(Bloomberg Opinion) -- This weekend, lots of people are finally getting their sourdoughs started. Others are enjoying Frozen 2 for the twentieth time. For me, this is the perfect time to kick back with some brainteasers.
I love puzzles of all forms. I’ve published a few of my own, and at least once a year I spend an entire weekend solving a massive puzzle competition that unfolds across a college campus.
But I haven’t forgotten the barriers to enjoying puzzles in the first place. They can be dense -- even impenetrable -- when you start out.
So over the next few weeks, let me introduce you to some of my favorite types of puzzles, and how to begin solving them on your own. With any luck, you’ll emerge from this anxious time with an enigmatic new hobby.
This week, we are looking at reasoning puzzles, which typically describe a simple setting -- often with constraints -- and ask you to unravel the situation with logic.
Here’s a simple example inspired by our current moment:
You have a panel of three light switches, and you know that one of those switches controls the bulb in your shed – but you can't remember which. In order to keep the handwashing to a minimum (for the sake of your dry, cracked skin), you want to figure it out with no more than one trip outside.
How can you do it?
At first it sounds impossible: Can you possibly test three switches with only one trip to the shed?
Now take a deep breath. You have options here; what are they?
(Seriously, give it a shot before reading on.)
For a puzzle like this, I usually start by thinking small, then try to work my way up to the solution.
If there were only one switch, then there’s no puzzle at all – that switch has to be the answer, and you don’t even have to go outside.
So what if there were only two? Well then, you can turn one “on” and leave the other “off,” and go check the shed. If the bulb is on, you know it must be controlled by the first switch; otherwise, it must be controlled by the second. (Note that here we really lean on the knowledge that at least one of the switches actually does turn on the light.)
But somehow three seems much harder than two. If, for example, you were to turn on the first and second switch and then see that the bulb is on, you wouldn’t know which of those two switches controls the light!
The trick, as it happens, is to introduce a dimension other than just whether the switches are on or off: time.
Lightbulbs heat up when you leave them on. So you can turn on the first switch for 20 minutes, then simultaneously turn it off and turn on the second one. If you then check the shed immediately, you’ll have the answer. If the light is on, you know the second switch is the winner. If the light is off, check the bulb. Is it hot? Then it must be controlled by the first switch. Cold? Bingo, it’s the third.
With just a few mental moves, a seemingly hopeless conundrum becomes simple. All it takes is expanding our view of the problem beyond just the switches in plain sight.
Fun, right? Next week, we’ll go deeper. Until then, check out Brainzilla and Riddles.com for more. And don’t forget to feed that sourdough.
I first learned this puzzle from Peter Winkler's Mathematical Puzzles: A Connoisseur's Collection – one of my all-time favorite books.
This column does not necessarily reflect the opinion of Bloomberg LP and its owners.
Scott Duke Kominers is the MBA Class of 1960 Associate Professor of Business Administration at Harvard Business School, and a faculty affiliate of the Harvard Department of Economics. Previously, he was a junior fellow at the Harvard Society of Fellows and the inaugural research scholar at the Becker Friedman Institute for Research in Economics at the University of Chicago.
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