Use the digits 3, 9, 7, and 6 to make 6 different numbers between 300 and 400.

Question

Repetition of digits is not allowed. 1. Write the numbers in order. 2. Find the pair of numbers with: a. The smallest estimated difference b. The largest estimated difference c. A difference as close as possible to 200 d. A difference as close as possible ro 400

Answer 1

1. The 6 numbers must all start with 3 and consist of exactly 3 digits. This limits the numbers to 367, 369, 376, 379, 396, 397.

2a) the difference between 397 and 396 is 1, the smallest difference.

All the possible 15 differences are:

1=397-396, 2=369-367, 3=379-376, 7=376-369, 9=376-367, 10=379-369, 12=379-367, 17=396-379, 18=397-379, 20=396-376, 21=397-376, 27=396-369, 28=397-369, 29=396-367, 30=397-367.

2b) the difference between 397 and 367 is 30, the largest difference.

2c) and d),  because the numbers are in the range 300 to 400, the maximum difference cannot exceed 100, so that’s the closest the difference can be to either 200 or 400 (?) Therefore 397-367=30 is the closest difference.