While I wait for a whole bunch of things to return so I can action them for the compendium, I figured I'd do some math as to just how many combinations you can have, just to see how (not) viable it is to assign absolutely every single OfA possibility a single number.

And I get people asking me from time to time why I haven't just made a video of every single possible combination, or made a compendium with a perfect preview. (It's still somewhat smaller, but see the idol combinations number, then multiply by 13 (Since there's 13 idols, and I only accounted for one).

If you're going to ask me how I got my numbers, I made the compendium, remember? I know exactly what's available for selection.

If you're going to ask me about how I did the calculations, the breakdown is below:

If you have 3 choices (eg, you run rock, sissors and paper) and you map out the resultant fight for 2 sides you have 3 * 3 possibilities. (As both sides can throw the same thing.)

If you have THREE people playing, the resultant fight ends up being 3*3*3, or 27 possibilities. If you don't believe me, write out EVERY possibility, then count them.

If you're checking for unique possibilities (Namely, no two sides can have the same thing) but want to count a side switch as separate (ie, rock/paper and paper/rock are two separate possibilities) on 2 sides it's 3 * 2 (one less choice for the second person) and 3*2*1 (last person's stuck with the remaining choice) on 3 sides.

(In the RPS scenario, it doesn't matter if the 3rd player exists or not for combinations, because they ALWAYS get stuck with the remaining item. It matters that I show it though, because the idol allocation has a number greater than 1, and consequently that number DOES matter.)

Once again, if you don't believe me write it out yourself and count. You might be there for a while (or a couple of years, depending) doing that though.

If you STILL don't believe me, go talk to your math teacher, and ask him to teach you math. If you don't believe your math teacher after he or she tells you the exact same thing as my explanation above, you deserve to fail math.

Now, I'm going to start at the very top, namely a quintet formation.

There are currently 8 songs you can do a quintet on.

There are 13 stages you can perform a quintet on.

Currently that means that there's 104 stage/song combinations you can pull.

So there's now 13 idols, and 5 slots to fill. This means you get a choice of all 13 idols in the first spot, then 12 for the second (You can't have the same idol twice) then 11, then 10, then 9.

So you can have 154440 different idol combinations.

Each idol can have their own setup now, so...

Each idol must wear a costume. There are currently 16 Floral, 15 Starry, 15 Luxury and 19 Extend costumes, to make a grand total of 65 costumes. An idol must pick one.

Now, each idol can wear 41 different accessories for the Head, Body and Leg, and 42 for the Hand, or they can opt to not wear one at all (+1 choice for all categories)

Which means combination wise, an idol can wear 42 * 42 * 42 *43 different combinations, ranging from nothing, to any possible crazy thing you could come up with. 3185784 total combinations

Combined with the 65 costumes that can be matched to this, we get 207075960 different combinations on one idol.

Except we now have FIVE of them (due to the quintet) and they can all be the same, or all be different. So...

1035379800 different combinations.

With 154440 different idol combinations (Remember, Haruka as lead is different to Haruka as the fifth member)

On 104 different stage combinations, for a quintet.

In short? There's a grand total of... 16630021856448000 different possible combinations for a quintet.

We're not done yet though. We'll skip through the logic, and do the math for the next set though.

Trio

40 stages (All stages support trio or less)

21 songs (All songs qualify for trio performances barring Guests)

13*12*11 idol combinations = 1716 combinations

207075960 different combinations on 1 idol (Cause this doesn't change)

3 idols to run a combination off.

= 895462715347200 trio combinations

Duo

40 stages (All stages support trio or less)

21 songs (All songs qualify for trio performances barring Guest songs)

13*12 idol combinations = 156 combinations

207075960 different combinations on 1 idol (Cause this doesn't change)

2 idols to run a combination off.

= 54270467596800 duo combinations

Solo

40 stages (All stages support trio or less)

21 songs (All songs qualify for trio performances barring Guests)

13 idol choices

207075960 different combinations on 1 idol (Cause this doesn't change)

= 2261269483200 solo combinations.

Guests:

There's also Ranka and Leon.

They both get 40 stages to change up their song, so +80

Compared to the numbers above, that's kinda no fun.

The grand total of the number of request combinations for OfA including all of Catalog 1 is...

17,582,016,308,875,280

Or basically 17 and a half Quadrillion combinations.

In short? Don't ever, ever ask me to make a screenshot library marking every combination of accessories to make a perfectly accurate preview. I will be DEAD before I finish.

For the rest of you, there's some math while I wait around for various people to provide various things...