Divide and Conquer the Knottiest Problems

The algorithm of binary search, or “chop,” popularized by computer scientists reminds us of the power of subtraction in decision making. Binary chop is the process through which we can identify any specific element within an array of options. By continually dividing a search in half and repeating the process, any unidentified target can be found relatively quickly, as if it was magic.

A popular parlor trick using Binary Chop is for one person to select a word on a given page in any book. Employing Binary Chop, an inquisitive party can identify this unknown word in 25 questions or less.

Here’s how it works: The sleuth asks a series of questions that continually divides the search in half. The search starts with the question: Is the word in the first or second half of the book? Now, is it in the first or second half of that section? Repeating this question several more times will quickly reveal the page that hosts the word. Is the word in the first or second half of the page? Repeating that question a few times identifies the sentence in which the word lies. Is it in the first or second half of the sentence? Two or three more questions and the logician can now say something like, “The word you selected is on page 122, 4th word of sentence 10.” Scientific magic.

Binary search reminds us of the power of divide and conquer. We can apply this same logic to any large or complex problem to great advantage. Breaking down a problem into subproblems, or splitting a problem into smaller problems, is a best practice known to all great decision makers.

Anything too complex or large to address—like a problem, opportunity, decision, or task—can be broken into smaller, less complex parts. Deconstructing a complex issue allows leaders to tackle smaller more manageable problems and wrestle them to the ground.

Good leaders remind themselves of this foolproof logic whenever they confront a problem too complicated or large to get their head around. Solving knotty issues requires it. Reducing the size of a challenge into something more manageable makes intuitive sense to everyone. The benefits of doing so is almost magic.