Math Problem Statement

What is the missing number in the third arrangement where the surrounding numbers are 28, 4, 23, and 6?

Solution

The image you uploaded contains a set of 3 puzzles where the numbers are arranged in a cross-like pattern with a central number in each arrangement. Each puzzle has four surrounding numbers, and the central number is either given or needs to be determined, depending on the puzzle. The goal is to figure out the pattern and complete the missing number in the third arrangement.

Breakdown of the Puzzles:

  • First arrangement (A):

    • Surrounding numbers: 25, 7, 21, 5
    • Central number: 24
  • Second arrangement (B):

    • Surrounding numbers: 29, 12, 26, 8
    • Central number: 30
  • Third arrangement (C):

    • Surrounding numbers: 28, 4, 23, 6
    • Central number: ?

Identifying the Pattern:

Let's analyze the relationship between the surrounding numbers and the central number in the first two arrangements.

  1. For arrangement (A): (25+7+21+5)4=584=14.5\frac{(25 + 7 + 21 + 5)}{4} = \frac{58}{4} = 14.5 This doesn't match the central number of 24 directly, so we should look for another pattern. Notice: (2521)+(75)=4+2=6and24=4×6(25 - 21) + (7 - 5) = 4 + 2 = 6 \quad \text{and} \quad 24 = 4 \times 6 Here, the difference between opposite pairs is used and then multiplied by 4.

  2. For arrangement (B): (2926)+(128)=3+4=7and30=4×7(29 - 26) + (12 - 8) = 3 + 4 = 7 \quad \text{and} \quad 30 = 4 \times 7 Again, the difference between opposite pairs is taken, then multiplied by 4 to get the central number.

Applying this to the third arrangement (C):

  • Surrounding numbers: 28, 4, 23, 6
    • Calculate the differences: (2823)+(46)=5+(2)=3(28 - 23) + (4 - 6) = 5 + (-2) = 3
    • Multiply the result by 4: 3×4=123 \times 4 = 12

Thus, the central number should be 12, but this isn't one of the given options (25, 28, 30, 32). Since the pattern doesn't seem to work here, let's reconsider the possibility that there's another formula, possibly considering sums or differences from the total.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Patterns and Relationships

Formulas

Difference of Opposites Formula: (a - b) + (c - d)

Theorems

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Suitable Grade Level

Grades 6-8