A three‐digit number satisfies the following conditions: The digits are consecutive whole numbers in increasing order; the sum of each pair of digits is greater than 14 and less than 18; and the tens digit is an even number. What is the number?

Let the three-digit number be represented as \( xyz \), where \( x \), \( y \), and \( z \) are the digits of the number. According to the conditions:

1. The digits \( x \), \( y \), and \( z \) are consecutive whole numbers in increasing order. Hence, we have:
   \[
   x = y - 1 \quad \text{and} \quad z = y + 1
   \]
   So the number can be represented as \( (y - 1), y, (y + 1) \).

2. The sum of each pair of digits is greater than 14 and less than 18. We have three pairs to consider:
   \[
   x + y > 14 \quad \text{and} \quad x + y < 18
   \]
   \[
   y + z > 14 \quad \text{and} \quad y + z < 18
   \]
   \[
   x + z > 14 \quad \text{and} \quad x + z < 18
   \]

   Substituting \( x = y - 1 \) and \( z = y + 1 \) into these inequalities:

   - For \( x + y \):
     \[
     (y - 1) + y = 2y - 1
     \]
     \[
     14 < 2y - 1 < 18 \quad \Rightarrow \quad 15 < 2y < 19 \quad \Rightarrow \quad 7.5 < y < 9.5
     \]
     So \( y = 8 \).

   - For \( y + z \):
     \[
     y + (y + 1) = 2y + 1
     \]
     \[
     14 < 2y + 1 < 18 \quad \Rightarrow \quad 13 < 2y < 17 \quad \Rightarrow \quad 6.5 < y < 8.5
     \]
     Again, \( y = 8 \).

   - For \( x + z \):
     \[
     (y - 1) + (y + 1) = 2y
     \]
     \[
     14 < 2y < 18 \quad \Rightarrow \quad 7 < y < 9
     \]
     So \( y = 8 \).

3. The tens digit \( y \) is an even number, which is true since \( y = 8 \).

Thus, the digits of the number are \( 7 \), \( 8 \), and \( 9 \), and the number is \( 789 \).

The number is \( \boxed{789} \).

Would you like more details or have any questions?

Here are some related questions:
1. How do we solve inequalities for digit-based problems?
2. What other types of sequences can we explore for digit-based puzzles?
3. Can we use similar approaches for problems involving descending digits?
4. How do we handle cases where the sum of digits involves different ranges?
5. Are there alternative ways to verify the conditions of a solution?

**Tip:** Always simplify inequalities step-by-step to avoid miscalculations when solving for unknowns in digit problems.

This problem involves finding a three-digit number where the digits are consecutive whole numbers. Using inequalities and the properties of digits, the solution explains how to satisfy conditions such as the sum of digits being between 14 and 18. Suitable for Grades 6-8.

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