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P07 [Combinatorics] - Turkish NMO 1st Round - 2003

Source:

May 9, 2014

Problem Statement

Starting with the sequence AAAIEE\text{AAAIEE}, we replace AIE\text{AIE} with EA\text{EA}, AE\text{AE} with IE\text{IE}, E\text{E} with AI\text{AI}. After repeating replace operations many times, which of the following cannot be got?
<spanclass=′latex−bold′>(A)</span> AIAIIAI<spanclass=′latex−bold′>(B)</span> AIAIAI<spanclass=′latex−bold′>(C)</span> AIAAA<spanclass=′latex−bold′>(D)</span> AIAA<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ \text{AIAIIAI} \qquad<span class='latex-bold'>(B)</span>\ \text{AIAIAI} \qquad<span class='latex-bold'>(C)</span>\ \text{AIAAA} \qquad<span class='latex-bold'>(D)</span>\ \text{AIAA} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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