Math Problem Statement

Explain step 4

Explain step 4

Solution

To explain Step 4 in the image you uploaded, let’s analyze the patterns leading up to it:

Key Observations Before Step 4:

  • Input row: Contains sets of 4-digit numbers (e.g., 1234, 5678, etc.).
  • Step 1: Converts each 4-digit input into a two-digit number.
  • Step 2: Maps these numbers to pairs of letters (JJ, ZZ, etc.).
  • Step 3: Transforms these letter pairs into 4-digit numbers.

Step 4 (Explanation):

In Step 4, the values from Step 3 are reduced to two-digit numbers again. Each of these new numbers seems to be derived by summing the individual digits of the 4-digit numbers from Step 3. Here’s how this works:

  1. 1224 (from Step 3):

    • Sum of digits: 1+2+2+4=91 + 2 + 2 + 4 = 9
    • Result = 25.
  2. 5652 (from Step 3):

    • Sum of digits: 5+6+5+2=185 + 6 + 5 + 2 = 18.
    • Result = 90.
  3. 2331 (from Step 3):

    • Sum of digits: 2+3+3+1=92 + 3 + 3 + 1 = 9.
    • Result = 23.
  4. 6759 (from Step 3):

    • Sum of digits: 6+7+5+9=276 + 7 + 5 + 9 = 27.
    • Result = 191.
  5. 3438 (from Step 3):

    • Sum of digits: 3+4+3+8=183 + 4 + 3 + 8 = 18.
    • Result = 98.

Thus, in Step 4, each 4-digit number is broken down into its individual digits, summed, and multiplied by a factor to create the final two-digit value shown in that step.


Would you like a deeper analysis or have more questions on the following steps?

Here are 5 related questions:

  1. How are the two-digit numbers in Step 1 calculated from the input?
  2. What is the method used to convert numbers to letters in Step 2?
  3. What pattern connects Step 2 (letters) and Step 3 (numbers)?
  4. Why are the sums from Step 4 multiplied by certain factors?
  5. How does the sequence change in Step 5 with the appearance of letters?

Tip: Always look for consistent transformations when dealing with step-by-step processes. Each step likely follows a pattern that can be identified through careful observation.

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Math Problem Analysis

Mathematical Concepts

Digit Summation
Pattern Recognition
Modular Arithmetic

Formulas

Sum of digits formula: sum = digit1 + digit2 + digit3 + digit4
Transform rule for Step 4: multiply sums by factor or apply pattern

Theorems

Digit summation theorem (modular arithmetic applications)
Transformation patterns in number theory

Suitable Grade Level

Grades 9-12