MathDB
1987 AMC 12 #12 - Secretary's Letter

Source:

December 31, 2011
AMC

Problem Statement

In an office, at various times during the day the boss gives the secretary a letter to type, each time putting the letter on top of the pile in the secretary's in-box. When there is time, the secretary takes the top letter off the pile and types it. If there are five letters in all, and the boss delivers them in the order 1 2 3 4 51\ 2\ 3\ 4\ 5, which of the following could not be the order in which the secretary types them?
<spanclass=latexbold>(A)</span> 1 2 3 4 5<spanclass=latexbold>(B)</span> 2 4 3 5 1<spanclass=latexbold>(C)</span> 3 2 4 1 5<spanclass=latexbold>(D)</span> 4 5 2 3 1<spanclass=latexbold>(E)</span> 5 4 3 2 1 <span class='latex-bold'>(A)</span>\ 1\ 2\ 3\ 4\ 5 \qquad<span class='latex-bold'>(B)</span>\ 2\ 4\ 3\ 5\ 1 \qquad<span class='latex-bold'>(C)</span>\ 3\ 2\ 4\ 1\ 5 \qquad<span class='latex-bold'>(D)</span>\ 4\ 5\ 2\ 3\ 1 \\ \qquad<span class='latex-bold'>(E)</span>\ 5\ 4\ 3\ 2\ 1