- The sum of the digits is 6.
- Each digit is different.
- The number is odd.
What is the greatest 4-digit number that has all of the characteristics listed above?
Correct Answer: 3,201
Since the sum of the digits of the four-digit number is 6, none of the digits can be greater than 6. The greatest four-digit number whose digits sum to 6 is 6,000. However, each digit must be different and the number must be odd. The greatest four-digit number having the given characteristics will have the largest digit in the thousands place. To maximize the number in the thousands place, let the units digit be 1. The thousands place cannot be 5 since 5,001 does not have four different digits. The thousands place cannot be 4 since 4,101 still does not have four different digits. If the thousands place is 3, then the number could be 3,201 and this is the greatest four-digit number that satisfies all three given conditions.
(from the October 20, 1998 test)