Plan the build

Each task has a length in days and a list of the tasks it needs finished first. A task is ready once everything it needs is placed. Press A or B on a ready task to give it to that person. It starts on the first day its needs are done and that person is free, and the button shows that day before you press it. A person never goes back to fill an earlier gap, so the order you place tasks in matters.The chart shows both people's days, an arrow from the task each one waited for, and the ship day so far. Undo takes back the last task and Start over clears the plan. When every task is placed you see your ship day against the best possible, the longest chain, half the total work and the best three people could do.Today's plan is the same for everyone, keeps your first finished plan of the day and counts for your streak. Practice deals a new puzzle that does not count, and its link brings back the same puzzle. Your results stay in this browser.

The longest chain of tasks that each need the one before is the critical path. No plan ships before it ends, however many people work on it, so the tasks on it are the ones to start first. James Kelley and Morgan Walker set out the critical path method in a 1959 paper, Critical-path planning and scheduling.The other floor is the work itself: two people cannot ship before half the total days of work are done. Ronald Graham studied list scheduling, where each person who comes free takes the next ready task on a list, and showed in 1966, and returned to it in a 1969 paper, that it never takes more than twice as long as the best plan; for two people the bound is one and a half times. The obvious plan here is simpler still: it keeps the list order exactly and gives each task to whoever is free first. Every puzzle is one where that obvious plan loses at least a day.A third person can help only when the longest chain is not the limit, and the result shows what three people would reach. Real teams pay more than that. Fred Brooks argued in The Mythical Man-Month in 1975 that new people have to be trained by the ones already on the project and that every extra person adds to the talking the whole team must do, so adding people to a late project makes it later; that is Brooks's law. The puzzle leaves that cost out, so the three-person day is the best case.Four lines sum it up: the longest chain sets the floor; start the long chain first; keep both people busy; a third person can help only when the longest chain is not the limit.The best plan comes from a branch and bound search that tries every way to place the tasks, in order of start day, and drops any branch that cannot beat the best plan found so far by those two floors. It runs in your browser and sends nothing. Planning comes before building in our process, as How we work sets out. Planning over coding says why our effort goes on requirements and scope, and Skip a stage shows what skipping a stage of our process costs one example project.