Sunday, February 23, 2014

Take the Simple 3 Question Challenge: The CRT

Here are 3 questions that I would like to pose to you. Go ahead and try answering them.

The first question:
A baseball bat and a baseball together cost $1.10. The baseball bat costs $1.00 more than the baseball. How much does the baseball cost?
The second question:
It takes 5 toy-makers 5 minutes to make 5 toys. How long would it take for 100 toy-makers to make 100 toys?
The third question:
There's a special patch of lily pads in a pond. The size of the patch doubles every day. On the 48th day, the patch has covered the whole pond. How many days did it take for the patch to cover half of the pond?
As you can see, the questions are quite simple for the most part. However it would be a mistake to conflate simple with easy. The test was given at world renown universities such as Harvard, Princeton, and MIT with results that may surprise you.
  • At Harvard, the average score was 1.47 correct answers with 57% getting a score of 0 or 1
  • At Princeton, the average score was 1.63 correct answers with 45% getting a score of 0 or 1
  • At MIT, the average was a bit higher at 2.18 correct answers with 23% getting a score of 0 or 1
But what does this mean?
I should tell you that the test you've just taken is known as the CRT, or Cognitive Reflection Test. It was a test formulated by Shane Frederick, a professor at MIT. It was used as an intelligence test, and tested how people responded to various biases.
Personally, I only heard about it through a book called "Mastermind" by Maria Konnikova (fantastic read if you ever get a chance). The version I wrote above is a bit different from the one given in the book, but the spirit is there.
Now then, onto the answers:
The answers are (SPOILERS):
  1. The ball costs $0.05
  2. It takes 5 minutes
  3. 47 days
If you are like the general populace, its likely that you got at least one of these questions wrong. But why? What does it mean for the way we think?
Here are the incorrect answers that are frequently given:
  1. $0.10
  2. 100 minutes
  3. 24 days
Now is time to look into why we might make those mistakes:
1. Why would someone think $0.10 is the answer? Well, just think about the numbers: the bat and the ball are $1.10 right? The bat costs $1.00 more than the ball. If we have that, then we might think that doing $1.10 - $1.00 would get the price of our ball of $0.10. If all we think about is the strict numbers, it makes perfect sense that we would get $0.10 as the answer.
2. This is sort of a matter of pattern recognition being used in the wrong way. We notice the pattern of 5, 5, 5: which is 3 of the same numbers in a row. With the new set up we have 100, 100, ___. We recognize that both seem to set up for a sequence of three of the same number, and are inclined to finish the sequence with a 100. Again, this is a matter of looking at the numbers without looking at the context.
3.The last one is the lily pond that is covered with lily pods in 48 days. We hear that the patch doubles in size every day, but seem to forget it quite quickly, or are inclined to push it aside. Instead we focus on the numbers of 48 days, and the key word of HALF. With some simple math we find that half of 48 days is 24 days. And thus we end up with our answer.
So what does this say about our intuitive and innate thinking?
Well essentially we are very good at ignoring context, but very good at pulling numbers out and recognizing patterns. The key reason why so many people were mistaken in their responses is because they would take the key numbers out of the problem, and try to figure out how to solve it like a simple math problem. Also that people don't naturally double check, as double checking or reading closely would probably have fixed many of the mistakes that were made.
However, it should be noted that people might do better if they think it is a riddle. They will read more carefully and look for pitfalls that could confuse them.


  1. if it takes 5 toy makers to make 5 toys in 5 mins, shouldnt it also take 100 toy makers 5 mins to make 100 toys and not 5 days?

    im not entirely sure where 5 days came from

    1. You are correct. I wrote it while having question 3 fresh in my mind and ended up typing "days" rather than "minutes".

      Thanks for catching that.

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