# Monthly Archives: July 2011

# When will quantity turn into quality?

Final position of the one and only Botvinnik – Fischer game (1962). Click on the image to enlarge. Analyzed the position with the 64 bit Rybka 3, and even after the depth of 39 moves it still can’t see that this is a draw. I wonder how many moves would reveal this draw for a chess program. It is really hard to estimate. The program tries every variation without repeating a position 3 times – because that means draw by the laws – and without any exchange, because that would also lead to draw in this situation, if white keeps

# An interesting proof of Turán’s theorem

In the past few days I have been reading a nice book about graph theory, including solving the exercises in it. Once I encountered an exercise which I couldn’t solve, so made a little research, and found that the solution is the proof of the Turán’s theorem. The usual proof for this theorem is built on induction, but later I have found a proof which is using a basic inequality. I am sure that I’m not the first one who have seen this solution, although I couldn’t find it on the net yet.