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.
https://www.mathsisfun.com/games/gomoku.html
http://gomoku.yjyao.com/
https://papergames.io/en/gomoku

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.

26 Feb 2020

The jigsaw puzzle that can express anyone's face

I believe someone who loves puzzles may also like to play with a jigsaw puzzle. I had played a lot with jigsaw puzzles when I was a kid, but I haven't played jigsaw puzzles recently. The last jigsaw puzzle I played with was M.C. Escher's artwork, "Ascending and Descending." As you probably guessed, I started the four corners of the puzzle first, then finished each edge of the picture and built all the pieces with the picture printed. So, what happened was there was a blank area left with no pieces between the edge and the centre of the picture like a moat of a castle. I only had white pieces remaining. This is my bad habit. I will get tired of finishing a jigsaw puzzle as I approach the end, especially when there are no pictures printed on pieces.


If you are the one who does like me, there is an interesting jigsaw puzzle for you. I had one when I was in Japan. It's "Jigazo Puzzle." Jigazo means self-portrait in Japanese. This is a pun that was named by the company Tenyo. Tenyo company was established in 1931 in Tokyo by a famous Japanese magician, Tenyo Shokyokusai. Their products are sets of magic tricks, mysterious goods, for example, savings boxes where money disappears and jigsaw puzzles. Probably, you have seen one of them. They have been producing ordinary jigsaw puzzles, but in 2009, they released an epoch-making jigsaw puzzle, "Jigazo Puzzle."

As you can see from the title, Jigazo Puzzle can make anyone's face using the same 300 pieces. You can make a dog face or cat face too. Those 300 pieces can be used again and again. Firstly, you take someone's face that you want to make and send it to Tenyo's website. They will reply attached with the design drawing. The details can be seen on the video below. Actually, this is so much fun. If you get bored with an ordinary jigsaw puzzle, why don't you try?


 

19 Feb 2020

The creator of unique works using gears, Kango Suzuki

I found a very talented young guy through Twitter whom puzzle lovers would definitely be interested in. His name is Kango Suzuki. Seeing is believing. Firstly, let me show you one of his works, "plock." 
plock
 

This was made for his graduation artwork when he was a university student. This clock doesn't have any electric parts and the time is displayed on the magnetic board in every minute.

Here is some information about Kango.
When he was small, he loved remodeling mechanical pencils and making rubber guns made of split chopsticks. He also loved origami like many other puzzle lovers. He had taken a mechanical engineering course at the local high school and after that he enrolled in Tohoku University of Art and Design, then took the course, product design, as the major study. There was a senior student named Takumi Umemura who made a mechanical clock, and his works inspired Kango. Then, he made the "plock." The "plock" was uploaded to SNS and has received a great response.

His artworks have been presented to several exhibitions and his "time castle" which uses the mechanism of "plock" got the Best Performance Award of MONOZUKURI Cultural Exhibition. The difference of "time castle" from "plock" is using the Theo Jansen mechanism for erasing the numbers. He spent about five months to complete.
 
time castle
 
Those works of his are mostly big, but I found a little funny one called, "Gear Dama." You can buy it from a 3D print service online shop, DMM. Unfortunately, this website is only written in Japanese, but it's worth trying if you really want to buy it.
 
Gear Dama 

His artworks made from complicated mechanism still attract anyone from adults to children. There is attractiveness in his works. I found his interview article on the internet. He says that he loves gears. I love gears too. It's so much fun to watch gears moving. On the interview, he says that he hopes to make a living with making those things he is interested in. Well, probably his dream will come true someday in the future, he is only 26 years old.

He says that he welcomes getting an order of his artwork. If you would like to offer a kind of mechanism or karakuri job to someone, you can contact him from the following page. I hope his dream comes true.
 
Kango Suzuki website (Japanese): https://www.uselesscrown.com/
Kango Suzuki Twitter: https://twitter.com/BellTreeNursing
Contact page: https://www.uselesscrown.com/contact  

ESC

23 Dec 2019

Something mathematical inside (Ring Case)

This is NOT an official Pluredro blog but I cannot help but writing about one of the tools of the new sequential discovery puzzle, Ring Case.
This coming Thursday, December 26th at 07:00 AM Brisbane time is the day of releasing two new kinds of puzzles.

The type of one of the two puzzles is a so-called sequential discovery puzzle which recently became very popular. We have produced more than 100 of them which is quite a lot for us.


This time, I have something to expect that would be fun. I cannot write about the details here. The only thing I can write is about one of the tools inside the puzzle. It would possibly be recognized what for it is by someone interested in mathematics or math enthusiasts. I wonder who will notice it first? Sorry that I cannot write it clearly, but if you notice what it is, then you will be able to guess the inside structure of the puzzle which is not visible from the outside.

He-he, I am looking forward to knowing whether puzzle lovers will like it.