MathDB
2020 Individual #11

Source:

May 1, 2022
2020 Individual

Problem Statement

The numbers 11, 22, 33, 44, 55, 66 are placed onto the following six spots such that the average of the leftmost two spots, middle two spots, and rightmost two spots are all equal. What is the difference between the largest and smallest possibilities of the number on the shaded spot shown below?
[asy] size(110); draw(Circle((0,0),0.7)); draw(Circle((2,0),0.7));label("11",(2,0)); filldraw(Circle((4,0),0.7),gray); draw(Circle((6,0),0.7)); draw(Circle((8,0),0.7)); draw(Circle((10,0),0.7));label("22",(10,0)); [/asy] <spanclass=latexbold>(A)</span>1<spanclass=latexbold>(B)</span>2<spanclass=latexbold>(C)</span>3<spanclass=latexbold>(D)</span>4<spanclass=latexbold>(E)</span>5<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>2\qquad<span class='latex-bold'>(C) </span>3\qquad<span class='latex-bold'>(D) </span>4\qquad<span class='latex-bold'>(E) </span>5