... +1 Otherwise, the entries of the center row, starting from the center entry and working toward either side, must be +1, 1, 1, +1, 1, 1, +1, , 1, 1, +1, 1, 1 But then the width of the ... obtain n 1 na1 > i =1 (n − i)bi ≥ 2(n − 1) n 1 (n − 1) !b1 b2 · · · bn 1 = 2(n − 1) n 1 (n − 1) !a1 a2 · · · an bn > 2(n − 1) n 1 (n − 1) !a1 a2 · · · an ≥ 2(n − 1) a1 n 1 (n − 1) !an Therefore, by noting ... suffice 62 MOP 2004 - 2005 Solutions to the Mathematics Olympiad Test 4 .1 There is a 11 × 11 chessboard Each square on the board has distinct color, and is assigned either a +1 or a 1 Replacing...