Problem:
On the trip home from the meeting where this was constructed, the Contest Chair noted that his airport parking receipt had digits of the form , where , and was the average of and . How many different five-digit numbers satisfy all these properties?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Once and are chosen, the integer is determined. For , we could have , or . For , we could have , or . For , we could have or , and for the only possibility is . Thus there are possibilities when is even. Similarly, there are possibilities when is odd, so the number of possibilities is .
The problems on this page are the property of the MAA's American Mathematics Competitions