Ask MetaFilter questions tagged with combinations

Pick my lock, please

Thorzdad — Fri, 30 Oct 2009 15:31:27 -0800

Help me tear-apart, clean and reset my combination lock. I have a slightly older version of this Master lock. It's a type where you can open it up and set the combination to whatever you want. Over the years, it has become very...sticky...in its operation. So much so that it sometimes takes quite a bit of force to make it work. So, I'd like to clean the works.

Unfortunately, I no longer have the instructions on how to disassemble and re-set the combination for this lock. MasterLock's website is a marvel of non-information for this, unfortunately. I know the end cap without the hasp can be pulled-off, but I'm not about to dive into dissection until I know how to set the combination.

Anyone have good lock-fu tonight?

Permutations: an extension of the odd sock problem

Beautiful Screaming Lady — Tue, 01 Sep 2009 15:00:02 -0800

I've annoyed myself by getting stuck attempting to work out a silly maths problem relating to permutations. It's an extension of the 'how many odd socks do I have to pull out of a drawer before I find a pair' problem. Only my theoretical sock-wearer has three legs. And a penchant for odd socks. Let's say I'm Jake the Peg. I have s socks in a drawer. There are n different types of sock. On average, how many socks must I remove from the drawer before I get three odd ones?

I've worked this out from scratch using a drawer containing only 5 socks. Obviously, if all 5 socks are different (s=n=5), then there are 5! different ways of pulling the 5 socks from the drawer, and every single one of those leads to me having an odd triplet after only 3 socks.

If I only have 4 types of sock (i.e. in the drawer of 5, there's 1 pair and 3 odd ones), again, there are 120 ways of pulling all 5 socks out of the drawer, but this time there are only 60 unique sequences [I managed to work out from first principles that the number of unique ways of withdrawing the socks is s!/(s-n+1)!, not that that seems to help me at all ]. 84 of these sequences lead me to have an odd triplet after the first three socks. 36 of these lead me to have an odd triplet after the first four socks. At no stage do I need to withdraw all 5. So now the average number of socks I need to withdraw to get an odd triplet is (3x84 + 4*36)/120 = 3.3.

If I now only have 3 types of sock (i.e. in the drawer of 5, there are three black ones, a 'Worlds Best Dad' and a Homer Simpson), there are 20 unique ways of removing them all, and, if I've counted right, 37 ways of getting an odd triplet after 3 socks; 35 ways of getting an odd triplet after 4 socks; 48 ways of only getting an odd triplet after removing all 5 socks from the drawer. This leads to an average of 4.09.

My tiny brain is now too overheated to take this further. There must be a connection between these numbers, but I can't get a handle on a pattern, and am too daunted by the prospect of writing out all the variations of 720 sequences for a drawer of 6 socks to do it by brute force. Can anyone please put me out of my misery and point me towards a general formula for this, to solve the average number of socks necessary to achieve an odd triplet given s socks and n different types?

Where are custom settings stored in Word 2000?

roxie110 — Sun, 18 Jan 2009 19:57:31 -0800

What file are settings (created macros, custom toolbar buttons, etc.) stored in in Word 2000? I want to try upgrading to Word 2003 but don't want to lose all the custom stuff in my current version of 2000 (in case I decide to go back). When I reinstalled Photoshop in a new computer, I was able to find a settings file that preserved all of my created actions. I think something similar must exist with Word, but I haven't been able to find it. Help!

Extra credit points if you know whether it's possible to import custom stuff from earlier versions into 2003 after you upgrade!

Movie Treats!

Sassyfras — Fri, 19 Sep 2008 14:29:08 -0800

What movies and treats go together? Tonight is Movie Night at our house. We're going to be watching E.T and as our treat, I'm serving Reese's Pieces. What other movie and snack combinations are there? I thought of Fried Green Tomatoes and um, serving fried green tomatoes. What else?

Help me play with my image collection!

apetpsychic — Tue, 08 Apr 2008 17:30:08 -0800

I have a large image collection that I use for illustration reference. Are there any programs (I have a mac, but could get access to a PC if there's something cool) that can play with large collections of images in unexpected ways? Here are two examples of something I'd like to play with. Since the collection is so large that I can never get an overview, one thing that I could use is something that can pull "X" number of images from a folder, and I can just hit refresh, pulling up unexpected combinations for inspiration. Another thing is something that uses math to maybe pull images and slice or rearrange, flip, make a rorsach, a mandala, etc. Basically I'm not looking for something to make art (I don't really have an interest on sorting things by dominant colors or anything like that) so much as something to use to view my images in new ways with very little manual input from me. Just slamming them together. The more random and simpler to modify variables, the better. Maybe I need to learn to make something myself?

Thanks!

Math help for the right brained

sonofslim — Sat, 28 Apr 2007 13:10:35 -0800

I have a math question involving combinations and sets. I just participated in my first MeFi CD swap, and I got to wondering if there was an algorithmic way to make sure each round's swap sets are as unique as possible. IANAMathPerson, so here's a wordy explanation of the problem:

Let's say we have 9 people who are going to be split up into groups of 3 over several rounds. How can I determine how many unique combinations there are?

For an example of this size, it's trivial by hand:
Round 1: [ABC] [DEF] [GHI]
Round 2: [ADG] [BEH] [CFI]
Round 3: [AEI] [BFG] [CDH]
Round 4: [AFH] [BDI] [CEG]

4 rounds, no one ever shares a set with the same person twice, and there are no further unique solutions. For larger sets of size N and subsets of size K, is there an equation that will tell me how many unique combinations can be made?

Website that will create combinations?

almostbarefoot — Mon, 12 Feb 2007 06:01:29 -0800

I'm working on a presentation for a public speaking class, and my chosen topic is group choice. Is there a website (or program) that I could use to generate all possible preference orderings for a specific set of preferences? Or just numbers in general? It's not central to my presentation, but I'd like to have a slide or two that I could use to demonstrate how many different sets of individual preferences are possible given a certain number of alternatives, in order to explain why group choice is such a difficult and interesting topic. Moreover, I'd rather not go through and do all of the preference orderings/rankings by hand...

Balls in boxes algorithm

davar — Fri, 09 Feb 2007 13:35:03 -0800

Is there a standard ball picking algorithm? I have 10 balls that I want put in four boxes (A-D). Every box can hold zero to all balls. So one possible combination is:
box A: 0,1,3
box B: 5
box C: 2,4,6,7,8,9
box D: -

I want to generate all possible combinations. I realise that this makes 4^10, which is over 1 million possibilities so efficiency is important.

I expected that this would be a common homework problem for computer scientists and I assumed there would be a sort-of standard way to do this (like "quicksort" is a standard way to sort). I don't think I know the terms to search for though, because I cannot find anything.

Any help with this specific problem would be appreciated (pseudo code is fine). If there is a language that is exceptionally suited for this kind of task, I would be interested in that as well. If there are useful websites about this problem, that would be great as well.

Catch a cheater by the toe...

snailer — Mon, 29 Jan 2007 16:41:20 -0800

How can one cheat and predict the outcome of eenie meenie miny moe? Given a fixed version of eenie meenie, (e.g. the english version from
wikipedia), a set number of people to choose among, and assuming the person pointed at changes with every word including "a" ,

My verse is:

Eeny, meeny, miny, moe
Catch a baby by the toe
If it squeals let it go,
Eeny, meeny, miny, moe.

My set is, from left to right:

Alice
Bert
Charlie
Derek
Eudora

Is it possible to devise a rule of thumb that will predict the final person in advance, e.g. If I start with Derek, I know I'll end up with Eudora. If I start with Alice, I'll end up with Bert.

Can this be boiled down to, for example : If I pick the second person from the right, I'll always end up with the first person on the left.

Yes, this really is the kind of thing that weighs heavily on my mind...

Yummy yummy in my tummy

masymas — Tue, 30 May 2006 11:18:27 -0800

Quick & healthy food pairing suggestions? In an effort to adhere to a better diet, I'm looking for additional food pairings that are (1) fairly healthy, (2) quickly and easily-prepared, and (3) good-tasting.

Examples:
- apple slices + peanut butter
- toast + honey + banana slices
- cottage cheese + pineapple chunks
- wheat crackers + gouda (or other) cheese
- tomato slices + mozzaralla

Thanks.

Sounding the horn for people who know something about math

Tuwa — Sat, 13 May 2006 22:22:30 -0800

Suppose there's a web form with 50 checkboxes (representing options or interests), and that checking one has no effect on any of the others. A user could select any two boxes, or a half dozen, or a different half dozen, or all 50. The only constraint on the form submission is that the user must check at least two boxes. How many possible combinations are there? Also, what is the underlying principle here and what is it called? (That is, how could I figure out this problem on my own later, if the situation changed or if a similar situation came up?)

Combinations and Permutations

forallmankind — Thu, 28 Apr 2005 11:07:37 -0800

Combinations and permutations are something that's starting cropping up a lot in my work and I need to rapidly elevate myself from utterly rubbish to vaguely proficient (example included). My current problem is this: in an 8 player game I have a start screen from which the user chooses what character they wish to be. After they've chosen, that character disappears from the screen and the next player chooses from the remaining 7, etc etc. So I need to work out how many different screens are required to show all the different possible combinations of characters.

I'm not necessarily looking for an answer to this question, more direction as to how I can solve this, and other problems of this nature which will inevitably come my way. I do remember doing combs and perms at school and being utterly confused by it, so if anyone knows a more user friendly approach, I'd be most grateful....

thanks.