# How Many Squares On A Go Board

How Many Squares on a Go Board?

It is a good idea to think about this and write your answer down before reading on. That way you can't change your mind as you go along.

This depends on you knowing what go is and a go board (also called goban). Go is an oriental game played on a board using black and white pieces called stones (actually shell for the white and slate for the black ones).

Originally written by RayTomes before the 1988 New Zealand Go Congress and published in NZ Go Journal in October 1988 in Kami Kaze's Korner. Used with permission. It is extremely funny to me that I wrote the article with the various answers and when I asked the people at the conference, the answers that I got were exactly the same ones as in the article. The last paragraph is an in joke for NZ go players:

Well 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 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?"

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 .....

Life the Universe and Everything

Of course there are loads of pages on the internet about "Life the Universe and Everything" as immortalized by Douglas Adams, but this is the only one (other than some cheap copies) where you will find out what was the question?

Afterthought

It is a matter of some debate what the exact ratio of the sides of the rectangles on a go board are. If the rectangles were 1/13 longer than wide then there would be 30 squares not 42. Some information on go boards are slightly different to the proportions stated here, but they usually refer to the whole playing surface and not the lined part. On my Japanese made board, the the 19x19 lines part is in fact 429 mm x 396 mm which is exactly in the proportion 13:12 that gives the 42 square result.

Anonymous: After Afterthought. Of course on a real go board the measurements are not mathematically precise, making the "no squares" answer correct. And if you don't like picking that nit and have a Chinese board then the small rectangles *are* squares and the 2019 answer is correct!

Another Anonymous: Wouldn't the goban itself be one square?

Answer to Another Anonymous: No, it is rectangular.

Objection

Anonymous: 2019! is a really big number, probably bigger than the number of baryonic particles in the observable universe. RayTomes Anonymous, the "!" after 2109 was for dramatic effect, not for factorial.

__Yet Another Anonymous__? Did everyone forget about the width of the lines? Also I can put as many squares as I want on a goban. Problem solved.