Math Problem Statement

Using a 4 digit number, rearrange the 4 digits to give the highest and lowest values. subtract the lowest result from the highest. start with 6561

Solution

Let's solve the problem step by step.

  1. The given 4-digit number is 6561.

  2. To find the highest value, we rearrange the digits in descending order:

    • Rearranging the digits of 6561 in descending order gives 6651.
  3. To find the lowest value, we rearrange the digits in ascending order:

    • Rearranging the digits of 6561 in ascending order gives 1566.
  4. Now, subtract the lowest value from the highest value: 66511566=50856651 - 1566 = 5085

So, the result is 5085.

Would you like more details or have any further questions?

Here are 5 related questions to explore:

  1. What if you used another 4-digit number, like 4321, and followed the same process?
  2. How would this process work for a 5-digit number?
  3. Can you form a general rule for finding the result for any 4-digit number?
  4. What happens if all the digits of the number are the same (e.g., 5555)?
  5. How does the Kaprekar process relate to this problem?

Tip: When rearranging digits for the highest and lowest values, always sort in descending and ascending order, respectively.

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Math Problem Analysis

Mathematical Concepts

Number Theory
Rearranging Digits
Subtraction

Formulas

Highest number = digits in descending order
Lowest number = digits in ascending order
Difference = Highest number - Lowest number

Theorems

Kaprekar Routine (related to repeated digit operations)

Suitable Grade Level

Grades 4-6