Problem:
How many four-digit numbers have the property that the three-digit number obtained by removing the leftmost digit is one ninth of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let denote the leftmost digit of and let denote the three-digit number obtained by removing . Then and it follows that . Dividing both sides by 8 yields . All the values of in the range 1 to result in three-digit numbers.
The problems on this page are the property of the MAA's American Mathematics Competitions