Unfortunately, I don't understand the game that introduces and illustrates the theorem.

As I understand it, you are supposed to fill in 4 blanks to complete a permutation of the first 10 positive integers. To me, this means all you have to do is see which 4 numbers are missing, and put them in the blanks in any order.

I looked at a few answers, and I see that the hidden numbers are indeed the numbers I expected, placed in ascending or descending order depending on the colors of the visible numbers. So what? Is this an example of killing a fly with a sledgehammer, or am I missing something about the game?

Yes, it is really nice.

>Unfortunately, I don't understand the game that introduces
>and illustrates the theorem.

From what you wrote I gather you have full understanding of the applet.

>As I understand it, you are supposed to fill in 4 blanks to
>complete a permutation of the first 10 positive integers. To
>me, this means all you have to do is see which 4 numbers are
>missing, and put them in the blanks in any order.

Not quite. The theorem claims existence of either ascending or descending sequence. The blanks are to be filled by one of these.

>I looked at a few answers, and I see that the hidden numbers
>are indeed the numbers I expected, placed in ascending or
>descending order depending on the colors of the visible
>numbers.

Right.

>So what?

So you (or your students) can check whether they indeed got the theorem right.

>Is this an example of killing a fly with a
>sledgehammer,

You may call it that, of course. Although I can assure you that the applet is quite simple. I would rather compare it to a, say, 3/8" drill than to a 6" sledgehammer.

>or am I missing something about the game?

Nope, I believe you got it right.