Quickly consider the following question:

**A bat and ball cost $1.10.**

**The bat costs one dollar more than the ball.**

**How much does the ball cost?**

Simple and logical isn’t it?

This question comes from one of the three items from the “Cognitive Reflection Test” introduced by Shane Frederick, a management science professor at the Massachusetts Institute of Technology.

Thousands of students from MIT, Harvard, and Princeton had been put through the quiz, and you’d think that anyone in these prestigious universities would be able to solve this problem with an unerring ease. Not so fast. It turned out that more than 50% responded with the knee-jerk—incorrect—answer.

## The two systems that led to the choices.

Israeli-American psychologist Daniel Kahneman examines what he calls the *machinery of the mind* — two distinct systems in our brain that dictate how we think and make decisions — in his book, Thinking Fast, and Slow.

*System 1 thinking* is quick, intuitive, spontaneous, and effortless. It’s the type of processing that instantly helps us to recognize faces, to act when confronted with dangers and solve simple questions.

*System 2 thinking*, on the other hand, is slow, rational, reflective, and effortful. It gets into the driver’s seat when you focus and concentrate on a complicated problem.

He explains why most people get the bat-and-ball question wrong in the below excerpt.

A number came to your mind. The number, of course, is 10: 10¢. The distinctive mark of this easy puzzle is that it evokes an answer that is intuitive, appealing, and wrong. Do the math, and you will see. If the ball costs 10 ¢, then the total cost will be $1.20 (10¢ for the ball and $1.10 for the bat), not $1.10. The correct answer is 5¢. It is safe to assume that the intuitive answer also came to the mind of those who ended up with the correct number—they somehow managed to resist the intuition.

Again by Kahneman:

“… a plausible answer comes to mind immediately. Overriding it requires hard work – the insistent idea that ‘it’s true, it’s true!’ makes it difficult to check the logic, and most people do not take the trouble to think through the problem.”

## Giving some thoughts to deliberation.

The question really belongs more to the science of the mind than it does to mathematics and logic— it is about the assumptions we make, rather than whether or not we *have* the ability to solve the question.

And it brings forth an insightful reminder that some deliberation, a little consideration of possibilities or consequences, and in this case, an additional check, can improve the quality of our judgements, albeit the ease to simply rely on our immediate intuition.

## Anyway, here are the other 2 questions:

2. If it takes 5 machines 5 minutes to make 5 toys, how long would it take 100 machines to make 100 toys?

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 to cover half the lake?