One of the most valuable techniques in problem solving I learned in the third grade. But it certainly wasn’t a lesson my teacher intended.
On a day with time to kill between the morning session and lunch bell, she passed out mimeographed sheets with a maze on them and told us to complete it. Busywork for nine-year-olds. Everyone picked up their pencils and began at the start. I looked at the maze for a moment and then—I don’t know why—began at the end, the goal. All the possible traps and dead ends in a maze are designed for the pencil moving forward. Moving backward, I found, was a clear path to the starting point. I was finished in about a minute.
When I took the paper up to the teacher’s desk, she was stunned. “How did you do it so fast?”
“I worked it backward,” I said. “I started at the goal.”
“Thomas!” she said loudly enough for the class to hear. “That’s CHEATING!”
I walked back to my desk, thoroughly embarrassed. Everyone was looking at me with an expression of triumph (“Aha, she caught you!”) or pity (“Don’t you know how to be good?”) or confusion (“How do you cheat on a maze?”).
Fortunately, although I was chagrined and abashed, I didn’t really take the teacher’s verdict to heart. After all, she had simply posed the maze as a problem. She didn’t say, “Start at the beginning.” That’s kind of assumed, but it wasn’t made into a rule. Working problems backward has served me well ever since.1
Take, for example, my third job out of college, as technical editor in an engineering and construction company. Only part of the technical editor’s work was to clean up the engineers’ spelling and grammar and make a collaborative effort like a proposal bid or technical report sound like one voice. The most critical task was to coordinate production. Since turning the engineering group’s findings into a deliverable document is a job that no one else cares about, because most engineers hate to write, and since all of this comes at the end of the process of doing the actual engineering, the technical editor was always working under a firecracker deadline.2
It was not uncommon on Monday morning to be assigned to a 500-page, multi-volume proposal that had to fly out on Friday afternoon. That’s less than five days to receive the engineers’ scribblings, edit them, have them typed fresh, get them printed along with charts and graphs, which also have to be professionally prepared, and have everything collated and bound. These days the work is done on word processors and graphics programs that format perfect pages and are attached to printers (“document centers”) that simultaneously print, collate, and bind perfect copies. But when I was working in the mid-’70s, engineers wrote with a pen; I edited with a pencil; teams of typists and graphic designers made the page masters; the print shop produced stacks of individual pages; collating was racks of stacked pages in order, with people running around the table pulling off individual sheets; and the final binding was done with a punch press and plastic combs. Every step was a separate event that the editor had to schedule.
If you sat there on Monday wondering when you were going to get copy to work on, you were already dead. So we had to plan backward. Final step: the courier leaves for the airport at 4 p.m. Friday.3 Immediately preceding activity: collating, binding, and packaging, which normally takes two hours on a job this size; so now we’re back to 2 p.m. That means all printing has to be finished by 1:30. With a mandatory one-day turnaround in the print shop, that means the bulk of the pages must be delivered by noon Thursday. Before then, the typists and proofreaders will want a minimum of an hour per page, times a team of—how many? Ten typists, working two shifts. That will push us back to about three p.m. Tuesday. So the bulk of the text has to be out of legal review and in my hands by noon Tuesday and leaves me about fifteen minutes per section for editing. … Better talk to the project manager to establish these deadlines and cutoffs.
This kind of thinking backward applies not just to publishing rush documents but to any project that supports a work breakdown structure. When you work a schedule backward, you’re forced to focus on the irreducible minimum time for each step. You also discover the dependencies—the links of “gotta have this before I can do that”—which leads you to slippages and float times. Just like the maze, all the traps and dead ends work for the pencil going forward. Moving backward, you’re dealing with the straight path. There’s no guessing about where you start: the starting point is suddenly staring you in the face.
The same principle works for storytelling and novel writing, too. If you plot backwards from your climax scene, you know who has to do what to get there. However, I don’t always follow this method, because my stories tend to evolve, moving forward in time. Also, I wouldn’t try to write the story backwards, because too much of what’s going through the character’s mind depends on what he or she has already experienced.
But if you have a tough plotting problem, or get stuck along the way, it’s a useful exercise to think about where the story is going to end up. That’s the goal at the end of the maze. Then you’re forced to think about what steps your characters need to follow to arrive there. And with the straight shot back to the start in mind, you have the leisure to invent dead ends, false turns, and red herrings for the reader’s entertainment. Plotting backward also lets you test the logic of your story, to make sure no one misses a critical step.
So, is working backward cheating? That would depend on the rules, wouldn’t it? And with most problems, from chess plays to project planning, you’re presented only with certain realities: the catalog of assets in place and goals to be achieved. The rules you have to make up for yourself.
1. I used this story verbatim in my first novel, The Doomsday Effect, when the cyber Jason Bathespeake explains how he solved the problem of dislodging various asteroids in order to manipulate the orbit of Ceres.
2. Remember that old Federal Express ad—“when it absolutely, positively has to be there overnight”? That’s the world of engineering reports and proposals. The document is due in Athens by nine o’clock Monday morning. One minute late, and you’ve failed to bid on a project worth billions, representing weeks or months of proposal preparation costing thousands of expensive labor hours. Cut-rate delivery service isn’t even an option—you need a dedicated courier with the box of documents riding beside him on its own airplane seat.
3. Oh, I wish. Couriers can take the red-eye out of San Francisco. That plane flies at 10 p.m. For five years running I never got home on a Friday much before 9 at night.