10. Freda wants to write a number in each of the nine cells of this figure so that the sum of the three numbers on each diameter is 13 and the sum of the eight numbers on the circumference is 40 .
What number must be written in the central cell?
A 3
B 5
C 8
D 10
E 12
Solution
A

Each diameter has the same sum and contains the central cell, so the pair at the end of each diameter must have the same sum. These four pairs have sum 40 , so each pair must have sum 10. Since each diameter has sum 13 , the central number must be 3 .