MathDB

5

Part of 2009 South East Mathematical Olympiad

Problems(1)

find │M│

Source:

9/18/2010
Let X=(x1,x2,......,x9)X=(x_1,x_2,......,x_9) be a permutation of the set {1,2,…,9}\{1,2,\ldots,9\} and let AA be the set of all such XX . For any X∈AX \in A, denote f(X)=x1+2x2+⋯+9x9f(X)=x_1+2x_2+\cdots+9x_9 and M={f(X)∣X∈A} M=\{f(X)|X \in A \}. Find ∣M∣|M|. (∣S∣|S| denotes number of members of the set SS.)
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