Baduk squares conversation

Have you ever wondered how many squares are on a Baduk board?

How Many Squares on a Go Board - October 1988

Kami Kaze: How many squares are there on a go board?
Go away and think about it and write your answer down before reading on!

20 kyu: 361 of course.
"Wrong" says Kami Kaze.

10 kyu: No silly, that's the number of vertices. There are 18x18 or 324 squares.
"Wrong" says Kami Kaze.

(A pause follows, but frantic calculations occur.)

1 dan: Aha, there are also squares 2x2 and 3x3 and so on, which means that the total is 18x18 + 17x17 and so on making a grand total of 2109!

crowd: Aaaahh very clever!

"But wrong" says Kami Kaze.

3 dan: You've forgotten that they aren't squares, they are rectangles. There are no squares on a go board!

crowd: That's a dirty trick.
"And still wrong" says Kami Kaze.

(Another pause, and many puzzled faces.)

crowd: Well how many squares are there on a go board then?

Kami Kaze: It is perfectly true that the smaller areas are rectangles, and each of these is one twelth longer than it is wide. Therefore, if we take an area twelve rectangles long and thirteen wide, we have a large square, and this is the only size which works. There are (19-12 ) x (19-13) or 42 such squares. The answer is forty-two.

Douglas Adams: We all knew the answer, it's the question that we didn't know. Thank you Kami Kaze, the whole question of the meaning of Life, The Universe and Everything is simply "How many squares are there on a go board?"

- adoreme