cs-018 — Digits and Their Sum
| Field | Value |
|---|---|
| id | cs-018 |
| difficulty | Foundational |
| topics | digits, loops |
| lecture | lecture-05 |
| 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
Compute the digit sum of a positive integer, and decide divisibility by 3 from it. Uses // and % to peel digits.
Your deliverable is the stated assumptions, the digit-extraction rule, the sum for the worked instance, and one boundary value (0, or a single digit) traced. 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: 4723
- Output: digit sum 16 -> not divisible by 3; peel: 4723 % 10 = 3, then 472, ...
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
- Peel the last digit with % 10, drop it with // 10; the loop ends when the number hits 0.
- 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: digits, loops.
- 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: Find the closed-form answer and prove it agrees with your loop.