This is the final page for the advanced levels. You’re almost done.
Looking for some other page?
As promised, I will return the “Repeat” feature to you.
Yes! We’ve got all the features back. We won!
Finally, we can use mathboxes to do additions and subtractions.
But guys… Do you really think it’s over now?
Hmm…?
Well, we are not done yet!
I still have an important thing I haven’t told you about. Let’s talk about it now.
What? You still have something to say?
First, take a look at this lunchbox:
Hmm… what is this?
It looks like you can fill each of and with a number…
Yeah. Try filling each of and with a random number.
Ok. Let’s use:
Now, let’s use this lunchbox that can be converted to …
And this lunchbox that can be converted to :
Ok, let’s see what happens when you run it.
Let’s run it.
It became this lunchbox that can be converted to .
Now: What numbers did you use for and ?
I used and , and the final result was …
Does that mean: It calculated ?
Exactly! Using the above lunchbox,
So: The above lunchbox can do addition of two numbers.
Oh wow…!
We thought we had to use the “Repeat” feature to calculate additions like this:
But it looks like we can do addition of two numbers without using the “Repeat” feature .
Exactly!
Next, how about this lunchbox? What do you think this lunchbox can do?
It’s similar to the previous lunchbox but slightly different.
Let’s fill and with and like the last time, and see what happens.
Ok, let’s run it.
This one takes time, so if you can’t wait, press “Skip to the end →”.
It became a lunchbox that can be converted to .
We started out with for and for …
And the result was .
Maybe: It can do multiplication?
Exactly! Using the above lunchbox,
So, it’s a lunchbox that can calculate multiplications.
By the way, we don’t have time to explain this, but lunchboxes can also do subtractions and divisions of two numbers.
So: Lunchboxes can do addition, multiplication, subtraction, and division.
What’s coming up next is the final topic we’ll cover. You’re so close to the finish.
Furthermore, lunchboxes can do even more complicated calculations.
Like what?
For example: Lunchboxes can calculate factorials.
Factorials? What’s that?
The factorial of a number can be calculated as follows:
Hmm… Can you give me an example?
For example: This is the factorial of . If you do the math, the result will be .
Another example: This is the factorial of . If you do the math, the result will be .
Ok, I think I got it…
Now, I will show you that: Lunchboxes can calculate factorials.
To calculate factorials, we need to use the lunchbox that can do multiplication (which we saw earlier).
But this time: Instead of using the actual lunchbox, we’ll use the following notation (abbreviation):
In this notation, the icon in the middle indicates multiplication.
Hmm… ok, but why do we need to use this notation instead of the original lunchbox?
It’s because: The lunchbox that calculates factorials is going to be very complicated.
Therefore: We need to use this simpler notation to describe multiplications in order to save some space. Otherwise, the lunchbox will be too big.
I see…
Before we move on, let’s take a look at an example that uses this simpler notation.
For example: This is the earlier lunchbox that calculates :
If we use the