A Mathematical Cognitive Reflection Test

A test to evaluate your ability to engage your System 2 when faced with questions that tempt you to use your System 1 instead.

October 21, 2024
3 min
By Matazart

First question:

A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?

Second question:

If it takes 5 machines 5 minutes to make 5 widgets, how long does it take 100 machines to make 100 widgets?

Third question:

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 of the lake? This cognitive reflection test is designed to measure a person's tendency to step back from their unconscious/instinctive/emotional reactions and engage cognitive reflection to answer these questions.

In other words, through the lens of Daniel Kahneman's System 1/System 2 framework, this test aims to measure the ability to activate System 2.

System 1: Automatic, intuitive, unconscious, emotional, fast cognitive system that operates without effort. All your daily tasks are performed using System 1. But this system also enables creativity by allowing multiple intuitive associations of ideas.

System 2: Conscious, logical, slow cognitive system that requires concentration and enables us to solve complex or new problems.

To remember this, when you learn to drive, the task is complex and new, so you use your System 2. After some time, driving becomes automatic: you only use System 1. It's fascinating to note that the vast majority of our tasks require no thought at all: walking, eating, manipulating objects, writing, speaking, etc. This test has only 3 questions, and it's interesting to note that all these questions are elementary-level mathematics questions.

You can now reread these questions and take the time to verify that your solutions are indeed correct...

These questions, due to the symmetry in the problem data, are specifically designed to mislead you; encouraging you to give an obvious... but wrong answer each time.

The intuitive solutions provided by System 1 are:

First question: The ball costs 10 cents.

Second question: It takes 100 minutes.

Third question: After 24 days.

If you haven't already, verify that these three solutions are completely wrong.

It's interesting to see why our brain, and more precisely our System 1, gives us these answers instantly.

  • First question: "$1.00 more."

  • System 1: "The solution is $1.00 less than the total."

  • Second question: "5 minutes, 5 machines, 5 widgets."

  • System 1: "So by symmetry, 100 minutes, 100 machines, 100 widgets."

  • Third question: "Doubles every day, total 48 days."

  • System 1: "Just divide the number of days by 2."

If you really take the time to engage your System 2, you should easily find the answer to these 3 questions.

At worst, you can proceed by trial and error: propose a solution, check if this solution is correct, and continue this process until you are completely certain that your solution is correct.