1. The problem is to find the missing numbers in the last row of the given matrix: 38 71 78 73 86 85 33 17 42 99 99 22 47 39 31 87 22 21 17 77 81 47 45 42 35 22 01 50 ?? ?? 2. To solve this, we look for a pattern or rule that relates the rows or columns. 3. Let's check if the sum of each row is consistent: - Row 1 sum: $38 + 71 + 78 + 73 + 86 = 346$ - Row 2 sum: $85 + 33 + 17 + 42 + 99 = 276$ - Row 3 sum: $99 + 22 + 47 + 39 + 31 = 238$ - Row 4 sum: $87 + 22 + 21 + 17 + 77 = 224$ - Row 5 sum: $81 + 47 + 45 + 42 + 35 = 250$ - Row 6 sum so far: $22 + 1 + 50 + x + y = 73 + x + y$ 4. The sums do not follow a clear arithmetic progression or pattern. 5. Let's check columns for patterns: - Column 1: 38, 85, 99, 87, 81, 22 - Column 2: 71, 33, 22, 22, 47, 1 - Column 3: 78, 17, 47, 21, 45, 50 - Column 4: 73, 42, 39, 17, 42, x - Column 5: 86, 99, 31, 77, 35, y 6. Check if columns have arithmetic patterns: - Column 4: 73, 42, 39, 17, 42, x Differences: 42-73 = -31, 39-42 = -3, 17-39 = -22, 42-17 = 25 No clear pattern. 7. Check if the last row is the sum or difference of previous rows or columns. 8. Another approach: check if the last row is the sum of the first and fifth rows: - 38 + 81 = 119 (not 22) - 71 + 47 = 118 (not 1) - 78 + 45 = 123 (not 50) No match. 9. Since no clear pattern emerges, the most reasonable assumption is that the missing numbers are 43 and 44 to complete the last row with a similar range of numbers. Final answer: The missing numbers are 43 and 44.