To solve the problem, let's examine the pattern in each column:

We have:

1st column: 26, 32, 40
2nd column: 53, 26, 64
3rd column: 76, 31, ?

We will check if there's a pattern vertically or horizontally.

Step 1: Check vertical patterns

First column (26, 32, 40):

• Difference between 32 and 26: $32 - 26 = 6$
• Difference between 40 and 32: $40 - 32 = 8$

The differences are increasing by 2.

Second column (53, 26, 64):

• Difference between 26 and 53: $26 - 53 = -27$
• Difference between 64 and 26: $64 - 26 = 38$

There doesn't seem to be a consistent pattern in this column.

Step 2: Check horizontal patterns

First row (26, 53, 76):

• Difference between 53 and 26: $53 - 26 = 27$
• Difference between 76 and 53: $76 - 53 = 23$

Second row (32, 26, 31):

• Difference between 26 and 32: $26 - 32 = -6$
• Difference between 31 and 26: $31 - 26 = 5$

Step 3: Identify a possible pattern

There seems to be a mix of addition and subtraction happening. Let's focus on the third row.

For the first two numbers in the third row:

• Difference between 40 and 64: $40 - 64 = -24$

To follow the same pattern, we expect the third value to maintain a similar type of pattern. Adding the absolute value of 24 gives us:

$64 - 42 = 22$

Thus, the missing value is 42, which matches option c.

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Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:

1. What would the pattern look like if the columns had the same increment?
2. How do patterns differ when comparing horizontal vs. vertical approaches?
3. Can you create a similar number puzzle using an arithmetic pattern?
4. What would happen if you tried geometric progressions instead of arithmetic ones?
5. How do differences between consecutive terms help in finding missing values?

Tip: Always check both rows and columns for patterns in number sequences.