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
Answer Choices:
A. 130
B. 131
C. 132
D. 133
E. 134
Solution:
The first row is 1,2,3,…,7,8 and the last row is 57,58,59,…,63,64. Thus the four corner numbers are 1,8,57, and 64, and their sum is 130.
OR
Listing the array yields:
191725334149572101826344245058311192735435159412202836445260513212937455361614223038465462715233139475563816243240485664
The sum of the numbers in the corners is 130.
Answer: A.
The problems on this page are the property of the MAA's American Mathematics Competitions