How many combinations ? Question

PS Its not for homework or anything, I just want to know.

The answer is 3^4 or 3x3x3x3 which is 81.

I don't think it's either a permutation or a combination, because they are about drawing things from a set. So for that you'd have to have three of each part and somehow use them all in each solution.

In your example, you need one item from a set of three - so there are three possible choices there - but you're doing it four times. You can choose from three heads, but when you add eyes you can have all three heads with each type of eye, so there are 3x3 or 9 possibilities. Then if you add bodies, you can have all those previous possibilities with each type of body so 3x3x3 or 27, and of course each of those possibilities can be done with each of the leg types giving 3x3x3x3 which is 81.

Simple as that 🙂 ... looks like I started overcomplicating things right from the outset.

Thanks.

Permutations would be how many combinations of x objects can you make from a population of N items.

And the answer is you take the first x numbers in the sequence N, N-1, N-2, N-3...... N-(x-1) and multiply together, and then divide by the same concept but this time using x, x-1, x-2, ...... 1

As world cup is starting, each group has 4 teams in it, everyone plays everyone else once, how many games (the answer, we all know is 6)

So we need the number of permutations where 2 out of 4 are selected, so

4x3 divided by 2x1 = 6

Now look at a PL season. 20 teams, 2 teams per game = 20x19 / 2x1 = 190. But .... they play each other home and away, so the true number of games per season is 380.

It's the same way we count, with our hundreds tens and units. In the units column, we draw one from ten symbols (0-9). Then in the tens column, we draw another symbol from ten and for each one of those symbols there are ten possible symbols in the units colum so 10x10 combinations i.e. 00-99

jumping on the NFT bandwagon? 😃

@zilog6128

After posting are started pondering that as well. Its just for fun in a drawing excercise I'm mucking around with.

However, I have noticed the above works but you got to deduct the repition that occurs in each set. So in the exmaple I sketched below (only way I can see it at the moment). It generates 27 less 8 repititions from the top set.

So the unique combinations IMO must be 19.

What would the formula be to achieve 19 ?

Anyway... this is fun ...or agony.

You've got circle (head), blob (body) and triangle (leg) where is your 4th shape (eyes)?

@scotroutes
Went back to three for simplicity.

First problem : 4 variables (V) each with 3 values (L)

Each variable has to have a value and those values can only be 1 to 3 and each is distinct so given the order can't change and the outcome of heads doesn't impact the outcome of eyes so it's just simple

heads AND eyes AND bodies AND legs
3*3*3*3 = V^L 81
(edited to agree with molgrips then re read it and decided I was right first time around...)
As you say each line repeats so h1 e1 b1 l1

So it's V^L-(V-1)^L (I may have this bum about face)

For 3 gives 19 possible

For 4 with three gives 101

For V=3 L=2 would give 5

If you could have eyes heads legs bodies then it's a different answer...

It's a long time since I did this...

The second problem: What's the drawing trying to show?

Edit, oh, it's the same first problem.

The head can be red, yellow or blue. (3 possibilities.)
The body can be R/Y/B for each of the above. (3x3=9 possibilities.)
The legs can be R/Y/B for each combination of the above. (9x3=27 possibilities.)

If you need to visualise it, it's basically just counting.

Imagine a 3-digit combination padlock. How would you try every possible combination? 000, 001, 002, 003... 009, 010, 011... 019, 020, 021... 098, 099, 100, 101, 102... 999.

Now say your padlock has three digits instead of ten. So we have 000, 001, 002, 010, 011, 012, 100, 101... 222.

And now, your three digits aren't 0,1,2, they're R,Y,B.

On the attached sketch I have missed some combinations and convinced myself its repititions. Back to the sketch book.

Do it with digits first and then paint by numbers. 😁

So we have 000, 001, 002, 010, 011, 012, 100, 101… 222.

Yarp, you're right. Molgrips is right and I was wrong then right and then wrong again.

[Edit] 15 minutes later and I've just twigged that I did the [wrong] maths for four and four instead of four and three, so doubly wrong 😔

I should just give up on today I think

It is 27. Thanks guys. (for the 3 x 3 version)

Free art here 🙂 STW Piet Mondrian Singletrack Boogie Woogie

The reason behind this is unknown and I'll leave this here 😉

It's 27 for three variables yes. But don't get sidetracked with repetition. In the original question, there is no correlation between any types of head, body and legs, they're all completely independent. So there can be no stipulation for repetition.

The word you are looking for is configuration.

Also, why?

You made that difficult for yourself.

@cougar

Illustrator to the rescue 😉

@scruffythefirst

The word you are looking for is configuration.

Also, why?

Just because 🙂

I wonder if a graphic character configuration program exists out there 🙂

I wonder if a graphic character configuration program exists out there 🙂

Tony Hawk’s Pro Skater 1 and 2?

I wonder if a graphic character configuration program exists out there

Well most video games have this feature but there are also standalone ones. My daughter uses something called Hero Forge for 3D models that you can then download as STLs for your 3D printer or you can have them print and send you a physical one. She also plays with a 2D one but I dunno what it's called. I'm guessing these aren't the only two options out there.

Looks like a custom program would be required to generate what I would like. Basically using my graphics as body parts and generating a set of unique images. Like the cat easter egg in Android.

I wonder if Excel could generate all the configurations as a series of numbers them assign an image to each letter, thus building the charater.

Outside of my pay grade.:(

Back to the sketch book.

Still for a reason ... just interesting and possibly arty.

🙂

This kind of thing 🙂

NFT warning.
https://nft-generator.art/app