Hex. Carlos Martinho

Transcription

1 Hex Carlos Martinho 1

2 History and Rules

3 Piet Hein The game of HEX was invented by Danish scientist, artist and poet Piet Hein ( ) in Royal University College of Fine Arts (Sweden) to become a painter. University of Copenhagen to study theoretical physics with Niels Bohr. Inventor of technical wonders and games, and writer of poetry, agitating for intercultural understanding and cooperation.

4 Piet Hein Affiliated with Danish newspaper Politiken, during occupation. Mostly known for his Grooks: The road to wisdom? Well, it s plain and simple to express: Err and err and err again, but less and less and less. Losing one glove is certainly painful, but nothing compared to the pain of losing one, throwing away the other and finding the first. Also contributed to Danish architecture and design.

5 Piet Hein Invented the game while trying to disprove the 4-Colour Theorem : The game builds on the simple geometrical property of a planar surface that two lines within a square each connecting a pair of opposite sides must intersect.

6 Would you like to learn Polygon? Piet Hein has constructed a game that can be practiced with equal joy by the chess expert and one who is merely able to hold a pencil. December , Politiken

7 Rules Black and white take turns occupying any unoccupied cell. The one to make an unbroken connection between his two sides wins. Board can be of any size, standard is 11x11.

8 Illustrative Game Red won

9 Real Game

10 Piet Hein The game cannot end in a draw.

11 Piet Hein Hein s conditions for games of real value guided the design: fair progressive finite clear strategic decisive

12 Piet Hein Wrote a regular column on Polygon until August 1943 (49 problems), when he left for Argentine. Problem 1

13 Hex is forgotten for years... Meanwhile...

14 John Nash American John Forbes Nash (1928-) re-invented HEX in Nash entered Princeton University in 1948 in Mathematics, were Go was played a lot (Chess less so). It took him a little over 1 year to finish his 27 pages thesis that would later give him his Nobel Prize in Economics in 1994.

15 John Nash Invented HEX as an example of a game in which the starting player has a winning strategy. The winning strategy is unknown.

16 David Gale David Gale ( ) is a distinguished mathematician and economist (invented Bridg-It game). David Gale was finishing is PhD in Mathematics at Princeton in Gale recognized the entertainment value of Nash s game and created a board available in the common room. The game nicknamed John became quickly popular among the students.

17 David Gale HEX is played on the vertices of a checker board with diagonals in one direction.

18 1953 HEX Parker Brothers

19 Martin Gardner Martin Gardner (1914-) is a American Popular Mathematician and Science writer (over 70 books). Wrote Mathematical Games column for Scientific American from 1956 to 1981.

20 Martin Gardner Wrote a column on HEX in 1957 mentioned in a number of scientific and popular science magazines: Hein as the author of the game. Nash s demonstration that the first player has a winning (but unknown) strategy. A winning strategy for nonsymmetrical boards.

21 Pie rule How to split equally two slices of pie? After the first move, the opponent has the option to switch sides.

22 Today HEX is a prime-example of modern games (XXth century) a connection s game. Played in abstract game competitions (e.g. Covilhã 2009) References Browne (2000) book and website Maarup s thesis (2005) Univ. of S. Denmark Neto & Silva (2008) Jogos Matemáticos, Jogos Abstractos Strategy: Revista Visão: Colecção Jogos do Mundo

23 Go 23

24 Create a variant of HEX Assignment

25 Assignment Due next week Groups of 4 students Create fiction for the game Create a variant in at least 2 of the following: Mode of movement Board layout Objectives For 3 players Playable prototype + Rulebook (max 2 pages with figures).