Intermediate 1
Intermediate 3
Hello! This is page 8 of the course called “Y Combinator for Non-programmers”. If you just got here, click here to read from the beginning.

Y Combinator for
Non-programmers

Intermediate 2: The Challenge Question

Slide 1 / 8

Things will get harder

Warning: From this page, things will get much harder. The lunchboxes will become more complicated.

Things will get harder

But: You don’t need to understand everything immediately. Even if you don’t completely get it, please keep reading!

Looking for some other page?

Intermediate 1·
·Intermediate 3
Slide 2 / 8

The problem

As promised: If you can solve this problem, I’ll return your mathboxes.

Minion, explain the problem!

Sure. First, take a look at this lunchbox.

We learned on the last page that I can convert this lunchbox to .

’s with on the bottom-right
→ Can be converted to

Now, take a look at this lunchbox.

Each icon represents a food item.

Each icon represents a food item
13
2
23
1

We now combine the above two lunchboxes.

If you combine them, it’ll look like this:

After combining the two lunchboxes
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1
13
2
23
1

Now, here’s the challenge:

  • Fill each icon in a way such that,
  • After you run it,
  • The resulting lunchbox can be converted to .
Challenge:
Fill each icon in such a way that,
1
1
13
2
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After you run it,
the resulting lunchbox can be converted to .
Lunchbox that can be converted to

This is the “very difficult question” I’ve been talking about.

If you solve this, I’ll return your mathboxes!

Slide 3 / 8

Try filling with random items

Hmm… I don’t know if I understood the problem.

And I have no idea how to solve it!

No problem! First, try filling each icon with a random food item.

By doing so, you’ll be able to understand the problem better.

Try filling each icon
with a random food item!
1
1
13
2
23
1

Ok, let me try…

Here it is: I randomly filled each icon with sushi , a sandwich , or a hamburger .

Randomly filled each icon with
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1
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2
23
1

Now, we’ll run the above lunchbox, and…

  • If it becomes a lunchbox that can be converted to , it’s a success!
  • If not, then it’s a failure.
We’ll run this lunchbox, and…
1
1
13
2
23
1
If it becomes a lunchbox that can be
converted to , success.
Otherwise, failure

Ok, let’s run it!

Need a review? To solve the above lunchbox, we’ll need to use the rules from Beginner 5.

If you want to review them, press “Do a Quick Review” below.

Slide 4 / 8

Let’s run it!

Let’s run it!

First: Because there are multiple pairs of 1’s, we start from the leftmost pair.

Press Run . (Or press to step through manually.)

If there are multiple pairs of 1’s,
start with the leftmost pair.
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1
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2
23
1

Second: We can’t start with the leftmost pair of 1’s because there’s only one item on the bottom (a sandwich ).

Therefore, we do the pair of 2’s.

Press Run :

If you can’t start with 1’s because
there’s only one item on the bottom row,
start with the pair of 2’s.
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2
23
1

Third: We’ll need to start with the pair of 2’s again, just like the last time.

Press Run :

If you can’t start with 1’s because
there’s only one item on the bottom row,
start with the pair of 2’s.
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2
1

So this is the final result!

Final result
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1
Slide 5 / 8

Can’t convert to a mathbox

Now, we want to convert this to a mathbox…

But unfortunately: I won’t be able to convert this.

Can’t convert this to a mathbox
1
1

Why not? Because it doesn’t follow this pattern:

There needs to be one
on the top-right and some number of
’s on the bottom-right
One
Some’s

There needs to be exactly one on the top-right, but that’s not the case here.

What’s on the top-right is not .
Instead, it’s . That’s why it cannot be
converted to a mathbox.
1
1

Hmm… if the top-right was a hamburger instead of a sandwich , it could have been converted to .

It was so close!

If the top-right was a hamburger ,
it could have been converted to
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1
Slide 6 / 8

Failure

So: Because it didn’t become a lunchbox that can be converted to at the end…

When you run it…
1
1
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2
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It didn’t become a lunchbox
that can be converted to
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1

Your answer was incorrect.

Filling each icon…
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In the following way was incorrect
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2
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1

Hmm… sad!

Slide 7 / 8

Let’s try again

Hopefully you understood what the problem is asking. So let’s state it again:

  • Fill each icon in a way such that,
  • After you run it,
  • The resulting lunchbox can be converted to .
Challenge:
Fill each icon in such a way that,
1
1
13
2
23
1
After you run it,
the resulting lunchbox can be converted to .
Lunchbox that can be converted to

Again: The “random” lunchbox you came up with was incorrect.

Try to see if you can come up with a different one that works!

This was incorrect
13
2
23
1

Hmm… I now understand the problem, but I don’t know how to solve it!

Slide 8 / 8

Can the villagers solve this problem?

The villagers are so close to getting their mathboxes back, but they’re struggling. Let’s see if they can solve it on the next page!

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3 more intermediate levels left!
Intermediate 1
Intermediate 3
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