MATH QUESTION: How Many Combinations Of Animations Are There In Agma?

[DoctorFinkle]

As most of you know, there are 5 chat commands that animate your cell:

• wacky
• shake
• flip
• jump
• spin
  

With these 5 commands, you can stack up to 3 to create a combo (e.g. wackyflipjump). Since we are all under quarantine, we have not been to school in a while, so I am going to ask you all a question that will work that mental muscle! How many combinations of animations are there?

Important details:

• You can have 1, 2, or 3 commands in one
• You can stack 2 more or of the same command to make it more extreme (e.g. spinspinspin spins your cell extra quickly, wackyjumpjump makes your cell laugh and jump extra high)
• The wacky command does NOT do anything when stacked (wacky=wackywacky=wackywackywacky)
  

The first one to reply with the correct answer will receive 9 powers of their choice from me. What you cannot do is list the commands and count them, you MUST have a formulaic approach (i.e. how would you solve this if there were 10 commands? 100 commands? 385,732 commands?).

For those of you feeling especially nerdy, here is a more challenging version of this question: how many combinations of animations are there excluding repeats (i.e. combinations like spinspinspin and wackyjumpjump are excluded)?

The first one to reply with the correct answer to THIS question will receive 18 powers of their choice from me.

Anyone who can correctly answer both questions before anyone else will win 36 powers

Multiple guesses are allowed.

Have fun! 

[DoctorFinkle]

(04-27-2020, 02:58 AM)samira Wrote: Hey;

Nice challenge!!

But I think u need to update it:
This should also work:
wackyspinspinspin

Also please clarify: is wackyjumpspin the same as spinjumpwacky?


Oh and has the formula to be mathematical? Like a single mathematical formula?
Or could it also be an algorithm? In pseudo code.

The third spin in wackyspinspinspin does not register and only spins at the same speed as spinspin.

Also, wackyjumpspin is the same as spinjumpwacky, and should therefore not be counted once, even though there are 6 ways of ordering it.

And yes, it has to be a formula, such as f(n)=(n^3+2)/7. In this case, n=5. Your answer should simplify to a polynomial.

[DoctorFinkle]

(04-27-2020, 04:09 AM)samira Wrote: i Assume that no matter how big n is (well it has to be 1 at least) wacky always is included.

Yes

[Squirrel]

I looked at this, and thought it was a fairly straight-forward perms&combs question... But I have very gleefully forgotten most of my previous mathematical ability, and now am just too plum lazy to figure it out again, when I could be talking to young friends instead.... or possibly unbeknownst to them rolling over them in SuperSonic. (lollll)

But kudos to @DoctorFinkle for coming up with it! You have the makings of a mathematics teacher, young lad!

[nachochesse]

you could automatically talk to friends on discord or on the agma.io community chat today if you want to talk to anyone