PN3
Path with Constraints
约束路径
Path / 路径Grades G5 - G8
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What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Grid navigation with movement restrictions
- 2Counting paths from A to B with rules
- 3Obstacles or required checkpoints
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What It Really Tests
The core mathematical idea behind this structure:
Count or find paths that satisfy specific rules (only right/down, avoid obstacles, etc.).
计算或找到满足特定规则的路径（只能右/下，避开障碍等）。
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Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Missing some paths or double-counting
- ⚠Not applying constraints consistently
- ⚠Trying to enumerate instead of using counting principle
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Your First Step
How to begin thinking about problems with this structure:
Use systematic counting: paths to each point = sum of paths to previous points that can reach it.
使用系统计数：到每点的路径 = 能到达它的前面点的路径之和。
Related Structures
These structures share similar patterns or thinking approaches: