cs-110 — The Percentage Maze
| Field | Value |
|---|---|
| id | cs-110 |
| difficulty | Foundational |
| topics | percentages, bases |
| lecture | lecture-28 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | lectures 1-2 (problem framing, precise pseudocode) |
| objective | recognise the pattern, translate it into precise steps, and trace it correctly |
| solution | held by the instructor; discussed after the attempt |
Problem
'Sales up 50% then down 40%' — why that's a net gain, not a loss. Percentage bases; then reconstruct a table from percentage claims.
Your deliverable is the stated assumptions, the percentage recomputed correctly with its base named, and one rewording that removes the ambiguity. If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.
Examples
- Input: sales 100 -> up 50% -> 150 -> down 40% -> 90; two claims 'up 50, down 40'
- Output: net change 100 -> 90 = -10%; bases differ (150 for the fall) - percentages never add across different bases
Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.
What to notice
- Each percentage has its own base. Track the absolute values and the mystery disappears.
- Writing the rules IS the solution; code is transcription.
- Every assumption is a place where two good answers can differ.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Which assumption would you attack first if you had to argue the other side?"
Constraints and assumptions
- Difficulty: Foundational (early-semester techniques assumed: precise statements, traces, simple loops).
- Topics: percentages, bases.
- Classroom-scale inputs unless the problem says otherwise.
- Time-box: about five minutes; naming the pattern and stating the assumption is already a pass, completing the calculation is the stretch.
- Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.
Hints and extension
- First nudge: identify the pattern the worked instance uses before computing anything.
- If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
- After the reveal, attempt the extension below before the next lecture.
- Extension challenge: Write the two honest headlines for this summary and their audiences.