TIOL-DDT 1241 · Friday, 20 November 2009 · story 3 of 4

Dui-Doku – Two-player variant of Sudoku

Apart from being a brilliant Economics Professor, Kaushik Basu is credited with creating a game called Dui-doku. The reason for this he says is, “I have wasted a lot of time on Sudoku and so developed the game of Dui-doku to help double the wastage of time by drawing two persons at a time into it.”

Why the name - Dui-doku?

Basu says, “because this is a two-player game, ‘dui' or ‘dvi' in Sanskrit means two, and all such games are considered to be of no value unless they have a mysterious oriental name.”

He said that it clearly falls in the category of games for which Zermelo's theorem applies.

In game theory, Zermelo's theorem , named after Ernst Zermelo, says that in any finite two-person game of perfect information in which the players move alternatively and in which chance does not affect the decision making process, if the game cannot end in a draw, then one of the two players must have a winning strategy.

So it must be that in a Dui-doku one of the following is true:

(1) The first-mover can always ensure a win,

(2) the second-mover can always ensure a win, and

(3) both players can always ensure a draw.

But which of these is true? Prof. Basu has no answer. He wants the players to find out. One thing is sure – babus in North Block cannot play games with Basu – except of course DUI-DOKU!