1996 AJHSME Problems/Problem 3
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Problem
The 64 whole numbers from 1 through 64 are written, one per square, on a checkerboard (an 8 by 8 array of 64 squares). The first 8 numbers are written in order across the first row, the next 8 across the second row, and so on. After all 64 numbers are written, the sum of the numbers in the four corners will be
Solution
Obviously is in the top left corner,
is in the top right corner, and
is in the bottom right corner. To find the bottom left corner, subtract
from
which is
. Adding the results gives
which is answer
.
See also
1996 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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All AJHSME/AMC 8 Problems and Solutions |