1. Problem: Find the missing number (□) in each vertical line graph where two numbers on top are connected and a vertical line descends to a missing number or given number.
2. Step 1: Understand the pattern. Each pair of numbers on top is connected, and the vertical line leads to a number or a missing number. The missing number is likely related to the two numbers above it.
3. Step 2: Analyze the first example to find the pattern.
Example 1: 25 and 9 on top, vertical line down to □.
Check if the missing number is the difference, sum, product, or some function of 25 and 9.
4. Step 3: Test difference: 25 - 9 = 16.
Test sum: 25 + 9 = 34.
Test product: 25 * 9 = 225.
Test average: (25 + 9)/2 = 17.
5. Step 4: Check other examples to confirm pattern.
Example 2: □ and 64 on top, vertical line down to 10.
If the missing number is x, then check if x and 64 relate to 10 by difference, sum, or other.
6. Step 5: Try difference: |x - 64| = 10 => x = 54 or 74.
Try sum: x + 64 = 10 (not possible since sum > 10).
7. Step 6: Check example 3: 36 and □ on top, vertical line down to 11.
Let missing number be y.
Try difference: |36 - y| = 11 => y = 25 or 47.
8. Step 7: Check example 4: 100 and 25 on top, vertical line down to □.
Try difference: 100 - 25 = 75.
So missing number is 75.
9. Step 8: From examples 2 and 3, the missing number is the number that when subtracted from the other top number gives the bottom number.
10. Step 9: Solve each missing number:
1) 25 and 9, missing number = |25 - 9| = 16
2) x and 64, bottom = 10 => |x - 64| = 10 => x = 54 or 74 (choose 54 as it fits pattern)
3) 36 and y, bottom = 11 => |36 - y| = 11 => y = 25 or 47 (choose 25)
4) 100 and 25, bottom = □ => 75
5) x and 16, bottom = 13 => |x - 16| = 13 => x = 3 or 29 (choose 3)
6) 49 and 81, bottom = □ => |49 - 81| = 32
7) 16 and y, bottom = 14 => |16 - y| = 14 => y = 2 or 30 (choose 2)
8) x and 64, bottom = 19 => |x - 64| = 19 => x = 45 or 83 (choose 45)
9) x and 49, bottom = 19 => |x - 49| = 19 => x = 30 or 68 (choose 30)
10) 100 and 81, bottom = □ => |100 - 81| = 19
11. Final answers:
1) 16
2) 54
3) 25
4) 75
5) 3
6) 32
7) 2
8) 45
9) 30
10) 19
This pattern shows the bottom number is the absolute difference of the two top numbers.
Missing Numbers
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