28 Mar 2020

Let's play Gomoku Narabe

Hello everyone!
I believe most of you are spending time at home due to the influence of the outbreak of the Coronavirus. Staying at home for a long time period would be stressful, isn't it? Hence, I thought that it would be a good idea to introduce a traditional Japanese indoor game. I feel that if you love puzzles, you will probably love this game as well.

A goban, the board used for the game of Go

The name of the game is "Gomoku Narabe" or just "Gomoku." What you need to play is the same as "Go"; a Go board, and black and white round pieces. If you don't have them, don't worry. You can play it on the internet.

It is said that the game was performed in the Nijo family (Japanese aristocratic kin group) in the mid-1700s and was transmitted to the private sector. If you attended the IPP36 Kyoto in 2016, you probably visited Ninja House (Nijo Jinya). There is the castle of the Nijo family next to the Ninja House.

I don't know how many people know about "Go", probably you may remember one scene of the movie "A Beautiful Mind." An American mathematician, John Nash, who won the Nobel Memorial Prize in Economic Sciences in 1994, loved playing "Go" very much.

A Beautiful Mind – A Game of Go

Sorry, I got off track. Let's explain how to play "Gomoku Narabe."
The rules of "Gomoku Narabe" are simple. Each two players use black and white round pieces. Two people alternately place a piece on the board. To win, you need to line up your 5 pieces without gaps. You can line them up vertically, horizontally or diagonally. Let's have a look at the images below.

As you see at the inside red rectangular of image No.1, white pieces have already lined up 4, so black piece should be placed on the red circle mark, otherwise the black pieces will lose.

Image No.2 below shows the game has advanced a little bit from No.1.

There are 9 white pieces and 10 black pieces which means the next turn is the white piece. If you are the next turn, where will the next move go? The correct answer is where the red circle is.
The following images show what will happen if you didn't place a white piece on the red position.

On image No.3, the white piece seems like making 3 pieces in line. It looks good but wait. Please look at the V-shape light blue lines carefully.

If the next black piece is placed in the red circle position, the black will be in 4 rows. Do you think it's OK because you will be able to block the black pieces?

By placing a black piece, a 3 horizontal black pieces row was completed. (See image No.5)

Therefore, a black piece can be added to the horizontal row, in total it would be 4 pieces. (See image No.6) Oops, this is a very tough situation! That is because there are no white pieces on each ends of the row and nothing can stop the black row growing.

You see, there are 5 black pieces. So, this game is a black win.

"Gomoku Narabe" has various different rules, it depends on the area in Japan. Rule I, taught from my parents, was it is prohibited to line up two crossed rows of 3 lined up pieces. (See image No.8) The reason is those positions are easy to be made and a game will be finished very soon. However, some people think it is OK to arrange those rows. So, please note that there are several rules on "Gomoku Narabe."

I have attached some links of the online "Gomoku Narabe" game.

Before finishing this post, I will introduce a little trivia about "Go." Those black and white pieces look the same but actually, black pieces were made slightly bigger than white because the illusion makes the white pieces look bigger. However, I think mass productions made from plastic are the same size.

I hope you guys will have a good time at home.

Wikipedia - Gomoku: https://en.wikipedia.org/wiki/Gomoku

photo credit: torisan3500 too many dead stones via photopin (license)

7 Mar 2020

The fun method of choosing a winner - Amidakuji

I've been here in Australia since 2011 and have noticed one thing. I haven't seen Amidakuji that is very common in Japan.

Amidakuji is convenient when you need to choose someone who will win a prize or prizes. For example, if there are four people and only one piece of cake remains, one guy can eat the cake. (Please do not say cutting a piece of cake into four.) Japanese people have two ways to solve this situation, one is Janken (Rock paper scissors) and another one is Amidakuji.

Firstly, you need to draw vertical lines the same as the number of people. There are four people, so draw four lines. There is only one piece of cake, so, make one cake mark somewhere under the line. 
Draw several horizontal lines between vertical lines, as many as you want.
However, there is a rule, you cannot exceed a vertical line with a horizontal line which means you cannot overlap the start and end point of a horizontal line with any other horizontal lines. For instance, if it would be a road, it wouldn't be a crossroads.
The next step is hiding the bottom part on which the cake mark has been drawn. The last step is depending on you. If you want to make it certain to be fair, you can ask attendees to add several horizontal lines as they want. Then all the preparation is done!

You ask the attendees to choose one of the vertical lines and write down their names. All right, it's fun time from here!
Pick up one of the names and trace the line from the top. When you meet a horizontal line, you must follow it. (Refer to the picture below) Follow the lines according to the rules and reach the bottom. If there is the cake mark, that name's attendee wins.

The interesting fact is each start point (the place where the name is written) doesn't duplicate with other end points. The picture below describes the easiest way to understand how it works.
I better tell you one more way of drawing horizontal lines. This is the one which Juno did when he was small. It's not common but maybe there are people who do the same. As I have written, the horizontal line should be drawn between two lines and not allowed to exceed a line. However, you can draw a horizontal line outside the amidakuji. Please have a look at the picture below. This looks like cheating, but it works.
It seems like Amidakuji stimulates mathematicians' interests. Some mathematicians have written about Amidakuji. If you are interested in it, please google it.

I'm going to continue to write about something interesting, especially information I can get from Japan. Unfortunately, most Japanese companies and creators don't have English pages on their website. I would be happy if I could introduce something fun to more people.