Understanding the Problem
To find the smallest number whose digits sum to 14, we need to consider how to arrange the digits effectively. The objective is to minimize the numerical value while ensuring that the sum equals 14.
Key Strategies
- Use the smallest digits first: Starting with lower digits (0-9) helps form a smaller number.
- Maximize the higher place values: Placing larger digits in the leftmost positions reduces the overall value of the number.
Constructing the Number
- Start with the largest digit possible: The largest single digit is 9. If we use 9, we need to make up the sum of 14 with the remaining digits.
- Calculate remaining sum: If we use 9, the remaining sum needed is 14 - 9 = 5.
- Combine digits: The next digit can simply be 5, which gives us the number '95'.
Exploring Alternatives
- If we don't use 9, we could try lower combinations:
- Using 8 would leave us with 14 - 8 = 6, leading to '86'.
- Using 7 would require 14 - 7 = 7, resulting in '77'.
- As we reduce the largest digit, the numbers formed, such as '68', '57', '46', etc., will all be larger than '95'.
Conclusion
After evaluating various combinations, the smallest number whose digits sum to 14 is:
- 95
This is confirmed as no other combination of digits starting from the highest to the lowest gives a smaller result while maintaining the same sum.