I need to find the shortest path from START to END in this grid. Let me work through this step by step.
First, let me identify the starting and ending points:
- START is at the node "3 x 4" (second row, first column)
- END is at the bottom right corner
Let me trace possible paths and calculate their costs:
Path 1: Going right along the second row
START (3×4) → 3×9 (cost 12) → 3×3 (cost 26) → 3×8 (cost 36) → then down to END area
From 3×8, I can go down to 3×12 (cost 25), then down to END (cost 36)
Total: 12 + 26 + 36 + 25 + 36 = 135
But wait, let me look for shorter paths...
Path 2: Going down from START
START (3×4) → 3×8 (cost 40) → 3×5 (cost 24) → 3×11 (cost 15) → 3×2 (cost 33) → END (cost 21)
Total: 40 + 24 + 15 + 33 + 21 = 133
Path 3: From START going diagonally or other routes
START (3×4) → 3×9 (cost 12) → 3×10 (cost 20) → 3×7 (cost 21) → 3×2 (cost 28) → END (cost 21)
Total: 12 + 20 + 21 + 28 + 21 = 102
Path 4: Let me try another route
START (3×4) → 3×9 (cost 12) → 3×10 (cost 20) → 3×2 (cost 4) → END (cost 21)
Wait, let me check if there's a direct connection from 3×10 to 3×2...
Looking at the grid more carefully:
- From 3×10 (cyan, third row, second column), I can go to 3×2 (cyan, fourth row, third column) with cost 4
- Then from that 3×2 to END with cost 21
So Path 4: START → 3×9 → 3×10 → 3×2 → END
Cost: 12 + 20 + 4 + 21 = 57
Path 5: Let me check if there are even shorter paths
START (3×4) → 3×8 (cost 40) → 3×10 (cost 30) → 3×2 (cost 4) → END (cost 21)
Total: 40 + 30 + 4 + 21 = 95
That's longer than Path 4.
Path 6: Another option
START (3×4) → 3×9 (cost 12) → 3×3 (cost 26) → 3×7 (cost 9) → 3×2 (cost 28) → END (cost 21)
Total: 12 + 26 + 9 + 28 + 21 = 96
Still longer.
Path 7: Let me check going through 3×7 differently
START (3×4) → 3×9 (cost 12) → 3×10 (cost 20) → 3×7 (cost 21) → 3×2 (cost 28)...
Actually, let me reconsider Path 4 more carefully. From the diagram:
- START is at 3×4
- Can go to 3×9 with cost 12
- From 3×9 can go to 3×10 with cost 20
- From 3×10 can go to 3×2 (the cyan one in row 4) with cost 4
- From that 3×2 to END with cost 21
Total: 12 + 20 + 4 + 21 = 57
Let me verify there isn't a shorter path by checking other connections...
Path 8: What about going through the top?
START (3×4) → 3×5 (going up, cost 20) → 3×6 (cost 15) → ... this seems longer
Actually, looking more carefully at connections from START:
- Right to 3×9: cost 12
- Down to 3×8: cost 40
- Up to 3×5: cost 20
- Diagonal to 3×6: cost 5
Path 9: START → 3×6 → ...
START (3×4) → 3×6 (cost 5) → 3×9 (cost 27)... that's already 32, which is worse than just going directly to 3×9 for 12.
Let me double-check Path 4 is valid by tracing the actual connections in the grid...
From START (3×4):
- Right to 3×9: ✓ cost 12
From 3×9:
- Down to 3×10: ✓ cost 20
From 3×10:
- Right-down to 3×2: ✓ cost 4
From 3×2:
- Right to END: ✓ cost 21
Total: 12 + 20 + 4 + 21 = 57
Let me check one more potential path to be thorough:
Path 10: START → 3×9 → 3×3 → 3×7 → 3×2 → END
12 + 26 + 9 + 28 + 21 = 96 (longer)
Path 11: START → 3×9 → 3×10 → 3×7 → 3×2 → END
12 + 20 + 21 + 28 + 21 = 102 (longer)
The shortest path I found is Path 4 with cost 57.
Final Answer: 57
Parent Tip: Review the logic above to help your child master the concept of multiplication maze worksheet.
