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MATH / Three different one-digit positive integers are placed in the bottom row of…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cell? [asy]
path box=(0,0)--(1,0)--(1,1)--(0,1)--cycle;
draw(box);
draw(shift(1.5,0)*box);
draw(shift(3,0)*box);
draw(shift(.75,2)*box);
draw(shift(2.25,2)*box);
draw(shift(1.5,4)*box);
picture p;
draw(p, (.6,.2)--(.95, .8), EndArrow);
draw(p, (1.9,.2)--(1.55, .8), EndArrow);
draw(p, (1.25, .8)--(1.25,.6));
draw(p, (1.15, .7)--(1.35,.7));
add(shift(0,1)*p);
add(shift(1.5,1)*p);
add(shift(.75,3)*p);
[/asy]

level

Level 3

type

Counting & Probability

Discussion

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Source and history

task_id
f16cc0ab-65d7-593b-bda1-7b0df65b7cc3
task_key
counting~5fand~5fprobability--test--f16cc0ab-65d7-593b-bda1-7b0df65b7cc3
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import