Math Problem Statement

What is the missing number in the grid: 35, 12, 17; 42, 23, 14; 19, 43, ?

Solution

The image shows a 3x3 grid with some numbers, and one missing value indicated by a question mark. The numbers are as follows:

35  | 12 | 17
42  | 23 | 14
19  | 43 | ?

To determine the missing number, we need to find a pattern within the rows or columns.

Looking at the first two rows:

  1. Row 1 (35, 12, 17): The sum is 35+12+17=6435 + 12 + 17 = 64.
  2. Row 2 (42, 23, 14): The sum is 42+23+14=7942 + 23 + 14 = 79.

Next, look at the partial third row:

  • The sum of the two known numbers is 19+43=6219 + 43 = 62.

It appears that the sum of each row may follow a pattern. The difference between the sums of the first and second rows is 15 (7964=1579 - 64 = 15).

To follow this progression, we could expect the sum of the third row to be 94, since the difference of 15 is being added. Therefore, the missing number xx should satisfy:

19+43+x=9419 + 43 + x = 94

Solving for xx:

62+x=9462 + x = 94

x=9462=32x = 94 - 62 = 32

Thus, the missing number is 32.

Would you like further details or have any questions?

Here are five related questions to consider:

  1. What would happen if the row sums followed a different pattern?
  2. Can you find a column-based pattern?
  3. Is there a multiplicative pattern between the rows?
  4. How would the solution change if the grid was 4x4?
  5. Could diagonal sums reveal any additional patterns?

Tip: Always check multiple ways (rows, columns, diagonals) to find patterns when solving number grids.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Number Patterns
Algebra

Formulas

Row Sum Formula: Sum of elements in the row = 64, 79, and 94

Theorems

Arithmetic Progression Theorem

Suitable Grade Level

Grades 5-7