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The 61st Russian Superfinal (Women) will take place in Moscow from August 18 to 28. Ten players will be taking part in the round robin. The prize fund is about $50,000 with the winner getting roughly $14,000.
Here is the line-up (the Kosintseva sisters declined their invitations due to an intensive tournament schedule):
Alexandra Kosteniuk (2497). Qualification: by rating.
Alisa Galliamova (2492). Qualification: gold at Russian Superfinal 2010.
Valentina Gunina (2487). Qualification: Top League 2011.
Natalia Pogonina (2442). Qualification: silver at Russian Superfinal 2010.
Anastasia Bodnaruk (2431). Qualification: by rating.
Elena Zaiatz (2419). Qualification: Top League 2011.
Tatiana Shadrina (2373). Qualification: Top League 2011.
Olga Girya (2371). Qualification: Top League 2011.
Baira Kovanova (2354). Qualification: Top League 2011.
Daria Charochkina (2310). Qualification: Top League 2011.
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LFKGOoYI
Squares:1 nxn square2 2 (n-1)x(n-1) seuarqs jXj (n-j+1)X(n-j+1) seuarqstotal = sum_{j=1}^n j^2 = n(n+1)(2n+1)/6 seuarqsRectangles:How many jxk rectangles are there?Put one in the top left corner, then slide it over until it hits the top right. That makes (n+1-k) along the top row.Sliding down, there are (n+1-j) down the side.The total number of rectangles issum_{j,k=1}^n (n+1-k)(n+1-j)first fix j and sum over k. you getsum_{j=1}^n (n+1-k)n(n+1)/2This is just a constant times the same sum you just did, so it comes to.n^2(n+1)^2/4.Another way to think of it is that any given rectangle can be specified by four numbers, x1, x2, y1, y2. x1 gives the starting row, x2 the ending row, y1 the starting column, y2 the ending column. Require0