MathDB
P06 [Combinatorics] - Turkish NMO 1st Round - 2001

Source:

April 18, 2014

Problem Statement

How many 55-digit positive numbers which contain only odd numbers are there such that there is at least one pair of consecutive digits whose sum is 1010?
<spanclass=latexbold>(A)</span> 3125<spanclass=latexbold>(B)</span> 2500<spanclass=latexbold>(C)</span> 1845<spanclass=latexbold>(D)</span> 1190<spanclass=latexbold>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 3125 \qquad<span class='latex-bold'>(B)</span>\ 2500 \qquad<span class='latex-bold'>(C)</span>\ 1845 \qquad<span class='latex-bold'>(D)</span>\ 1190 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}