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P23 [Combinatorics] - Turkish NMO 1st Round - 2002

Source:

August 10, 2014

Problem Statement

What is the arithmetic mean of the smallest elements of rr-subsets of set {1,2,…,n}\{1, 2, \dots , n\} where 1 \leq r \leq n?
<spanclass=′latex−bold′>a)</span> n+1r+1<spanclass=′latex−bold′>b)</span> r(n+1)r+1<spanclass=′latex−bold′>c)</span> nrr+1<spanclass=′latex−bold′>d)</span> r(n+1)(r+1)n<spanclass=′latex−bold′>e)</span> None of above <span class='latex-bold'>a)</span>\ \dfrac{n+1}{r+1} \qquad<span class='latex-bold'>b)</span>\ \dfrac{r(n+1)}{r+1} \qquad<span class='latex-bold'>c)</span>\ \dfrac{nr}{r+1} \qquad<span class='latex-bold'>d)</span>\ \dfrac{r(n+1)}{(r+1)n} \qquad<span class='latex-bold'>e)</span>\ \text{None of above}
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