MathDB
2019 Individual #18

Source:

May 1, 2022
2019 Individual

Problem Statement

A class of 1010 children is divided into 55 pairs of partners. Each pair of partners sits next to each other and works together during class. One day, the teacher decides he wants to divide the class into two groups. In order to make sure the students work with new people, he makes sure not to put any student in the same group as his or her partner. How many different ways can he divide the class into these two groups?
<spanclass=latexbold>(A)</span>2<spanclass=latexbold>(B)</span>5<spanclass=latexbold>(C)</span>10<spanclass=latexbold>(D)</span>16<spanclass=latexbold>(E)</span>32<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>5\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>16\qquad<span class='latex-bold'>(E) </span>32