How Many Squares are there on a Go Board?

Kami Kaze: How many squares are there on a go board? Go away and think about it for a while and then come back and we will discuss it!

20 kyu player: 361 of course.
Kami Kaze: Wrong...

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


(A pause follows, but frantic calculations occur.)

1 dan player: 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!
Kami Kaze: But wrong...

3 dan player: 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.
Kami Kaze: And still wrong...

(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?"

Marvin: I tried to tell them, but you know what humans are like, they have the attention span of a dead gnat. Here I am with a brain the size of a planet, and having worked out all the possible games of go, the meaning of life is to have two eyes except in seki when ......

Crowd: Which restaurant shall we eat at tonight?

(The crowd departs leaving Marvin talking to himself.)

Marvin: I can tell you what the strictly correct komi is if you really want to know? Oh never mind me, just carry on. I haven't got any feelings of course .....

(From Sensei's Library)