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P32 [Combinatorics] - Turkish NMO 1st Round - 2013

Source:

April 20, 2013

Problem Statement

How many 1010-digit positive integers containing only the numbers 1,2,31,2,3 can be written such that the first and the last digits are same, and no two consecutive digits are same?
<spanclass=latexbold>(A)</span> 768<spanclass=latexbold>(B)</span> 642<spanclass=latexbold>(C)</span> 564<spanclass=latexbold>(D)</span> 510<spanclass=latexbold>(E)</span> 456 <span class='latex-bold'>(A)</span>\ 768 \qquad<span class='latex-bold'>(B)</span>\ 642 \qquad<span class='latex-bold'>(C)</span>\ 564 \qquad<span class='latex-bold'>(D)</span>\ 510 \qquad<span class='latex-bold'>(E)</span>\ 456