Select the correct answerHow many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?Options6578

Break Down the Problem

1. Identify the range of numbers to consider between $106$ and $107$.
2. Determine the condition that the sum of the digits of these numbers must equal $2$.
3. Find all the positive integers that meet the criteria.

Relevant Concepts

• The integers we're interested in are those between $106$ and $107$, which includes only $106$ itself as $107$ is the upper limit and is not included in the range.
• The sum of the digits of $106$ is $1 + 0 + 6 = 7$, which does not equal $2$.

Analysis and Detail

1. The range of integers between $106$ and $107$ is:
   • Only $106$.
2. Check the digits of $106$:
   • Digits: $1$, $0$, and $6$
   • Sum of the digits: $1 + 0 + 6 = 7$

Verify and Summarize

• Since $106$ is the only integer in the given range and the sum of its digits (7) does not meet the requirement of equaling 2, no integers satisfy the criteria.

Final Answer

There are $0$ different positive integers between $106$ and $107$ whose digits sum to $2$.