Please help, my brain has stopped working

Can somebody here help me out with some basic maths, please? I've got a
problem[1] which I think should be trivial, but when I try to work it out my
head starts hurting, my vision goes blurry and I feel sick[2].

I have 12 variables, each of which has a number of permitted values. Each
variable has between 1 and 10 permitted values.

If we call the number of permitted values V1, V2, V3, etc. then obviously
the total number of combinations is V1 x V2 x V3 x V4 x V5 x V6 x V7 x V8 x
V9 x V10 x V11 x V12 and this equals roughly 207,000.

However, what I'm interested in is the number of combinations one gets if
you also make how many variables you consider a variable.

So I know that the total number of combinations for 12 variables is 207,000
and the total number of combinations for 1 variable is V1+V2+V3...+V12 = 39,
but I'm sure there must be an easy formula to work out the total number of
possible combinations. Damned if I can think of it though.

Anybody care to help?

[1] I have so many problems, but I'm trying to focus on this one right now.
[2] To be fair this may be more to do with school-night drinking.

 

Buggered if I can work out what you mean.

Possibly the fact that you don't appear to be able to state your
requirements[1] clearly is hindering you. Have another go.


[1] Doubtless someone here will be able to understand you, but it
ain't me.

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Depends what you mean by formula. I suspect it'll involve a sigma
function, which I don't think Excel, for example, can handle.

 

Sorry, what I want to know is the sum of ...

The number of possible values I could have if I only look at one (any one)
of the 12 variables (which is 39)

Plus

The number of possible combinations of values if I look at any two of the 12
variables

Plus

The number of possible combinations of values if I look at any three of the
12 variables

And so on to ...

Plus the number of possible combinations of values of all 12 variables
(which is 207,360)

So I should be able to add the 12 numbers, but I don't know what 10 of them
are.

Moving to the second step, where I consider the number of combinations of
any 2 values that should be:

V1+V2+2(V3)+3(V4)+4(V5)+5(V6)+6(V7)+7(V8)+8(V9)+9(V10)+10(V11)+11(V12)

I think, but I'm not sure.

Any the wiser?

 

Explain how you get this result...

.... and this result...

.... and I might be able to work out what you mean.

How about your friendly, local maths teacher?

Lightweight.

 

Is it? What do you mean by "look at"?

I'm afraid your "specification writing" skills, if you had any, seem
to have deserted you.

From the fact that you're trying to add the combinations, I might
infer that you're wanting to combine all twelve variables into one,
which could indeed give 39 distinct values, but only if there are no
common values across the 12 variables, which, as you only know the
number of possible values for each, you presumably can't guarantee.

Nope.

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AndrewR wrote:

Nope, still don't follow that.

 

OK.

Variable 1 has 3 possible values (E, A and C)
Variable 2 also has 3 possible values (P, C and N)
Variable 3 has 4 possible values (U, B, E and S)
Variable 4 has 2 values (T and F)
Variable 5 has 2 values (N and C)
Variable 6 has the same 2 values as variable 5
Variable 7 has 3 values (E, L and N)
Variable 8 has the same 3 values as variable 7
Variable 9 has 4 values (X, L, N and B)
Variable 10 has 2 values (O and N)
Variable 11 has 10 values (bugger it)
and variable 12 has 1 value (NA)

So, considering the variables as a set (which is how they're used) the
number of possible combinations is 3x3x4x2x2x2x3x3x4x2x10x1=207,360 (or
something very close to that)

If I were to deal with a single variable at a time then I'd be looking at 1
or 39 possible values (ignore the fact that some values are the same - a
value of 'N' for variable 1 means something different to a value of 'N' for
variable 5, for example)

Now, if I considered any 2 variables how many possible combinations of
values are there?

Then any 3, and so on.

Basically what I'm trying to do is a write a series of nested loops which
will loop through all of the possible values of a single variable, all the
values of 2 variables and so on all the way to looping through all of the
possible values of 12 variables, but I want to know how many loops will be
involved.

The code inside the loops is going to be fairly complex and will involve,
among other things, looping through another list of 200-300 items for every
iteration of the loop, which is (I suspect) going to make for a
stratospheric number of loops. If so then I might not bother as I'm working
in Excel on a lap-top, so I'm not going to waste my time writing something
that's going to have a processing time of days.

 

I think I'm with you now... at a rough guess, without bothering to think
about it too much: 39! = 2.03978821 × 10^46

 

STILL not getting through. What do you mean by "deal with"?

If you're "dealing with" V1 then you have 3 possible values, v3 has 4,
etc. etc. But this is your starting point, so you know that. But where
do you get the idea of adding all the ranges together from?

If you don't know which variable you'll be "dealing with" you
presumably would like to know the greatest number of possible values,
but that would just be max(V1_vals-V12_vals).

So you are trying to combine them into a single variable?

Ahh, you really are trying to combine them - why didn't you say so?
You want to know how many unique combinations there may be across any
or all of the variables. Let's see.... around 207,000 ought to do it.

Although it sounds like you may also want to add a _null_ value to
every range, to represent the values of a combination of variables Vx
and Vy, where values of Vother are ignored, so you'd need to calculate
(V1+1)*(V2+1)*(V3+1) etc.

Doing your "adding all the possible numbers of values together" is
just a very long way of performing the multiplication.

It's all right - just post it here and some other **** will do it for
you, I'm sure.

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D'Oh! Of course - that's both blindingly obvious and keeps my number of
loops down to a reasonable value.

Thank you, sir.

My apologies for not explaining myself very well, but this is a very small
piece of a very large puzzle and I was trying not to suck all of the
bandwidth out of the Internet by explaining everything.

--
AndrewR, D.Bot (Celeritas)
Aprilia RSV-1000R, Honda VFR750F-L, Kawasaki ZX-6R, Fiat Coupe 20v Turbo
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The speccy Geordie twat.

 

At the age of 18, in around 1975, when I got my hands for the first time
on a real computer, I decided to solve the problem of the caterpillar on
the infinitely extensible piece of elastic[1] iteratively[2]. I waited
around for a few minutes but no answer was forthcoming, so I went home
intending to return next day for the answer. What I actually got the
following morning was a surprisingly polite and sympathetic note from
the computer centre staff explaining that they had had to end the job as
the computer was devoting its entire time to projecting my virtual
caterpillar across light years of elastic, followed by a solution to the
problem in about three lines (they'd inferred the problem from my
program, which may or may not have had a comment or two) and a
suggestion that a more sophisticated approach might be in order next
time.

You're not trying to do something similar, are you?

--
Jeremy
R1200RT

[1] The elastic is initially 1m long, and the caterpillar starts from
one end at 1cm/s. At the end of each second the elastic is stretched by
another metre (so it's 2m after 1 second, 3m after 2 seconds etc.). Will
the caterpillar ever reach the other end?

[2] Being fairly useless at maths, but ever enthusiastic to apply a
combination of ignorance and brute force.

 

= A Suffusion of Yellow.

HTH.

 

No, I'm trying to do something infinitely more futile ... work out if a
government agency is going to fall flat on its face in 6.5 weeks.

--
AndrewR, D.Bot (Celeritas)
Aprilia RSV-1000R, Honda VFR750F-L, Kawasaki ZX-6R, Fiat Coupe 20v Turbo
BOTAFOT#2,ITJWTFO#6,UKRMRM#1/13a,MCT#1,DFV#2,SKoGA#0 (and KotL)
BotToS#5,SBS#25,IbW#34, DS#5, COSOC# Suspended, KotTFSTR#
The speccy Geordie twat.

 

Well, duh.

 

It could be, as the other list of 200-odd items that I'm looping through
with every iteration is independent of the 12 variables, but, even though it
sounds cool, I suspect it's going to be much easier to code out the
completely null case.

--
AndrewR, D.Bot (Celeritas)
Aprilia RSV-1000R, Honda VFR750F-L, Kawasaki ZX-6R, Fiat Coupe 20v Turbo
BOTAFOT#2,ITJWTFO#6,UKRMRM#1/13a,MCT#1,DFV#2,SKoGA#0 (and KotL)
BotToS#5,SBS#25,IbW#34, DS#5, COSOC# Suspended, KotTFSTR#
The speccy Geordie twat.