00:01
Hello, i am super excited to see this question.
00:03
This might be my favorite topic in all mathematics.
00:06
This is exploding dots.
00:08
What is exploding dots? so here we have, first, a two -to -one machine.
00:13
We have our boxes here for a two -to -one machine, a two -to -one machine.
00:18
And what do we start with? while we start with, it looks like one, two, three, four, five dots in our.
00:27
So this would be, again, a two -machine.
00:29
Our boxes are powers of two.
00:31
So one, two, and then four, and then eight, and then 16, 32, and so on.
00:36
But in our one box, what do we have? we have one, two, three, four, five, six, seven, eight, nine.
00:46
All right.
00:47
So if we do our explosions, what do we get? well, we can explode anywhere we want.
00:51
If we want to start in the second box over, how many explosions do we have? we have two, right? a pow, that's two explosions.
00:58
Each one explosion makes a dots one box over okay and then looking at the ones box what do we have in the ones box in the one box what we have here we have one two it's one explosion two explosions three explosions four explosions so four explosions make four dots right here so we have four dots now so we have one two three four but now we have what two explosions right two explosions in the second box so kapau -c -c -c -p -all right two two explosions.
01:29
That's going to make two dots.
01:31
One box over.
01:33
And then we have one more explosion in that box, right? one more explosion there.
01:37
Kapao.
01:38
Uh, two, no, actually two exposures, two explosions, two explosions.
01:41
Two explosions.
01:42
He makes two dots, two dots.
01:44
And then one more explosions.
01:45
We need one more box, right? we need one more box.
01:49
That's going to be our 16 and then one explosion here, kapow, and that's going to be a dot.
01:56
One box over.
01:58
And what we love with? we're left with one dot.
02:00
So we have one and then nothing and then nothing and then one -one.
02:05
So therefore, the code for this number in a two -tweat machine is 1 -0 -0 -1.
02:10
What number is that? that's 116, 1 -2, and 1 -1.
02:13
That is the number 16, 18, 19.
02:17
That's the number 19 written in a two -to -one machine or written in binary.
02:23
All right.
02:24
Now the next, we have a 3 -1 machine.
02:27
It's the same type of machine.
02:29
But now, whenever there are three dots in a box, they explode to make one dot, one space to left.
02:34
So we have our boxes.
02:35
We have four boxes to start.
02:36
One, two, three, four...