Saturday, September 21, 2002 

TWO
persons, Shakuni and Senapati, play a game on a board divided into 3x100
squares. At stake is the kingdom of Gandhara (modernday Kandahar) that
Senapati has annexed from Shakuni. Shakuni gets Dhritarashtra to
announce that Shakuni shall play the first move; and Senapati, thinking
himself to be royal, agrees to give Shakuni this advantage (big
mistake). Shakuni and Senapati move in turn: the first player places
tiles of size 1x2 lengthwise along the axis of the board), the second in
the perpendicular direction. The loser is the one who cannot make a
move. Which of the players can always win (no matter how his opponent
plays), and what is the winning strategy? 
Reading Shakuni's mind was so difficult that only one man tried to play this game with him. He is Puneet Goyal of Nabha, who sent us this answer: "Shakuni always tries to keep one empty box that the Senapati has filled. Consider that the chess is made of 3*10 squares. a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 Suppose a1 represents
First Square, a2 second square, a3 third (b1…in second row and c1…in
third row) and so on. "First, Senapati makes a move. Sena: He fills
a1 a2. Shak: He keeps b1 c1 empty and fills b2 c2. Sena: He fills a3 a4.
Shak: He keep b3 c3 empty and fills b4 c4. This process continues and it
can be extended to 300 squares. Senapati may fill anywhere, or take
second turn, but Shakuni will win if he keeps empty column just ahead of
every move made by Senapati. My solution is desi." Letting Senapati
play first would surely have ruined Shakuni. Write at The Tribune or
adityarishi99@yahoo.co.in. 