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P19 [Combinatorics] - Turkish NMO 1st Round - 2004

Source:

November 15, 2013

Problem Statement

If we have a number xx at a certain step, then at the next step we have x+1x+1 or −1x-\frac 1x. If we start with the number 11, which of the following cannot be got after a finite number of steps?
<spanclass=′latex−bold′>(A)</span> −2<spanclass=′latex−bold′>(B)</span> 12<spanclass=′latex−bold′>(C)</span> 53<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ -2 \qquad<span class='latex-bold'>(B)</span>\ \dfrac 12 \qquad<span class='latex-bold'>(C)</span>\ \dfrac 53 \qquad<span class='latex-bold'>(D)</span>\ 7 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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