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Geometry/Polygon Shaped Board games.

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Question
Dear Prof Azeem

http://en.wikipedia.org/wiki/Polygon
http://en.wikipedia.org/wiki/Board_game
http://www.scrabble.com/
http://en.wikipedia.org/wiki/Monopoly_(game)

Will it be difficult to design and construct all Board games geometrically viz scrabble, monopoly, snakes and ladders, ludo etc where maximum number of players can exceed 4 ?.

Games like Chess, Checkers can be excluded as it is a 2 player game.

The advantages could be more number of players can play the Board Game. i.e. n>4.

As a example, The scrabble board game rules will remain the same, more tiles has to be constructed for the same.

For example : Hexagonal Scrabble Board, Pentagonal Monopoly,
Octagonal snakes and ladders, decagon ludo game etc.

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

Answer
Hello Prashant,

Boards are often square or rectangular because of ease of construction and layout.  Your question seems to imply that the number of sides of the board is the limiting factor in the number of players, but that generally is not the case.  Monopoly can support up to 8 players despite its square board.  Snakes and Ladders has a square board, but does that prevent a fifth player from joining?

Most board games are not "one player per side," so the number of sides of the board does not have that great an effect.  More than anything, it would just help with the seating arrangements for the players.  However, it would be much more complicated (and expensive) to design and manufacture these boards.  For these reasons, most boards are square.

If anything, games like chess and checkers would be more interesting on a larger or differently shaped board, as it would transform a head-to-head game into an "every man for himself" scenario, with the potential for alliances.  (There is a game called 4Chess, I believe, which is born out of this principle.)

Thanks for asking,
Azeem

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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