Solving the Mystery Number: A Digits Puzzle

The world of puzzles is fascinating, especially those that rely on numerical reasoning. In this article, we will delve into a specific numerical puzzle, breaking down the steps to find the solution and providing a comprehensive guide for solving similar puzzles in the future.

Understanding the Problem

The mystery number is a 6-digit number composed of the digits 3, 0, 9, 8, 4, and 7. The clues provided help us determine the position of each digit within the number. Let's decode the puzzle step by step.

Clues and Equations

Let's denote the digits of the number as follows:

A hundred thousand digit B ten thousand digit C thousand digit D hundred digit E ten digit F unit digit

Based on the given clues:

A is 4 less than the hundreds digit. The tens digit is 2 times bigger than the thousands digit. A is 1 less than the thousand digit.

We can derive the following equations:

A D - 4 E 2C A C - 1

Solving the Equations

Let's solve these equations step by step by substituting the values and testing the possible solutions.

Step 1: Substitute equation (3) into equation (1)

A C - 1

A D - 4

C - 1 D - 4

Now we have:

A C - 1 D C 3 E 2C

Now we need to test possible values forC. The digits must be among 3, 0, 9, 8, 4, and 7.

Step 2: Test possible values for C

IfC 4:

A 4 - 1 3 D 4 3 7 E 2 * 4 8

So far, the number is:

A 3 B is yet to be determined. C 4 D 7 E 8

This leaves us with the digits 0 and 9 for B and F. Let's test both possibilities:

- If B 0, the number is 304780.

- If B 9, the number is 394780.

Step 3: Check the possibilities

Check for 304780:

A 3, Hundred thousand digit. B 0, Ten thousand digit. C 4, Thousand digit. D 7, Hundred digit. E 8, Ten digit. F 0, Unit digit.

Let's check:

A D - 4, 3 7 - 4, True. E 2C, 8 2 * 4, True. A C - 1, 3 4 - 1, True.

Check for 394780:

A 3, Hundred thousand digit. B 9, Ten thousand digit. C 4, Thousand digit. D 7, Hundred digit. E 8, Ten digit. F 0, Unit digit.

Let's check:

A D - 4, 3 7 - 4, True. E 2C, 8 2 * 4, True. A C - 1, 3 4 - 1, True.

Both numbers satisfy the conditions, and they do not use all the digits provided. Therefore, the mystery number can be either 304780 or 394780.

Conclusion

The mystery number can be either 304780 or 394780 based on the given clues. Both numbers fulfill the conditions stated.

Additional Information

This puzzle is a great example of how numerical reasoning can be fascinating and challenging. Understanding how to break down the problem and follow the clues step by step is essential in finding the solution. If you have any other numerical puzzles or questions, feel free to explore and solve them using similar methods.