Difference between revisions of "2006 AMC 8 Problems/Problem 22"
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==See Also== | ==See Also== | ||
{{AMC8 box|year=2006|n=II|num-b=21|num-a=23}} | {{AMC8 box|year=2006|n=II|num-b=21|num-a=23}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 19:43, 15 April 2023
Contents
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?
Solution
If the lower cells contain and
, then the second row will contain
and
, and the top cell will contain
. To obtain the
smallest sum, place
in the center cell and
and
in the outer ones. The top
number will be
. For the largest sum, place
in the center cell and
and
in
the outer ones. This top number will be
. The difference is
.
Video Solution
https://youtu.be/2Ujn43JWiwM Soo, DRMS, NM
https://www.youtube.com/watch?v=_FAL-t93VIk ~David
See Also
2006 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.