Problem:
The three row sums and the three column sums of the array
are the same. What is the least number of entries that must be altered to make all six sums different from one another?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If only three entries are altered, then either two lines are not changed at all, or some entry is the only entry in its row and the only entry in its column that is changed. In either case, at least two of the six sums remain the same. However, four alterations are enough. For example, replacing by , by , by , and by results in the array
for which the six sums are all different.