Saturday, July 27, 2002 

"FOR all their wealth of content, for all the sum of history and social institution invested in them, music, mathematics, and chess are resplendently useless (applied mathematics is a higher plumbing, a kind of music for the police band). They are metaphysically trivial, irresponsible. They refuse to relate outward, to take reality for arbiter. This is the source of their witchery," says G. Steiner. Mr Spock of chess, master
of logic, tutor of Garry Kasparov, father of modern "Soviet"
chess, Mikhail Botvinnik, whose method was tireless prematch research,
once said that chess was the art that complemented the science of logic,
just as music complemented acoustics, and painting optics, etc. In 1948,
he became the World Champion, a post made vacant by the death of
Alekhine in 1946. Botvinnik relinquished the world title on two
occasions, only to win it back in revenge matches: the only player ever
to have achieved this. 
Let eij be the result of the game between the ith and the jth player. eij={ 1 if ith player wins; 1 if jth player wins; 0 if both have a draw or i=j} Is it possible that for every particular player, the sum of points of the players who were beaten by him is greater than the sum of points of the players who beat him? This means: is it possible that: n å eij C j >0 " i j=1 where C j is a score of the jth player. Multiplying these inequalities by C i and summing up for all i, we find that n å eij C i C j >0 i,j=1 which is impossible, since the left hand expression is 0 because eij = eji for all i, j. For every particular player, the sum of points of the players who were beaten by him is, thus, neither greater nor less than the sum of points of the players who beat him. Master Mayur Bhatt of Sujanpur Tihra and Pawan Goyal answer "no", but give no reason for it as well. "No, it is not possible, because it is true only for the players who beat all other players," says Sudhanshu Arya. Honey Deep says that it is possible (checkmate!). Write at The Tribune or [email protected] *DELAYED BUS: Correct solution to the 'Japanese chip' problem was also received from Mohit Bhambri of Patiala. — Aditya Rishi
