Don't Mistake a Solution Method for a Problem Definition¶
Definition¶
Clients rarely hand a problem solver a bare problem — they hand over a half-built solution method and expect it implemented. "DON'T TAKE THEIR SOLUTION METHOD FOR A PROBLEM DEFINITION," the book warns, and, in a harder form, "DON'T MISTAKE A SOLUTION METHOD FOR A PROBLEM DEFINITION — ESPECIALLY IF IT'S YOUR OWN SOLUTION METHOD." A method presented as if it were the problem forecloses better solutions before they're even considered, and a solver's own favorite method is the most dangerous of all, because it never even feels like an assumption.
In the Book¶
A comptroller arrives with 24 hours left before sealed government-property bids must be finalized, carrying a "plan": have a computer generate and rank all roughly 4,000,000 possible bid combinations so the executives can scan the list for the best one meeting the rules. The programmer team treats this enumeration scheme as the problem and spends effort making it run in 1 hour instead of 12. Billy Brighteyes instead reads the actual bidding rules for a few minutes and solves the underlying allocation problem with logic and common sense in under five minutes — a solution so fast the executives don't believe he solved their real problem. A year later, at a new job, Billy learns from an operations researcher that a different company faced with the same rules used a linear programming "package" to solve it in two days for $1,400 — yet another solution method mistaken for the definition, and just as beside the point, since Billy realizes the real problem was never the arithmetic at all but how each bidder should act knowing the others might also be seeing and revising their bids.
Why It Matters¶
Whoever asks for help typically arrives already anchored to a technique — a spreadsheet, an algorithm, a familiar procedure — and describes the problem in its terms. Recognizing that the technique is a proposed answer, not the question, is what lets a solver notice cheaper solutions, catch a problem that was framed wrong from the start, or discover that the requester doesn't yet know their own real problem. It's especially dangerous when the solution method is the solver's own specialty, since expertise makes a habitual approach invisible as a choice.