Problem:
Driving along a highway, Megan noticed that her odometer showed (miles). This number is a palindrome - it reads the same forward and backward. Then hours later, the odometer displayed the next higher palindrome. What was her average speed, in miles per hour, during this -hour period?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
In order to get the smallest palindrome greater than , we need to raise the middle digit. If we were to raise any of the digits after the middle, we would be forced to also raise a digit before the middle to keep it a palindrome, making it unnecessarily larger.
So we raise to the next largest value, , but obviously, that's not how place value works, so we're in the s now. To keep this a palindrome, our number is now .
So Megan drove
Since this happened over hours, she drove at
The problems on this page are the property of the MAA's American Mathematics Competitions