People almost always get this simple math problem wrong: Can you solve it?  (2024)

The question goes: "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?"

Is your knee-jerk response that the ball costs 10 cents? That is a common answer, but also an incorrect one.

If the ball costs 10 cents, then the bat would cost $1.10, which would bring the total to $1.20. The correct answer is the ball costs 5 cents and the bat $1.05.

This question is part of the Cognitive Reflection Test, CRT, which was first described in 2005 by psychologist Shane Frederick. Frederick wanted to examine how people fight, or don't fight, their intuitive thinking.

The original test contained two additional questions:

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

Research about whether the test measures cognitive ability, or intelligence, has been mixed.

However, why so many people get it wrong is due to a psychological trap we all fall into sometimes. This same psychological trap can hinder our ability to make sound decisions.

Why so many people get this math problem wrong

We think in two distinct ways: Psychologists refer to these cognitive processes as System 1 and System 2. System 1 is your initial reaction, which is often made quickly and without reflection. System 2 is when you use conscious thought and effort. Daniel Kahneman popularized this idea in his bestselling book "Thinking, Fast and Slow."

For System 2 to kick in, you must realize that System 1 did not produce the right answer.

For some people, the intuitive answer is the ball costs 10 cents. In order to come to the correct answer, you need to realize that System 1 didn't work, and assess the problem again.

Giving people another chance to solve a problem, though, doesn't automatically mean they will get it right.

Even when given two chances, many people remain loyal to their knee-jerk answer, according to a recent study. In the experiment, researchers gave participants 50 versions of the bat-and-ball problem.

Participants had to first give their System 1 answer, or their initial hunch, and then were allowed to give a System 2 answer, which was supposed to be more thought-through.

"Results showed that both people's first hunches and the responses they gave after deliberation predominantly remained biased from start to finish," the study reads. "But in the rare cases in which participants did learn to correct themselves, they immediately managed to apply the solution strategy and gave a correct hunch on the subsequent problems."

While making decisions, it's important to not always go with your hunch. Re-evaluate your choice, even if your intuition is telling you that you made the right one, and reflect on whether you are actually analyzing the problem or just looking for the easiest answer.

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People almost always get this simple math problem wrong: Can you solve it?  (2024)

FAQs

What is the simplest math problem that Cannot be solved? ›

What is the simplest equation no one can solve? 3x+1 popularly called the Collatz conjecture is the simplest math problem no one can solve. Even though it's easy for almost anyone to understand it's also at the same time impossible to solve. It's was named after Lothar Collatz in 1973.

Why do I always get math wrong? ›

Your dyscalculia may mean you don't get as much practice at using numbers as others. Perhaps because it takes you more time to do the same maths work, perhaps your teacher hasn't realised you have dyscalculia and is giving you work that's far beyond your current understanding.

What is the answer to the bat and ball IQ test? ›

If the ball costs 10 cents, then the bat would cost $1.10, which would bring the total to $1.20. The correct answer is the ball costs 5 cents and the bat $1.05. This question is part of the Cognitive Reflection Test, CRT, which was first described in 2005 by psychologist Shane Frederick.

Do math problems always have one answer? ›

Yes, there are a lot of math problems that only have one answer. But, there are problems that can have more than one answer and all math problems have more than one way to get to the answer.

What is the 1 hardest math problem? ›

The Riemann hypothesis deals with the behavior of the Riemann zeta function, a mathematical function used to study the distribution of prime numbers in the complex plane. It posits that all nontrivial zeros of the Riemann zeta function lie on a particular critical line in the complex plane.

What math problem has no answer? ›

The problems consist of the Riemann hypothesis, Poincaré conjecture, Hodge conjecture, Swinnerton-Dyer Conjecture, solution of the Navier-Stokes equations, formulation of Yang-Mills theory, and determination of whether NP-problems are actually P-problems.

What did Einstein score on IQ test? ›

Most theorists peg Einstein's IQ score between 160-190. Because he never took any kind of test to measure his intelligence, the definite score is still a mystery. But without a doubt, he was a brilliant man with an incredible brain.

What number is the top 2% of IQ? ›

The top 2% IQ corresponds to IQ scores above 130. In terms of percentiles, this means that the 98th percentile of IQ distribution lies around the score of 130.

What is the smartest IQ score? ›

These individuals are incredibly intelligent and have made significant contributions to their fields of study. Learn more about these brilliant minds and their remarkable accomplishments. As of 2024, the Highest IQ ever recorded is of YoungHoon Kim from South Korea whose IQ is 276.

What is the most confusing math problem? ›

The Riemann Hypothesis holds one of the seven unsolved problems known as the Millennium Prize Problems, each carrying a million-dollar prize for a correct solution. Its inclusion in this prestigious list further emphasizes its status as an unparalleled mathematical challenge.

Is math always hard? ›

For many students, math is one of the more difficult topics they must take. Some students may have trouble grasping the concepts, while others may struggle with the mathematical abilities required to do the required calculations. The method by which math is taught may also contribute to its perceived complexity.

What to do when you can't solve a math problem? ›

Strategies for Difficult Math Problems — and Beyond
  1. Do something. Yeah, the problem is hard. ...
  2. Simplify the problem. Try smaller numbers and special cases. ...
  3. Reflect on successes. You've solved lots of problems. ...
  4. Focus on what you haven't used yet. ...
  5. Work backwards. ...
  6. Ask for help. ...
  7. Start early. ...
  8. Take a break.

Why is 3X 1 unsolvable? ›

In the 3x+1 problem, no matter what number you start with, you will always eventually reach 1. problem has been shown to be a computationally unsolvable problem.

Has 3X-1 been solved? ›

In 1995, Franco and Pom-erance proved that the Crandall conjecture about the aX + 1 problem is correct for almost all positive odd numbers a > 3, under the definition of asymptotic density. However, both of the 3X + 1 problem and Crandall conjecture have not been solved yet.

What are the 7 hardest math problems? ›

Contents
  • 1 The Riemann Hypothesis. 1.1 Clay description.
  • 2 The Yang-Mills Equations.
  • 3 The P vs. NP Problem. 3.1 Clay description.
  • 4 The Navier–Stokes equations. 4.1 Clay description.
  • 5 The Hodge Conjecture.
  • 6 The Poincaré Conjecture. 6.1 Clay description.
  • 7 Birch and Swinnerton-Dyer conjecture.

What is the real answer to 1 1? ›

1+1 is a mathematical expression that evaluates to: 2 (number) (in ordinary arithmetic) 1 (number) (in Boolean algebra with a notation where '+' denotes a logical disjunction) 0 (number) (in Boolean algebra with a notation where '+' denotes 'exclusive or' operation, or in a quotient ring of numbers modulo 2)

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