# simple math problem may not be so simple after all

Recently Jackie O, an Australian radio host made news by failing to answer a simple math question.

What was the question? A bat and a ball together cost \$1.10. The bat costs \$1 more than the ball. How much does the ball cost?

She answered that the ball costs 10 cents. But this is clearly incorrect; since, in that case, the bat must cost \$1.10 since the bat costs \$1 more than the ball. But, if that were true, then the two together cost \$1.20, \$1.10 for the bat and \$0.10 for the ball, rather than \$1.10.

The correct answer is that the ball costs \$0.05 and the bat costs \$1.05.

But here is the rub. Faced with this question a vast majority of people provide the same response that Jackie O did; that the ball costs 10 cents. This is because the correct answer that the ball costs 5 cents is far from intuitive.

Before I get to this here are a couple more problems. You will enjoy this column more if you try them first before reading on.

Problem 1: In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days to cover the entire lake, how long does it take for the patch to cover half of the lake?

Problem 2: Suppose you are running a race. You have just passed the person running second. What place are you in?

For the first problem, the answer is not 24 days as most people respond. The correct answer is 47 days. Since the lily pads double every day, if the pond is half-full after 47 days, then it doubles and gets filled the very next day, the 48th.

For the second one, a common intuitive response is say that you are in first place. But this is not right; if you overtook the person running second then you are now in second place.

These problems, designed by an Yale behavioural scientist, are neither math problems nor are they particularly simple.

They are designed to demonstrate the limits of relying on our intuition.

Every day we are faced with a multitude of decisions; some trivial, some more complex. They range from what to have for breakfast and which suit to wear to an important meeting to which car or house to buy, what type of home loan to take out, whether to sign up for life insurance or to take out the extra super-cover warranty on the new big flat-screen television.

In many such instances, we tend to rely on our intuitions; go with our gut.

The questions above show why this may not be ideal. Very often the answer that is intuitively appealing ends up being incorrect.

In these simple riddles the price of being incorrect is minimal; a minor loss of face.

But when it comes to the bigger things in life like buying a car or a house getting things wrong can be costly.

One can think of our decision making as the result of two processes: System 1 and System 2.

System 1, which is essentially intuitive thinking, operates automatically and quickly, with little or no effort and little voluntary control. System 2, on the other hand, is deliberative and effortful. System 1 quickly gets into action as soon as we are faced with a decision. System 2 on the other hand requires time to engage.

One good analogy is to think of System 1 as an elephant that lurches into action quickly, while System 2 is the rider trying to guide the elephant; this can be done but is not easy and requires practice.

So, when it comes to decision-making should you go with your intuition or should you engage in careful thinking and maybe some research?

The answer is simple. If it is a problem that you have lots of experience with, say, grocery shopping or driving on the motorway, it is fine to rely on your intuition and operate on auto-pilot.

But if it is a problem where you have little or no experience or decisions that we face infrequently, such as buying a house (at least for most of us), then relying on intuition may drive you astray. In this case, it is better to rely on System 2 and careful deliberation.

Jackie O need not feel embarrassed. She has plenty of company. Most people struggle with these questions. It is the way our brains are designed; to come in with an immediate answer that feels feels right in our guts.

These problems are not simple, setting up as they do, a conflict between System 1 and System 2 thinking.