Here’s a puzzle: See if you can solve it before reading further.
A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?
No problem? OK, here’s one more puzzle:
In a lake is a patch of lily pads. Every day, the patch doubles in size. If it takes forty-eight days for the patch to cover the entire lake, how long does it take for the patch to cover half of the lake?
Smart people are sometimes not so smart. In fact, the smarter people are, the dumber they may be. That’s the view of Daniel Kahneman, a Nobel Laureate and highly influential professor of psychology, who for many years has been doing ingenious experiments that demonstrate this point.
According to Kahneman, most people who look at the ball-and-bat problem quickly respond that the bat costs a dollar and the ball is ten cents. If that was your answer, you’re wrong, and just a moment’s thought will make that obvious. The bat costs $1.05 and the ball costs five cents.
If it’s any consolation, in experiments by Kahneman and others, more than fifty percent of students at Harvard, Princeton, and M.I.T. gave the incorrect answer.
And the lily pad problem? In this case, people are quick to divide the forty-eight days by two and come up with twenty-four as the answer, but that is not correct. Think about it: If the patch doubles in size every day, then it was half the size one day before the final day, or day forty-seven.
The surprising finding, as Kahneman and other researchers have found, is that smarter people are more vulnerable to these thinking errors. In his book, Thinking Fast and Slow, Kahneman describes systematic errors in the thinking of normal people. It seems that when people face an uncertain situation, instead of evaluating the information or looking up relevant statistics, they make decisions based on a list of mental shortcuts, which often lead to foolish decisions. Instead of doing the basic arithmetic which, in both puzzles, would generate the correct answer, they default to the answer that requires the least mental effort.
Mental shortcuts aren’t bad in and of themselves. Just imagine the impossible challenge you’d face if you had to analyze every single decision before doing anything. But as these puzzles have shown, sometimes mental shortcuts can trap people into missing the point.
If you’re like some people (me, for example), once you’ve encountered puzzles like the above two, you’ll think twice, or maybe even three or four times, the next time someone gives you a puzzle. You’ll anticipate the possibility that the answer isn’t the obvious one that comes to mind. You’ll recognize the mistakes many people make—including those people who are ever so much smarter than you—and you’ll come up with the right answer.
But be forewarned: We humans are subject to way more thinking errors than just this one. The good news with these two puzzles, however, is that if you got the right answers, you’re obviously exceedingly sharp. And if you got them wrong, well, so did some mighty brainy people, so you’re obviously exceedingly sharp. Kudos!
Naomi Karten is a writer and speaker who draws from her background in both psychology and IT. Naomi's recent books are Presentation Skills for Technical Professionals and Changing How You Manage and Communicate Change. Readers have described her newsletter, Perceptions and Realities, as lively, informative, and a breath of fresh air. Naomi is a regular columnist for StickyMinds.com.