Looking Forward to Monday Morning
A series of essays on business, architecture, and the business of architecture.
I’m Not Good at Math
by Daniel Frisch
Posted October 19th, 2023
Four people stand on one shore of a river and are keen to get to the opposite shore as quickly as possible.  The ‘rules’ stipulate that an individual can cross the bridge either alone or with a companion. As it is dusk, a flashlight must accompany each crossing.  Each individual walks (or runs) at a different rate and can travel the bridge respectively in one minute, two minutes, five minutes, or ten minutes.  When traveling as a pair, the two individuals travel at the slower rate., For example, if the one-minute traveler goes with the ten minute, it takes ten minutes to cross and one minute to return.
Q.:  How can all four travelers get to the opposite shore following these ‘rules’ in only seventeen minutes?

A half a lifetime ago, a cousin shared the above riddle with me.  He claimed the problem was an interview question with which Microsoft executives tested potential hires.  I struggled mightily at first to solve it and for a short time I was indignantly convinced it was impossible and that the riddle was flawed (the answer is at the end of the essay).  More recently, the same cousin shared another favorite interview question; “Why are manhole covers round?”, that I have borrowed and use to this day to see how candidates react when they do not know the answer and cannot simply Google it.  In 2012, William Poundstone published a non-fiction book titled: Are You Smart Enough to Work at Google?: Questions, Zen-like Riddles, Insanely Difficult Puzzles, and Other Devious Interviewing Techniques You Need to Know to Get a Job Anywhere in the New Economy (Little Brown Spark, 2012).  Having read much of this book, I would be no more likely to get a job at Google or Microsoft, or anywhere in the new economy. Fortunately, I sit on the other side of the table these days.

Interviewing at our firm is far less intimidating, I hope, even if we do ask the borrowed question of why manhole covers are round (the answer is also at the end of this essay).  When interviewing, we seek to understand how potential hires solve problems, especially under pressure.  We also try to tease from candidates their career goals, which can be similarly awkward for candidates seeking their first job after years dwelling in the ivory tower. While few candidates bring to our conference room a well-defined five-year plan, thinking on our feet and looking to the future are big parts of our every day. While all interview topics are fair game, we have not gone so far as giving a challenging math riddle. We take for granted the math fluency of future architects who possess one or more professional degrees, especially since our daily math problems are invariably straightforward.

We use math every day.  Most of which is simple algebra and geometry, never as much as a quadratic equation or the derivatives we studied in calculus.  Our student conviction that calculus (a prerequisite in architecture school) has little real-world use, at least in the design and architecture fields, has been confirmed. We use math to perform simple tasks like calculating area (square footage), and evaluating budgets, often on a price-per-square-foot basis. We undertake these tasks conversationally, and in most cases, without the help of calculators or computers on which we rely when precision trumps estimation. When calculating square footage, anyone in our office (except myself) can place a cursor on a to-scale plan and working around the perimeter of a room, apartment, or building, have the computer provide a precise square footage calculation. When a scaled plan is not available, however, a computer is not of much use, and square footage approximations are extrapolated by adding up individual rooms.  Sometimes we pace off spaces.  From many years walking golf courses, I can get eerily close to building dimensions by confidently pacing with an exactly three-foot gait (yards to the hole in golf).  Sometimes we count tiles and multiply.  Sometimes we look at the proportion of a wall to judge a ceiling height.  While we do, of course, deploy tape measures and laser measuring devices, and now LiDAR scanners, it is amazing how often the tape measures and lasers are not at hand when needed – and our converted LiDAR scans usually take a week to arrive.

When interviewing interns, and then when training them for a career in architecture, we rarely pause to think that the basic math we use every day might intimidate.  And yet, we often hear a very nervous entreaty in a response to a very basic mathematic question while searching through pockets for an iPhone calculator; “But, …I’m not good at math.”  In my opinion, the reflexive reaction “I’m not good at math” often comes without even hearing the question.  While I try not to be similarly reflexive, I don’t always handle this situation well.  I have to check by desire to blurt, “I’m not good at math, either;” or to admit that I sometimes struggle to help my sixth and eighth grade children with their homework. While I usually don’t rise to the bait, I know I should have known better than to have printed and laminated the multiplication tables for a young associate with a significant math blind spot.  As might be expected, the associate soon thereafter found another job with a more sympathetic boss, and neither the employee nor the firm was better for the histrionics.

We all recognize that “I’m not good at math” is symptomatic of our ever-increasing reliance on technology, and is no different than resolving arguments by asking “Alexa” or by using ChatGPT to write an essay.  This essay was written, and rewritten several times, without such assistance, and I’ll let the reader judge as to whether this was a prudent decision. Although technology has improved our lives immeasurably, I suppose I take after my mother, whose favorite subject was math, and always said, “Math is fun; math is just a game.”  I wish more people felt this way, and I sure hope my kids do.  Yay or nay, I fear I will always not too apologetically bristle when I hear, “I’m not good at math.”

Bridge Riddle Answer:  The one and the two go over (two minutes spent), and the one comes back with the flashlight (one more minute expended for a running total of three minutes).  Next, the five and ten go over together (ten more minutes for a total of thirteen), and the two runs back (fifteen minutes expended).  Finally, the one and two go over again for a total of seventeen minutes.  Once solved it seems so obvious, no?
Manhole Covers Answer:  Why are manhole covers round?  We have heard creative responses including the ability to roll them from place to place, to less material (saves money), to less likely to cut one’s foot on a sharp edge.  The real answer is safety. A round manhole cover cannot fall thorough on a person p=below, no matter which way the cover is turned.  This, too, comes down to math, specifically geometry, and the hypotenuse of anything other than a circle.  A combination of Vitruvius and Newton in one simple question.