The Bat, Ball Problem

It took me two or three times to completely understand the answer to the famous bat, ball problem. If you haven’t heard about it, here’s what it says: A baseball bat and a ball cost $1.10 together, and the bat costs $1.00 more than the ball, how much does the ball cost?

The second I read this, my brain prompted 10 cents because well of course 10 cents and one dollar together make up $1.10. But that’s wrong. The reason behind this is that if we subtract 10 cents from 1 dollar, it’s 90 cents and “the bat costs $1.00 more than the ball”.

The actual cost of the ball should be $0.05 so that the bat would be $1.05 ($0.05 + $1.00) and together the ball and bat make up $1.10 ($0.05 + $1.05). This is something we have learnt in school – solving pairs of linear equations – x + y = $1.10 and x – y = $1.00. Most people know how to solve these but fail at recognising them in the first place.

While discussing analytic thinking in an article, R. Douglas Fields writes, “Cognitive theory of decision making supports the hypothesis that there are two independent processes involved in decision making. The first process is based on gut instinct, and this process is shared by other animals. The second cognitive process is an evolutionarily recent development, exclusive to humans, which utilizes logical reasoning to make decisions.”

Learning subjects is about understanding the established rules and facts we have been taught over the years. We know how to use them but end up forgetting where to use them. It is very easy for our brain to be lazy, ignore the technical method and either give the wrong answer or rely on the phrase “I can’t do maths”.