Explanation:

Playing with Numbers is a chapter that teaches students how to form numbers using different digits and how to check if a number is divisible by a certain number. In this question, we are asked to replace the "_" with the smallest and greatest digit to form a number that is divisible by 3.

Steps to Solve the Problem:

1. Find the sum of the digits in the number
2. Determine if the sum is divisible by 3
3. If the sum is not divisible by 3, then find the smallest and greatest digit that will make the sum divisible by 3
4. Replace the "_" with the smallest and greatest digit found in step 3
5. Check if the new number is divisible by 3

Example:

639_16

1. Sum of digits = 6+3+9+1+6 = 25
2. 25 is not divisible by 3
3. The smallest digit that can be added to 25 to make it divisible by 3 is 1, and the greatest digit is 4
4. Replace "_" with 1 and 4
5. New numbers are 639116 and 639416
6. Check if both numbers are divisible by 3
- 6+3+9+1+1+6 = 26 (not divisible by 3)
- 6+3+9+4+1+6 = 29 (not divisible by 3)

Conclusion:

In this problem, we learned how to determine if a number is divisible by 3 and how to find the smallest and greatest digit that can be added to the sum of the digits to make it divisible by 3. We also learned how to replace the "_" with the smallest and greatest digit to form a number that is divisible by 3.

Answer is 5