Super Mario 64, released in 1996 by Nintendo,
is a game in the Super Mario series of platformer
games. It was the first 3D game in the series
and is considered one of the most iconic games
in the entire Mario franchise.
Now the way you play the game is with an N64
controller. Perhaps the most important button
on the controller is the A button. You use
it to jump, which is the most important action
in the game.
To complete the game, you are intended to
collect 70 out of 120 stars. Stars are objects
placed at the end of a small path as a sort-of
trophy for completing the objective in one
of the 15 courses or secret courses, which
are located within the hub castle, which is
the setting of the game.
Almost all of these in some way want you to
jump at some point. Even just entering courses
require jumps. However, for over 7 years,
YouTuber Pannenkoek2012 has been the primary
contributor to ideas that has taken the full
game run of all 120 stars from over 200 A
presses down to 19. Yes, only 19 times do
we have to actually jump when competing the
game. This is known as the A button challenge
(or ABC for short).
Now why.... do all this? Why not just play
the game casually? And what... does this have
to do with #MegaFavNumbers ?? Well..... let
me explain that now...
You could just play the game casually. However,
say you’re really good at the game and you’re
playing it competitively. Say you’re so
good that you can play it fast and take it
one step further and you're speedrunning the game. Say speedrunning just isn’t enough and you want to see just
how perfect a playthrough of a game could
be using tools on an emulator - with that
you have Tool-Assisted Speedruns (TASes).
Bismuth has a great video explaining the difference
between all of these and what it means to
make TASes so please check that out in the
description.
Anyway... with the Super Mario 64 A Button
Challenge... there is currently a work-in-progress
TAS being made that is hopeful to complete
the game without pressing A even once, doing
so by collecting the minimum 70 stars. Because
it needs to be picked which 50 stars to cut,
some planning ahead must be done.
There are some very obvious stars to leave
out, such as stars that require the A button
to be pressed or held. This includes any courses
that require an A press to enter it. That
gets rid of 24 stars immediately. 96 remain.
Next we can ignore any stars that are way
too obviously slow. Similarly to the last
cut, this includes any courses that take too
long to enter. This gets rid of 14 stars.
82 remain.
Before cutting any more stars I'll explain
one quick thing about the overall route that
has to be taken into account. There are 5 stars in the
game that are always guaranteed to be in a
run as they take no time to collect except
for travelling to the character that is keeping
the star. In the castle, there are three toads
(one in the basement, one on the second floor,
and one on the third floor) . There are also
two rabbits named MIPS (one of which appears
in the basement at 15 stars and one at 50
stars).
Due to the ability to be collected almost
instantly, they are essentially mandatory
to collect. However because the second MIPS
star is well over half way through the run
and still in the basement, it. is. a. DETOUR,
that is unless you plan accordingly. I won't
go into the details about the actual reason
behind this but basically we collect 50 stars
from downstairs before collecting the MIPS
2 star and then collect 19 more stars upstairs
without picking up any objects.
Because of that last requirement, there is
one star that's also cut, Mystery of the Monkey
Cage. Splitting these from before MIPS 2 and
after MIPS 2 and you get 57 downstairs and
23 upstairs. Cutting 7 stars downstairs and
4 stars upstairs and we have the planned amounts
at 50 and 19.
Now to find out which 11 stars to cut...
If you take the 81 stars, and adjust their
star times for the actual amount of time it
adds to a full game run, then cut the slowest
ones (making sure to also take into account
opportunities to skip course re-entries and
courses themselves where it's worth it), you
can easily figure out which stars to cut.
Two people have already shown that this is
possible however it requires a little extra
amount of thinking to actually pick the routes
yourself based on what you could see on the
sheet and what you knew about the game. Now,
myself, being a lazy and mathematically inclined
individual, wanted to try to automate the
process of picking stars to cut because surely
it couldn't be that hard...
Two weeks later and I was done with an early
version of an automatic bruteforcer that I
made on Google Sheets. How did I do it? Well
first I listed out every combination of different
amounts of stars I could collect in each of
the courses, then left only the ones that
were actually useful (meaning those that collected
70 stars total), and then listed out all possible
ways of collecting each number of stars in
each course, then gathered all the times for
each individual segment of each of the arrangements
then did formula magic to add all the sections
together to make a list of every possible
routes’ times and then it tells me which
is the best without me ever having to think…why.
Ok kierio... so what? you made a really simple
thing complicated and then made a video about
it, why? Well the reason I wanted to make
the video wasn’t just about the process
but actually about the fact that I narrowed
down so many theoretical possibilities to
one single fastest route, although most of
those possibilities were completely useless.
And yeah I kinda just wanted a reason to make
a video related to a big number so I thought
"hey why not talk about Super Mario 64?"
Ok finally. The actual numbers. How many routes
did I actually get rid of... Well, the original
sheet that I used to get the star arrangement
numbers was an overly copied and pasted list
of numbers counting up to less than 10 over
and over again. After making the list I narrowed
it down immensely as the vast majority of
them didn't collect 70 stars.
There were 2 possibilities for Shifting Sand
Land, 6 for Hazy Maze Cave, 2 for Vanish Cap
under the Moat, 7 for Jolly Roger Bay, 5 for
Big Boo’s Haunt, 4 for Dire Dire Docks,
2 for Bowser in the Fire Sea, 6 for Wet Dry
World, 2 for Tiny Huge Island, 7 for Tall
Tall Mountain, and 8 for Snowman’s Land,
which is not the number in the title of the
video.
The thing is I've actually left out one small
thing from the calculations. I only used the
different possible star counts I could have
used instead of the actual different possible
star arrangements of those stars. What I mean
by this is that just because I collect 6 stars
in one course doesn't mean that's the only
way to collect 6 stars in that course.
So how many extra arrangements are there that
I didn't take into account before? Well, 1
in HMC, 7 in JRB, 1 in BBH, 2 in WDW, 1 in
TTM, and 3 in SL.
This brings the long multiplication product
from 4,515,840 up to 26,492,928.
And THAT is the number in the title 
of the video. Thanks for watching.
Also, please enjoy the couple of math facts I just put at the end of this video, I just didn't
want to leave it ending at that. And also, thanks for watching through my first ever
commentated video! I am really surprised at how difficult this is to do
um... I'm probably not going to make another one in the future so
this is all you'll have to ... just handle.
Again, thanks for watching.
