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Possible arrangments of 5 switches
Valcien
Registered User regular
Registered User regular
Does anyone know the formula to determine the possible permutations of a given number of switches?
In other words each switch a, b, c, d or e is either on or off. Order doesn't matter.
In figuring it out for five, this is what I have so far:
xxxxx
xxxxo
xxxoo
xxooo
xoooo
ooooo
oooox
oooxx
ooxxx
oxxxx
xoxox
oxoxo
oxooo
ooxoo
oooxo
xoxxx
xxoxx
xxxox
xooox
oxxxo
xooxx
oxxoo
xxoox
ooxxo
xoxoo
oxoxx
xxoxo
ooxox
That's 28. How many would there be for six? Seven? And did I miss any?
This is for a starcraft map.
In other words each switch a, b, c, d or e is either on or off. Order doesn't matter.
In figuring it out for five, this is what I have so far:
xxxxx
xxxxo
xxxoo
xxooo
xoooo
ooooo
oooox
oooxx
ooxxx
oxxxx
xoxox
oxoxo
oxooo
ooxoo
oooxo
xoxxx
xxoxx
xxxox
xooox
oxxxo
xooxx
oxxoo
xxoox
ooxxo
xoxoo
oxoxx
xxoxo
ooxox
That's 28. How many would there be for six? Seven? And did I miss any?
This is for a starcraft map.
Valcien on
0
Posts
So for 5 it's 32 possible combinations.
edit:
xxxxx
xxxxo
xxxox
xxxoo
xxoxx
xxoxo
xxoox
xxooo
xoxxx
xoxxo
xoxox
xoxoo
xooxx
xooxo
xooox
xoooo
oxxxx
oxxxo
oxxox
oxxoo
oxoxx
oxoxo
oxoox
oxooo
ooxxx
ooxxo
ooxox
ooxoo
oooxx
oooxo
oooox
ooooo
Is the actual list of solutions for 5.
2^(number of switches)
So you should have a total of 32 for 5 switches, 64 for 6 switches, 128 for 7 switches.
Edit: Woah, beaten. Well played gents, well played.
I was going to say exactly like this. Think in binary (1,2,4,8,16,32,etc.)
A more complicated version of this exists for sets such as a deck of cards (where you are removing elements as you go). I loved my discrete math class in college. Unfortunately, it is a dark voodoo which exits the brain upon completion of the semester.
Good times.
Murphy's Paradox: The more you plan, the more that can go wrong. The less you plan, the less likely your plan will succeed.
Thanks muchly guys.
I just typed five X's or O's over and over to get all the possibilities in a trial and error fashion. If that's thinking in binary than look what I can do. :winky:
A better way to order it (with only three switches, because I'm lazy) would be:
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7
Where 1 is on and zero is off. Note the patterns in the columns - The least significant bit (rightmost) alternates on and off. One full cycle of on and offs toggles the middle bit, which has a pattern of two off and two on. One full cycle of that toggles the most significant bit.
then in each box, put the number of possible answers for it (in this case 2; on and off)
Then multiply all the boxes together and you have the number of possible combinations.
_ _ _ _ _
and then in each element, think about what you are doing. How many different things can go into this element? 2 (either on or off). What about the next element? Well, you still have two choices, either on or off.
After you fill all of the elements, you multiply them together.
2 * 2 * 2 * 2 * 2 = 2^5
And there you go.
Let's do it now for the alphabet. Aka how many combination of 5 letters can you make, given you can reuse the same letter (as in aaaaa counts).
Make your elements:
_ _ _ _ _
Then put numbers in your elements. (26 possible letters in the alphabet.. contrast this to 2 possible positions in a switch (either on or off))
26 * 26 * 26 * 26 * 26 = 26^5
Not too bad.
That's a rather visual representation of 2^n
It's even more useful if you have a situation where you can't reuse the same letter. You'd end up with something like 26*25*24*23*22
And they could throw a hook in there where theyd ask for the number of possible five digit numbers that don't reuse the same digit: 9*9*8*7*6
Or trying to figure out how many area codes there are: 9*2*9
If you can make a tree diagram for it, you should multiply!
No, the point was that you weren't thinking in Binary, which not only made it confusing to look at, but had you missing a few.
Count in binary and it goes like this:
1
10
11
100
101
110
111
1000
etc.
Other way to look at it:
(00000)
(0000)1
(000)10
(000)11
(00)100
(00)101
(00)110
(00)111
(0)1000
etc.
Now just replace the 1s and 0s with xs and os if that's what you want to use
xxxxx
xxxxo
xxxox
xxxoo
xxoxx
xxoxo
xxoox
xxooo
etc.
It sounds like it's more intended for multiple combinations (like, you're trying to figure out how many different outfits you can make with 3 pairs of pants, 8 shirts and 7 pairs of shoes). It's called combinatorics.
http://www.youtube.com/watch?v=w0i_ZFlGTVY