Problem:
The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the three whole numbers be . The set of sums of pairs of these numbers is . Thus , and . If follows that . Therefore the middle number is .
The problems on this page are the property of the MAA's American Mathematics Competitions