Cognitive Bias: Reasoning Fallacy

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 the lake?

Answer 1: The answer is 47 ( the patch was twice as small on the 47th day – half the size of the lake). Most people answer 24.

Answer 2 : Most people, even in famous American universities such as MIT or Harvard, answer 10 ct for the first question (the right answer is 5 ct) and ‘’right’’ for the second question but it is the wrong reasoning.

Why? In the first question, people tend to jump from the uncommon question ”costs £1.00 more than” to the common question ”costs £1.00”.

Answer 3: 5 minutes. But most people tend to say automatically 100 minutes as our mind is used to symmetrical reasoning.

What do these small games show? That it is not always a good idea to use heuristics or intuition to solve problems. Numerous mathematical reasonings are counter-intuitive and in such cases it is better to use our analytical systems.


Frederick, S. (2005). Cognitive reflection and decision making. The Journal of Economic Perspectives, 19(4), 25-42.