There's something incomparably satisfying about grappling with a problem and coming up with an elegant solution: one that achieves maximum effect with minimum effort. In the following excerpt--adapted from his new book "Winning the Brain Game: Fixing the 7 Fatal Flaws of Thinking"--Matthew May presents a real-life business challenge with a brilliantly simple answer that should be obvious, but isn't. See if you can solve it or if--like most people--you fall into the thinking traps that bedevil problem solvers.

It's 2005. I am seated in a conference room on the top floor of an eight-story building in southern California, surrounded by 12 highly skilled bomb technicians from the Los Angeles Police Department. They have been handpicked to address a complex challenge regarding new methods to respond to bomb calls in this age of everyday terrorism. The problem is a wicked one: how to handle fluid, potentially catastrophic situations involving highly lethal improvised explosive devices (IEDs) capable of massive devastation and death in public places.

I am excited to facilitate over the next two days, after which they will present their solution to the LAPD's counterterrorism senior command.

By way of introduction, I ask the good problem-solvers to raise their hands. Every hand goes up. No surprises there. Bombs are problems; problem solving is the air they breathe. I tell them to keep their hands high and ask those who consider themselves great learners to raise their other hand. Same result: all hands up.

Then, I ask the true innovators to keep their hands up. Every hand comes down. No takers. None.

I didn't ask that question to destroy confidence, but to change the frame. I make the point that, as a practical matter, innovation, problem-solving, and true learning employ the same iterative process: questioning, framing, hypothesizing, ideating, testing, reflecting. So, I've essentially now dubbed them innovators.

Because they're accustomed to working closely with a partner, I split the group into six pairs and give them a quick thought challenge. It's based on a real-life problem but is much simpler than any problem they will face on the job.

The Brain Teaser

Imagine that you own a luxury health club. As part of the membership perks, each of the 40 shower stalls--20 men's and 20 women's--is stocked with a bottle of very expensive ($50), salon-only shampoo, which is only available in beauty supply retail stores to licensed hair stylists. The customers love it and rave about this particular perk. Unfortunately, bottles disappear from the showers all the time. In fact, the theft rate is 33 percent: a costly situation and a bad experience for members reaching for the shampoo, only to find the bottle gone. Your staff must constantly resolve complaints among your "honest" members. You've tried a number of things to solve the problem: reminders, penalties, and incentives. But nothing has worked. The front desk even sells the bottles at a very slim profit margin.

You decide to ask your employees, all of whom are hourly, to help solve the problem, and give them several nonnegotiable conditions: the solution must completely eliminate theft; it cannot involve discontinuing or limiting the current shampoo offering in any way (one full-size bottle of the current brand per stall must not change); any solution must be of extremely low--preferably no--cost (pennies per stall, at most); there can be no additional burden on the member; and the solution must be easy to implement, without disrupting the normal operation of the club.

Try your hand at solving this thought exercise. You have 10 minutes. Enlist the help of someone else if you like. Jot down all your ideas, select the best one, and then we'll continue.

Back? How did it go? Do you think you came up with the elegant solution? If you're like 95 percent of the people I give this kind of problem to, including the LAPD bomb techs, you undoubtedly came up with several ideas.

Here are the most common ones:

  • keep bottles at the front desk to check in and out
  • hire a locker room attendant to check them in and out
  • put travel-size bottles in the stalls
  • install cameras
  • loyalty program offering a free bottle for keeping a ?clean record
  • install lockable pump-top dispensers in each stall
  • have a gym bag-checker at the exit
  • discontinue the shampoo in the stalls
  • charge a separate fee for shampoo
  • sell the shampoo at cost
  • "most wanted list": pictures and names of offenders
  • chain the bottles somehow to the wall
  • put the shampoo in unmarked bottles?
  • install "do not remove shampoo" signs in stalls
  • give out free sample-size bottles at the front desk
  • hire shower security guards?
  • puncture the side of the bottle near the top?
  • install radio-frequency identification (RFID)
  • consider loss due to theft a cost of doing business
  • keep the bottles near empty at all times

Unfortunately, all of these solutions violate one or more conditions. None approaches the solution ultimately produced by the health club employees.

Every time I watch folks wrestle with this challenge, I'm amazed at how consistently they fall victim to the same thinking traps and exhibit the same kinds of behaviors. (The LAPD bomb squad did not disappoint.) The scientific community has a host of labels for these behaviors. Let me simplify things: they are fatal thinking flaws. There are seven of them:

  • Leaping to a solution before you understand the problem
  • Getting stuck in mental ruts that prevent you from thinking differently
  • Overthinking the problem and actually making it worse
  • Making do with a satisfactory solution
  • Downgrading the goal so you can declare victory
  • Automatically dismissing the ideas of others
  • Censoring your thinking and prematurely killing your own ideas

Those seven flaws prevent people from achieving the maximum effect with the minimum means. It prevents them from seeing the best of all possible outcomes: an elegant solution.

Adapted from Winning the Brain Game: Fixing the 7 Fatal Flaws of Thinking (McGraw Hill Education) by Matthew May. May's new column, "Brain Games," is coming to this site soon.