# RE8 | anthropic/claude-haiku-4.5 | run 1

## Prompt

Minimize total time to finish these tasks, one at a time, respecting dependencies: A (2h, no deps); B (3h, needs A); C (1h, no deps); D (2h, needs B and C). Give a valid order and the total time.

## Response

A valid task order is: **A → C → B → D**, with a **total time of 8 hours**.

## Execution Timeline

| Task | Duration | Dependencies | Start | End |
|------|----------|--------------|-------|-----|
| A | 2h | None | 0h | 2h |
| C | 1h | None | 2h | 3h |
| B | 3h | A (ready at 2h) | 3h | 6h |
| D | 2h | B (ready at 6h), C (ready at 3h) | 6h | 8h |

## Why This Works

Since tasks must be completed sequentially (one at a time), dependencies only determine which tasks are *eligible* to start. The optimal strategy is to complete independent tasks as early as possible to satisfy downstream dependencies.

- **A must run first** (no dependencies, enables B)
- **C runs second** (independent, enables D; completing it before B starts means D's second dependency is ready earlier)
- **B runs third** (A is now complete; B's completion unblocks D)
- **D runs last** (both B and C are complete)

Any other valid order (like A → B → C → D) takes at least 8 hours as well, since the critical path—A → B → D—requires 2 + 3 + 2 = 7 hours, and one additional task must fit somewhere.

Would you like to explore how the timeline changes if tasks could run in parallel instead of sequentially?
