- For the tree with top number 20 and bottom numbers 3 and 2:
- The two numbers directly above 3 and 2 must sum to the number above them, which is part of the path to 20.
- Let the number above 3 be A and above 2 be B. Then A + B = C (the next level up), and so on until reaching 20.
- One possible solution: Fill from bottom up.
- Bottom row: 3, 2
- Next row: 3+2=5 (but this is only one number; we need two numbers above the bottom two).
- Actually, the structure has 4 bottom hexagons, with two given: 3 and 2. The other two are unknown.
- Let’s denote the bottom row as: X, 3, 2, Y
- Then the row above: (X+3), (3+2)=5, (2+Y)
- Then the next row: (X+3+5), (5+2+Y) → Wait, no: each number is sum of the two directly below it.
- So row above bottom: position 1: X+3, position 2: 3+2=5, position 3: 2+Y
- Then row above that: (X+3)+5 = X+8, and 5+(2+Y) = 7+Y
- Top: (X+8) + (7+Y) = X+Y+15 = 20 → X+Y=5
- Choose X=1, Y=4 (or any pair summing to 5).
- Then:
- Bottom: 1, 3, 2, 4
- Next: 1+3=4, 3+2=5, 2+4=6
- Next: 4+5=9, 5+6=11
- Top: 9+11=20 ✓
- For the tree with top number 25 and bottom numbers 4 and 3:
- Bottom row: 4, A, B, 3
- Row above: 4+A, A+B, B+3
- Row above: (4+A)+(A+B) = 4+2A+B, (A+B)+(B+3) = A+2B+3
- Top: (4+2A+B) + (A+2B+3) = 7 + 3A + 3B = 25 → 3A+3B=18 → A+B=6
- Choose A=2, B=4 (or any pair summing to 6).
- Then:
- Bottom: 4, 2, 4, 3
- Next: 4+2=6, 2+4=6, 4+3=7
- Next: 6+6=12, 6+7=13
- Top: 12+13=25 ✓
- For the tree with top number 32 and bottom numbers 2 and 5:
- Bottom row: X, 2, 5, Y
- Row above: X+2, 2+5=7, 5+Y
- Row above: (X+2)+7 = X+9, 7+(5+Y) = 12+Y
- Top: (X+9) + (12+Y) = X+Y+21 = 32 → X+Y=11
- Choose X=4, Y=7 (or any pair summing to 11).
- Then:
- Bottom: 4, 2, 5, 7
- Next: 4+2=6, 2+5=7, 5+7=12
- Next: 6+7=13, 7+12=19
- Top: 13+19=32 ✓
Parent Tip: Review the logic above to help your child master the concept of 3rd grade math puzzle worksheet.
