MathDB
2020 Individual #10

Source:

May 1, 2022
2020 Individual

Problem Statement

In the diagram below, for each row except the bottom row, the number in each cell is determined by the sum of the two numbers beneath it. Find the sum of all cells denoted with a question mark.
[asy] unitsize(2cm); path box = (-0.5,-0.2)--(-0.5,0.2)--(0.5,0.2)--(0.5,-0.2)--cycle; draw(box); label("22",(0,0)); draw(shift(1,0)*box); label("??",(1,0)); draw(shift(2,0)*box); label("??",(2,0)); draw(shift(3,0)*box); label("??",(3,0)); draw(shift(0.5,0.4)*box); label("44",(0.5,0.4)); draw(shift(1.5,0.4)*box); label("??",(1.5,0.4)); draw(shift(2.5,0.4)*box); label("??",(2.5,0.4)); draw(shift(1,0.8)*box); label("55",(1,0.8)); draw(shift(2,0.8)*box); label("??",(2,0.8)); draw(shift(1.5,1.2)*box); label("99",(1.5,1.2)); [/asy] <spanclass=latexbold>(A)</span>6<spanclass=latexbold>(B)</span>8<spanclass=latexbold>(C)</span>12<spanclass=latexbold>(D)</span>13<spanclass=latexbold>(E)</span>14<span class='latex-bold'>(A) </span>6\qquad<span class='latex-bold'>(B) </span>8\qquad<span class='latex-bold'>(C) </span>12\qquad<span class='latex-bold'>(D) </span>13\qquad<span class='latex-bold'>(E) </span>14