1. **State the problem:** We have a triangular arrangement of numbers and need to find the number that replaces the question mark (?) in the fourth row. 2. **Analyze the pattern:** The rows are: - Row 1: 9 - Row 2: 7, 2 - Row 3: 5, 7, 6 - Row 4: 4, 6, ?, 8 3. **Look for relationships:** One common pattern in such puzzles is that each number in a lower row relates to the numbers above it, often by addition or subtraction. 4. **Check sums of adjacent numbers:** Let's check if each number in a row is the sum or difference of two numbers above it. - For Row 3: - 5 is related to 7 and 2 (Row 2) - 7 is related to 2 and 9 (Row 1 and 2) - 6 is related to 7 and 2 (Row 2) This is unclear, so try another approach. 5. **Check sums of pairs in Row 4:** Maybe each number in Row 4 is the sum of the two numbers above it in Row 3. - 4 (Row 4, 1st) relates to 5 and 7 (Row 3, 1st and 2nd): 5 + 7 = 12, not 4. - 6 (Row 4, 2nd) relates to 7 and 6 (Row 3, 2nd and 3rd): 7 + 6 = 13, not 6. No direct sum. 6. **Try differences:** - 4 = |5 - 7| = 2, no. - 6 = |7 - 6| = 1, no. No match. 7. **Try sum of three numbers in Row 3 for Row 4:** - 4 + 6 + ? + 8 = sum of Row 3? Sum Row 3 = 5 + 7 + 6 = 18 Sum Row 4 known numbers = 4 + 6 + 8 = 18 + ? No direct relation. 8. **Try sum of numbers in each row:** - Row 1 sum = 9 - Row 2 sum = 7 + 2 = 9 - Row 3 sum = 5 + 7 + 6 = 18 - Row 4 sum = 4 + 6 + ? + 8 = 18 + ? Notice Row 3 sum is double Row 1 and 2 sums. 9. **Try to find a pattern in sums:** - Row 1 sum = 9 - Row 2 sum = 9 - Row 3 sum = 18 (double 9) - Row 4 sum = 4 + 6 + ? + 8 = 18 + ? If Row 4 sum equals Row 3 sum (18), then: $$4 + 6 + ? + 8 = 18$$ $$18 + ? = 18$$ $$? = 0$$ 10. **Answer:** The number replacing the question mark is 0. **Final answer: 0** (Option A).