Case Counting
分类计数
Counting / 计数What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Several possible forms or scenarios
- 2The answer depends on a first choice
- 3Different conditions lead to different sub-counts
What It Really Tests
The core mathematical idea behind this structure:
Split the problem into non-overlapping cases and count each separately.
将问题分成不重叠的情况, 分别计数后相加。
Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Mixing cases together in one messy count
- ⚠Forgetting one case entirely
- ⚠Accidentally overlapping cases and double-counting
Your First Step
How to begin thinking about problems with this structure:
Choose a clean classification criterion first, then count each case.
先选一个清晰的分类标准, 再逐个情况计数。
Try a Problem
A cafeteria offers 3 kinds of sandwiches and 2 kinds of soup. A lunch consists of either: one sandwich only, OR one sandwich and one soup. How many different lunches are possible?
💡 Show Solution & Key Insight
Answer
B
Explanation
Case 1: sandwich only = 3 choices. Case 2: sandwich + soup = 3 × 2 = 6 choices. Total = 3 + 6 = 9.
Key Insight
Split into non-overlapping cases before counting.
Common Wrong Path
Multiplying everything together: 3 × 2 = 6, missing the sandwich-only option.
Related Structures
These structures share similar patterns or thinking approaches: