Difference between revisions of "2006 AMC 8 Problems/Problem 22"
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==Solution== | ==Solution== | ||
| − | (D) If the lower cells contain A, B and C, then the second row will contain | + | ('''D''') If the lower cells contain A, B and C, then the second row will contain |
A + B and B + C, and the top cell will contain A + 2B + C. To obtain the | A + B and B + C, and the top cell will contain A + 2B + C. To obtain the | ||
smallest sum, place 1 in the center cell and 2 and 3 in the outer ones. The top | smallest sum, place 1 in the center cell and 2 and 3 in the outer ones. The top | ||
number will be 7. For the largest sum, place 9 in the center cell and 7 and 8 in | number will be 7. For the largest sum, place 9 in the center cell and 7 and 8 in | ||
the outer ones. This top number will be 33. The difference is 33 - 7 = 26. | the outer ones. This top number will be 33. The difference is 33 - 7 = 26. | ||
Revision as of 13:51, 3 November 2012
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 the smallest number possible in the top cell?
Solution
(D) If the lower cells contain A, B and C, then the second row will contain A + B and B + C, and the top cell will contain A + 2B + C. To obtain the smallest sum, place 1 in the center cell and 2 and 3 in the outer ones. The top number will be 7. For the largest sum, place 9 in the center cell and 7 and 8 in the outer ones. This top number will be 33. The difference is 33 - 7 = 26.
