyond M. A man with M is mightier than that same man without.

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 2015-02-12 18:58:47

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Restricted partitions

But where to start looking! I need to have some idea of the solving technique before I begin.

I've worked out (I think) how to solve the puzzle 'with replacement' (answer 24704), but that's as far as I've got. All I can think of for a 'without replacement' solution is to program a simulation, but that wouldn't give an exact result.

"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

Offline

#8 2015-02-12 19:01:15

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

Re: Restricted partitions

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 2015-02-12 19:20:12

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Restricted partitions

Sorry, but all this looks too advanced for me. I've never done GFs and don't understand the concept.

"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

Offline

#10 2015-02-12 19:21:50

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

Re: Restricted partitions

That is okay to start. M handles all the gf's for you. Take a look at the first line of my signature.

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