Create graded coding exercises

Good exercises isolate one skill, rise in difficulty in small steps, and give immediate, objective feedback through tests. Hints should unblock without giving the answer away, so they are staged from a nudge to a near-solution. Exercises fail learners when the tests do not match the instructions, when the starter code already passes, when a step jumps in difficulty, or when the "beginner" exercise quietly needs a concept that was never taught.

Create 5 exercises on [CONCEPT] in [LANGUAGE] for beginner learners.

1. State the learning objective and the prerequisites you assume for this level. If the concept is too broad for 5 exercises, narrow it and say how.
2. Plan the progression: the first exercise applies the concept in its simplest form; each next one adds exactly one new difficulty (an edge case, a combination with another known concept, a performance or design constraint). The last one is a small realistic task.
3. For each exercise write:

• a title and a one-line objective;
• the problem statement with input, output and constraints, and one or two examples;
• starter code: signatures, types and docstrings, with the body left for the learner (it must run, and the tests must fail against it);
• tests in the language's standard test framework covering the examples, edge cases (empty, boundary, invalid input as specified) and one case that catches the most common wrong approach;
• three staged hints: hint 1 points to the relevant idea, hint 2 outlines the approach, hint 3 gives the key line or structure without the full solution;
• common mistakes the tests are designed to catch.

1. Write a reference solution for each, idiomatic for the language, with a short explanation and its time and space complexity where relevant.
2. Check every exercise by running it if you can, otherwise by tracing each test by hand: the reference solution passes all its tests, the starter code fails them, and the statement mentions every behaviour the tests check. Fix any mismatch before answering.

• Every test must follow from the problem statement. No hidden requirements.
• Use only the language's standard library unless the concept is about a library, and name the version if behaviour depends on it.
• Keep each exercise solvable in 10 to 30 minutes at the stated level.
• Keep solutions out of the exercise section so it can be handed out alone.

Overview

Objective, assumed prerequisites, and a table: # | Title | New difficulty | Estimated time.

Exercises

For each: title, objective, statement, starter code block, test code block, hints (labelled Hint 1, 2, 3), common mistakes.

Solutions

For each: reference solution code block, explanation, complexity.