HIP のバックアップ差分(No.12)

追加された行はこの色です。
削除された行はこの色です。
* HISTORY [#k8760bc4]
HIPはマーチン・ガードナー氏によって、発明されたゲームです。

1960年ごろに、Scientific American誌上の[[数学ゲーム>参考文献/別冊サイエンス 数学ゲーム]]で紹介されました。[[参考文献/My Best Mathematical and Logic Puzzles]]に再掲されています。

Square(= 正方形)ができてしまったら負けになるこのゲームを Hipと名付けた理由は、"because of the hipster's reputed  disdain for squares" (流行の先端をいくHipな人たちが Square=四角四面でまじめな人たち を馬鹿にする傾向があるから)、という、ガードナー氏独特のジョークです。
// Hip to be Square by Huey Luis ?

[[参考文献/世界のゲーム事典]]では、スクェア(Square)という名称で紹介されています。


//** Background & Techniques [#of36c11d]
//Here's another interesting Martin Gardner puzzle/game,  originally  published  in  his "Mathematical Recreations" Scientific American magazine column in the 60's.  Which explains his use of the the terms "Hip" and "Hipster" - terms probably unfamiliar to most of today's viewers. 

//In his write-up in the book referenced  above, he relates that for several months after first publication he had  assumed that a tie game was possible.   Then a reader,  computer science major of course, found the tie game configuration.     I'll confess up front that I didn't  succeed in rediscovering the tie game -  this program  plays a tie game when  when computer plays computer, but the game played is simply a random display of the moves from the solution published in Gardner's book.   

//Two classes are defined:  TSquare defines the four corners of any square and identifies the how many of the corners are "owned" by each player.  Squarelist is a TStringlist that has a string version of the  sorted coordinates as a unique key for each square and a Tsquare object stored as a Objects entry.    Squarelist will always contain 105 entries.   In general it has been proven, (not by me),  that n2  x (n2-1) / 12 squares may be formed on an n x n board.

//TPlayer identifies each player, whether it is a computer, and the points currently owned.  When a player makes a move,  the MakeMove procedure  scans Squarelist  to see if this point gives  4 corner ownership to this player for any square in the list  (i.e. he just completed a square and lost).

//Custom cursors are defined to indicate the current player by color, red for player A and blue for player B.   Cursors are contained in resource file  Cursors.res.  Four files used to build Cusors.res;  (Cursors.rc, Genres,bat, Red.cur, and Blue.cur), are included with the source  for completeness but not required for compiling Hip.  Check the Custom Cursors page in the Delphi-Techniques section for more information.

//Addendum August 20, 2008: This is the first update sine the program was posted in 2001.  Version 3 of HIP wad prompted by an email from Sadanand Kasargod [s_vkasargod@yahoo.com]  who spent what must have been a considerable amount of time searching for additional tie games on the 6x6 board.  I had quoted Gardner's comment that there is "essentially" only one way for a a game to end in a tie.  Sadanand found 3 others, but two are the same if one is rotated and the colors reversed.  We settled on three "essentially" different tie games that cannot be transformed into another by rotation, mirroring, or color reversal.    I added a button to replay tie games.  Other changes include the ability to retract moves to aid in studying game and choice of playing on 5x5, 6x6, and 7x7 game board sizes.   Again according to Gardner's book, My Best Mathematical and Logical Puzzles, ties are not possible for 7x7 boards or higher.  

//Addendum August 25, 2008:  When  updating this page last week, I noticed the suggestion for a variation of the rules which requires selecting 2 points for each turn after the first.    I created Version 4 with that option along with some enhancements to the retraction process.   

* BOARD & PIECES [#wbab2ebb]
#ref(./HIP_2setup.jpg,around,right,HIP 初期状態,70%)
オリジナルのルールでは、6x6のマスが並んだ正方形のチェッカーボードを使います。

それぞれのプレーヤーは、それぞれ赤と黒の色の駒(相手と区別がつけば何色でもかまいません)を18個ずつもちます。紙の上でプレーする場合は、自分を識別できる文字、記号、色をつけていきます。

手番のプレーヤーは、開いているマスに一つずつ駒を置きます。

着手は交互でパスはできません。

#clear

* GOAL [#x3809ec3]
自分の手番において、自分の色の四点を結んだ四角形に、一つでも正方形が出来上がってしまったら、負けになります。できる正方形は、斜めに傾いていても、どのようなサイズでも、正方形とみなされます。

#ref(./HIP_3.jpg,HIP)
赤が勝った例


* STRATEGY [#wdd586bb]
6x6ボード中、4個のマスを選んでできる正方形の組は、105個あります。

「真似碁」(相手の手をそっくりそのまま点対称にまねる)戦略が使用できるため、偶数盤を使用するこのゲームは、後手に圧倒的に有利(間違いを犯さなければ、勝つか、引き分けになります。)です。

ガードナー氏本人が、このゲームのリリース後何ヶ月間も、「引き分け」はない、と思っていたところ、オクラホマ大学で数学科の学生であった C. M. マクラリー氏が、このゲームが、「引き分け」で終了することがあることを発見し、デモンストレーションしてくれたということです。「引き分け」で終了するパターンは、「基本的にたった一つ」である、とガードナー氏は言っています。&br;
最近では研究者たちが、この「引き分け」スコアを、コンピュータを使って解いていますが、「引き分け」で終了するパターンは、どうやら全部で3つあるらしい、ということが分かっています。

//ある研究者？は、プログラムでこのゲームを解くために、次のようなクラスを定義しています。
// - 盤上のいずれかの四角形の4つの角と、それらの角が、各プレイヤーによって、いくつずつ所有されているか
// - 

//There is essentially only one way for a complete game to end in a tie.

//For months after I had devised this game I believed that it was impossible for a draw to occur in it. Then C. M. McLaury, a mathematics student at the University of Oklahoma, demonstrated that the game could end in a draw. The problem is to show how the game can be drawn by dividing the 36 cells into two sets of eighteen each so that no four cells of the same set mark the corners of a square.

* NOTE [#g97be6fe]
[[ダウンロードできるリソース>ダウンロードできるリソース#HIP]]に印刷して使える、HIP 6x6, 7x7と5x5のボードがあります。

//Hip by Martin Gardner (around 1960)

//Hip is published in Gardner’s New Mathematical Diversions, published by the Mathematical Association of America,  © 1995.  (This is a revised edition of New Mathematical Diversions from Scientific American, © 1966, which compiled Gardner’s “Mathematical Games” columns from 1959, 1960, and 1961.)  The two players alternately place stones of their color, trying to avoid placing them at the four vertices of any square.

//For example, the Black player would lose if he places a stone at b6, by forming the square b6-a2-e1-f5.  The White player would lose if he places a stone at a1, by forming a1-d1-d4-a4.  Squares can be at any orientation, but they must be geometrically accurate squares -- equilateral and rectangular.  I’ve used Hip in my math classes to try to get across the idea of perpendicular slopes.

//Double-Move Hip (my own variant):

//As Gardner says, Hip on an even-order board is “strictly for squares.”  It is a solved game:  the second player can play the reflection of the first player’s moves and thereby assure himself of eventual victory.  To avoid this problem, I suggest a variant, Double-Move Hip, in which each move consists of placing two stones onto the board, except the first player’s first move.  In this way neither player has a clear advantage.  The same modification might save the game of Bridg-It.

//Hip can be played using Jeff Mallett’s Zillions of Games program, which every abstract gamer should own.  I’ve also made the needed modifications to allow ZoG to play my two-move variants, which are easy.  I wrote Jeff Mallett about them; he may have incorporated the Double-Move Hip variant into the Zillions product by now.
* SEE ALSO [#rb89780a]
#related
- [[Martin Gardner's HIP Game>http://www.delphiforfun.org/programs/HIP.htm]] に、より詳しい情報と、Windows上で動くHIPプログラムがあります
- [[Hip by Martin Gardner>http://home.flash.net/~markthom/html/hip.html]]に、後手有利を修正するためのルール変更案などが掲載されています。
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