Did the answer 10 cents immediately spring to mind? It certainly did me for me when I first attempted to solve this puzzle and I confidently predict that 10 cents would be the answer offered by the vast majority of your students were you to present them with the puzzle in class.
Of course, once you take the time to reflect on the fact that the difference between $1.00 and 10 cents is only 90 cents, then it becomes obvious that the 10 cents answer is wrong and the correct answer is actually 5 cents.
The Bat cost: $1.05
The Ball cost: $0.05
This 'simple' but ingenious puzzle was devised by Shane Frederick as part of a 3-item Cognitive Reflection Test (CRT), which he developed to help illuminate his research into cognitive ability. The brilliant thing about the bat and ball puzzle is that to arrive at the correct solution (which is easily understood when explained) requires as Frederick states: The suppression of an erroneous answer that springs "impulsively" to mind.
Most notably addressed by Nobel Prize winning psychologist Daniel Kahneman in his book 'Thinking, Fast and Slow', the idea that we draw upon two distinct types of cognitive processes, i.e., those employed quickly with very little thought and significantly slower processes which require much more conscious deliberation is an enduring and engaging topic within psychology.
The Cognitive Reflection Test provides a great way for psychology instructors to explore 'fast' and 'slow' thinking with their students. It also provides a solid foundation from which to examine other cognitive topics such as decision making and IQ.
(1) A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? _____ cents
(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes
(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? _____ days
I'm sure you don't need me to tell you the answers to the other two items in the test but just in case.
2. The correct answer is 5 minutes (most people answer 100 minutes).
3. The correct answer is 47 days (most people answer 24 days)
Frederick, Shane (2005). "Cognitive Reflection and Decision Making". Journal of Economic Perspectives. 19 (4): 25-42.
David Webb is the owner, writer and host of three websites built around his teaching and research interests; including All-About-Psychology.Com which receives over two million visits a year.
A passionate promoter of psychology through social media, over 850,000 people follow his psychology Facebook page and he is featured on the British Psychological Society list of the 100 most followed psychologists and neuroscientists on Twitter.
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