A New Twist on a Classic Puzzle

May xi, 2015

A picture of a baseball and bat.

"A bat and a brawl cost $1.10 in full. The bat costs $1.00 more than than the ball. How much does the brawl cost?"

Take a minute to call back nigh information technology … Practice yous have the reply? Many people respond by saying that the ball must cost 10 cents. Is this the reply that you came up with? Although this response intuitively springs to mind, information technology is wrong. If the brawl cost 10 cents and the bat costs $ane.00 more than than the ball, then the bat would cost $one.ten for a yard total of $1.20. The right answer to this problem is that the ball costs five cents and the bat costs — at a dollar more — $1.05 for a grand total of $1.10.

So why do so many people reply incorrectly? The answer is that people often substitute difficult problems with simpler ones in society to apace solve them. In this case, people seem to unconsciously substitute the "more than" statement in the problem (the bat costs $1.00 more than the ball) with an absolute statement (the bat costs $one.00). This makes the math easier to work with; if a brawl and bat together cost $ane.10 and the bat costs $i.00, so the ball must cost 10 cents.

Time and over again enquiry using the bat-and-ball problem has shown that that this intuitive process leads people astray. Merely are intuitions always detrimental to trouble solving? In a 2014 Journal of Cerebral Psychology article, Université de Toulouse researcher Bastien Trémolière and Université Paris-Descartes researcher Wim De Neys sought to reply this question.

Trémolière and De Neys point out that the intuitively generated response to the bat-and-ball problem (that the ball costs ten cents) is neither highly believable nor highly unbelievable. It is not unreasonable to think — specially for someone who isn't an expert in baseball — that such a brawl could toll 10 cents. They wondered how a person might respond if a similar problem cued an intuitive — but unbelievable — response. What would happen if the intuitive response contradicted other intuitions such as past knowledge most the cost of an item?

To detect out, the researchers had participants answer a classic or a modified bat-and-ball-type problem. In the classic trouble, participants were asked the following question:

"A Rolls-Royce and a Ferrari together cost $190,000. The Rolls-Royce costs $100,000 more than than the Ferrari. How much does the Ferrari price?"

In the modified version of the trouble, participants were asked the following question:

"A Ferrari and a Ford together cost $190,000. The Ferrari costs $100,000 more than the Ford. How much does the Ford cost?"

As in the original bat-and-brawl trouble, people often will try to make the problem seem easier by unconsciously removing the "more than" wording in the problem, leading them to read the problem as saying either "The Rolls Royce costs $100,000" or "the Ferrari costs $100,000."

The intuitive but incorrect answer is that the less expensive car (either the Ferrari or the Ford, depending on the problem) costs $90,000; even so, in the modified version of the problem this answer (that the Ford costs $xc,000) conflicts with people's prior knowledge almost Ford cars: The idea of a Ford being that expensive is not conceivable. This conflict is non nowadays in the classic problem, every bit the idea of a Ferrari costing $90,000 would seem reasonable to most people.

The researchers found that significantly more people correctly answered the modified version of the trouble than the classic version of the trouble. The authors posited that when intuitive answers conflict with other intuitions, such equally those based on by cognition, people are more likely to engage in more deliberate and cogitating reasoning leading to a higher likelihood that they will answer the problem correctly.

Reference

Trémolière, B., & De Neys, Due west. (2014). When intuitions are helpful: Prior behavior can support reasoning in the bat-and-ball trouble. Journal of Cognitive Psychology, 26, 486–490.

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