Draw the straight lines joining opposite numbers. Check the total of each known opposite pair, then subtract the number opposite the question mark from that common total.
Step 1: Analyze the pattern in the numbers.
The numbers are arranged in a diamond shape with four triangles, and we are looking for a relationship between the numbers. Upon examining the rows and columns, we observe that the number on the top side is the sum of the two adjacent numbers below it, minus 2. Step 2: Apply the pattern to find the missing number.
We have the numbers:
\[
\textRow 1: 43, 35 \quad \textRow 2: 29, 31, 40 \quad \textRow 3: 38, ?
\]
Looking at the adjacent numbers, we find the missing number to be 34. Step 3: Conclusion.
Thus, the number that replaces the question mark is \( \boxed34 \).
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Approach Solution -2
Concept:
Compare numbers placed at opposite ends of each straight line through the centre.
A constant opposite-pair total determines the missing value.
Step 1: Test the first opposite pair.
The numbers $29$ and $40$ lie opposite each other, and $29+40=69$.
Step 2: Confirm the constant with other opposite pairs.
$31+38=69$ and $35+34=69$. Thus every opposite pair has the same total, $69$.
Step 3: Apply the rule to the pair containing the question mark.
The number opposite the question mark is $35$, so $?+35=69$.
Step 4: Solve for the missing number.
$?=69-35=34$.
