Solving a Three-Digit Number Puzzle: A Comprehensive Guide for SEO

In this article, we will explore a fascinating three-digit number puzzle and break down the process of solving it step-by-step. Understanding such puzzles and their solving methods can be a helpful tool in improving your SEO skills, particularly in content creation and keyword optimization.

The Problem Statement

Consider the following problem statement:

The sum of the digits of a three-digit number is 17. The sum of the first and third digits is one more than three times the second digit. If the digits are reversed, the new number is 297 greater than the original number. What is the original number?

Defining Variables and Constraints

We can denote the three-digit number as (abc), where (a, b,) and (c) are the digits of the number. The problem can be translated into a set of equations as follows:

(a b c 17) (a c 3b 1) (100c 10b a 100a 10b c 297)

Breaking Down the Problem

Let's begin by simplifying and solving these equations step-by-step:

Step 1: Simplifying the Equations

The third equation simplifies to:

(100c 10b a 100a 10b c 297)

Subtracting (10b) from both sides:

(100c a 100a c 297)

Subtracting (c) and (a) from both sides:

(99c - 99a 297)

Dividing both sides by 99:

(c - a 3)

This allows us to express (c) in terms of (a):

(c a 3)

Step 2: Substituting (c) into the Earlier Equations

Substituting (c a 3) into the first equation:

(a b (a 3) 17)

Combining like terms:

(2a b 3 17)

Subtracting 3 from both sides:

(2a b 14)

Substituting (c a 3) into the second equation:

(a (a 3) 3b 1)

Combining like terms:

(2a 3 3b 1)

Subtracting 1 from both sides:

(2a 2 3b)

Dividing by 3:

(3b 2a 2)

Step 3: Simplifying Further

From the first simplified equation:

(b 14 - 2a)

Substituting this expression for (b) into the second simplified equation:

(3(14 - 2a) 2a 2)

(42 - 6a 2a 2)

Adding (6a) to both sides:

(42 - 2 8a)

(40 8a)

(a 5)

Substituting (a 5) back into the expression for (b) and (c):

(b 14 - 2(5) 4)

(c 5 3 8)

Thus, the digits of the original number are (a 5, b 4,) and (c 8). Therefore, the original three-digit number is:

(548)

Verification

Let's verify the conditions:

Sum of the digits: (5 4 8 17) Sum of the first and third digits: (5 8 13), which is indeed one more than three times the second digit: (3 times 4 1 13) Reversed number: (845 - 548 297)

All conditions are satisfied, confirming that the original number is indeed (548).

Conclusion

This comprehensive guide not only solves the problem but also provides a clear and structured approach to solving similar puzzles. Such puzzles are excellent for honing your analytical skills and can be immensely beneficial in SEO content creation, where logical reasoning and problem-solving are critical. Whether you are creating educational content or optimizing technical SEO solutions, understanding these concepts can significantly enhance your content’s appeal and engagement.