IndexHow Russia will try to bring peace to SyriaTower problem 1Tower problem 2How Russia will try to bring peace to SyriaTower polynomials are the number of ways place k non-attacking rooks on an original board where no two rooks can be in the same row or column. The general formula for calculating the number of non-attacking rook arrangements is: Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay The formula for calculating non-attacking towers is The following polynomials show the layout of each tower. The notation Rn(x) indicates the number of towers used, for example r1(x) means 1. The powers of x indicate the number of towers, so for example the first row means that 1 tower can be arranged 1 way and zero rooks can only be arranged in one way.Rook Problem 1A famous problem called the “eight rook problem” by HE Dudeney shows that the maximum number of non-attacking rooks on a board is eight by placing them on a diagonal of the board covering 8 squares. The question of the problem “How many ways can eight rooks be placed on an 8×8 chessboard so that neither attack the other?”. The answer is eight factorial since it behaves like an injective function. On the first row of the board the rook has eight positions to place on. Then the rook has seven positions it can be in in the second row and so on until the eighth row where the rook only has one position it can be in. Consequently, there are 8 different ways in which a rook can be placed on a chessboard without attacking each other! which equals 40,320. Please note: this is just an example. Get a custom paper from our expert writers now. Get a Custom Essay Tower Problem 2 Another problem related to towers is "How many ways can k towers be arranged on an m?" × na edge so that they don't attack each other?”. To address this problem k should be less than or equal to the number m and n. Since the number of rows is m of which k must be chosen, the formula becomes mCk. The set of k columns on which to place the towers can also be chosen in nCk ways. Since the ways to choose k from M and N are independent of each other, the formula becomes mCk multiplied by nCk ways to choose the square on which to place the tower. However, to calculate the number of non-attacking rook arrangements, the number of ways to choose the square to place the tower on must be multiplied by k!, since this is the number of ways k rooks can be arranged so that they do not attack each other. . Consequently the number of ways you arrange for non-attacking rooks is mCk times nCk times k!.