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(190) 3

Part of 1988 Tournament Of Towns

Problems(1)

TOT 190 1988 Autumn J3 S=sum a_k /k

Source:

3/6/2021
Let a1,a2,...,ana_1 , a_2 ,... , a_n be an arrangement of the integers 1,2,...,n1,2,..., n. Let S=a11+a22+a33+...+an1.S=\frac{a_1}{1}+\frac{a_2}{2}+\frac{a_3}{3}+...+\frac{a_n}{1}. Find a natural number nn such that among the values of SS for all arrangements a1,a2,...,ana_1 , a_2 ,... , a_n , all the integers from nn to n+100n + 100 appear .
number theorypermutations