Welcome to a fun exploration of logic riddles featuring Caitlin from SciShow Space, Jessi from Animal Wonders Montana, and Hank Green, known from SciShow, CrashCourse, and VlogBrothers. Let’s dive into some intriguing questions that challenge our thinking!
Here’s a classic puzzle: A bat and a ball together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?
At first glance, you might think the ball costs $0.10. However, if the ball were $0.10, the bat would be $1.10, making the total $1.20. The correct answer is that the ball costs $0.05, and the bat costs $1.05, totaling $1.10.
Next, consider this: If 5 machines take 5 minutes to make 5 widgets, how long would 100 machines take to make 100 widgets?
Your initial instinct might be to say 100 minutes, but let’s think it through. Each machine makes 1 widget in 5 minutes. Therefore, 100 machines would also take 5 minutes to make 100 widgets. The answer is 5 minutes.
Imagine a lake with a patch of lily pads that doubles in size every day. It takes 48 days for the patch to cover the entire lake. How long does it take to cover half the lake?
The answer is 47 days. Since the patch doubles in size each day, it would have covered half the lake the day before it covered the entire lake.
These riddles are part of the Cognitive Reflection Test, developed by psychologist Shane Frederick in 2005. The test is designed to make you reflect on your initial gut responses, which are often incorrect. It highlights the difference between two types of thinking: System 1, which is fast and intuitive, and System 2, which is slower and more analytical.
Interestingly, when this test was given to students at prestigious universities like MIT and Princeton, a significant number struggled to answer all questions correctly, demonstrating the challenge of overcoming intuitive but incorrect answers.
Here’s a thought-provoking scenario: A father and son are in a car accident. The father dies, and the son is rushed to the hospital. The surgeon says, “I can’t operate on him; he’s my son.” Who is the surgeon?
The answer is the boy’s mother. This riddle challenges our assumptions and biases, as many people initially overlook the possibility of the surgeon being a woman due to societal stereotypes.
These riddles not only test our logical thinking but also challenge our assumptions. For example, the Draw-a-Person Test often reveals that children tend to draw scientists as men, highlighting ingrained stereotypes.
Thank you for joining us on this journey through logic and reflection. We hope these riddles have sparked your curiosity and encouraged you to think more deeply about the assumptions we make every day.
Revisit each of the four riddles presented in the article. Write down your initial answers and then the correct solutions. Reflect on why your initial answers might have been incorrect and what assumptions led you there. Share your reflections with a partner and discuss how cognitive biases might have influenced your thinking.
Using the principles of cognitive reflection, create your own logic riddle that challenges common assumptions or intuitive thinking. Exchange riddles with a classmate and attempt to solve each other’s puzzles. Discuss the thought processes involved in solving these riddles and the assumptions they challenge.
Form small groups and discuss the concept of cognitive reflection as introduced in the article. Consider how System 1 and System 2 thinking apply to your daily decision-making processes. Share examples from your own experiences where intuitive thinking led you astray and how analytical thinking helped you find the correct solution.
Reflect on the “The Surgeon” riddle and its implications about societal stereotypes. Research and present on how stereotypes can affect decision-making and perception in various fields, such as science, medicine, or education. Discuss strategies to overcome these biases in academic and professional settings.
Take the full Cognitive Reflection Test, which includes additional riddles beyond those in the article. Analyze your responses and identify patterns in your thinking. Discuss with classmates how this test can be used to improve critical thinking skills and the importance of questioning initial instincts.
Here’s a sanitized version of the provided YouTube transcript:
—
This is Caitlin from SciShow Space and sometimes SciShow. This is Jessi from Animal Wonders Montana. This is Hank Green, who you may know from SciShow, CrashCourse, and VlogBrothers.
So, first question for you, Jessi. A bat and a ball cost $1.10. The bat costs $1 more than the ball. How much is the ball?
The bat costs $1 more than the ball. This is like flashbacks to the SATs.
Wait. The bat costs $1 more than the ball. How much is the ball?
$0.10? Am I wrong?
You’re not wrong, except there’s another answer.
That’s right. The bat is $1.05. How much is the ball?
$0.05.
Yes. Most people are with you. And to be honest, the question is designed for you to give that answer.
Yes.
Which is why I knew I was wrong.
Yes! I was going to say $1.05, but then I thought, isn’t the ball $1?
But you corrected yourself immediately as you were talking.
But there are more questions. And now, you may stop and reflect on what you should be saying.
I don’t want this to cause you deep emotional anguish. Question number two.
If 5 machines take 5 minutes to make 5 widgets, how long do 100 machines take to make 100 widgets?
100 minutes.
My very first instinct was to say 20 minutes.
Oh, interesting.
So we have 5 machines taking 5 minutes to make 5 widgets. And then we just increase the machines and the output.
So we have 100 machines making 100 widgets.
Yes.
So then you have 100 machines. You don’t have 5 making 100 things.
Yes. That makes perfect sense.
It does when you think about it. But the thing is with this test, it’s not designed to allow you to think about it, right? It wants you to give this quick answer.
That is two for two for Caitlin. Caitlin is doing a great job.
How many questions are there? I’m nervous.
In a lake, there’s a patch of lily pads that doubles in size every day. It takes the patch 48 days to cover the entire lake. How long does it take for the patch to cover half of the lake?
I’ve heard this one before. It takes 48 days to fill up the entire lake, so how many days does it take to fill up half of the lake?
So 47 days?
Yes.
Hey, I got one right!
But I’ve heard that one before, so I kind of cheated.
You didn’t cheat. You thought about it correctly.
This test is called the Cognitive Reflection Test. It was developed by American psychologist Shane Frederick and was first published in 2005. He first gave this test in over 35 different scenarios to over 3,000 people. The point of the test is that it causes you to cognitively reflect.
33% of the people missed all of the questions. You have different systems of processing in your brain, which you’ve probably heard about before. There’s a theory called Dual Processing Theory which talks about System 1 and System 2.
System 1 is like your gut response to something. It’s often referred to as your intuition. And it’s very fast and quick. That is the system that wants you to go, “Oh, of course it costs $1,” rather than saying $1.05.
And System 2 is a more slow, considered, and logical way of thinking that we don’t always do, but we have to step back and look at it differently.
When he gave the questions to students at MIT, only 48% of the students could answer all of the questions correctly. At Princeton, only 26% of the students could answer all of the questions correctly.
It’s difficult.
When I first did it, I got the lily pads one correct. I got the bat and the ball wrong.
So we’re going to move on to the second test. This is another riddle.
A father and son are in a car accident. The father dies at the scene and the son is rushed to the hospital. When the son is being prepped for surgery, the surgeon comes in and says, “I can’t perform this operation. This is my son.” Who is the surgeon?
What do you mean?
The father and the son are in an accident. The father dies at the scene. The son is rushed to the hospital. The surgeon walks in and says, “I can’t do this. This is my son.” Who is the surgeon?
I mean, I have come up with several different scenarios.
Let’s talk through them.
There are many different ways in which you can have more than one father. You could have a gay couple that are your parents. You could have an adopted father and a biological father. You could have a stepfather.
You can have many different stepfathers.
You can have a grandparent.
You can have a priest who is your father.
And then his actual father is…
But that doesn’t make sense.
Is this anywhere where we’re headed in the right direction?
It’s one direction.
But it’s a logic problem, so I’m like, oh, it’s his mother.
Oh, yes!
The question is set up in a way that leads people to not think of the mother as the surgeon.
This test has been done on both men and women, and both genders have the same response where people don’t think that the mother is the surgeon.
It’s not just the bias that we think a doctor must be a man. It is also the way the question is framed.
It’s designed to trick you.
There’s another test with kids that you may have seen that tests assumptions. It’s called the Draw-a-Person Test. Kids are often asked to draw what a scientist looks like, and they often draw a man in a lab coat.
These questions challenge the assumptions we have about people when we’re not given the full information.
Thank you so much for asking me hard questions.
You’re welcome.
Thank you.
Hank, thank you so much for being on BrainCraft.
Thank you for the discussion!
—
This version removes any informal language, laughter, and unnecessary repetitions while maintaining the essence of the conversation.
Logic – The systematic study of valid rules of inference and the structure of propositions. – In mathematics, logic is used to determine the validity of arguments and proofs.
Riddles – Problems or puzzles that require critical thinking and ingenuity to solve. – Solving mathematical riddles can enhance students’ problem-solving skills and logical reasoning.
Thinking – The process of considering or reasoning about something. – Critical thinking in mathematics involves analyzing and evaluating evidence to form a logical conclusion.
Cognitive – Relating to mental processes such as awareness, perception, reasoning, and judgment. – Cognitive development in students is crucial for mastering complex mathematical concepts.
Reflection – The process of introspection and evaluation of one’s own thoughts and methods. – After solving a problem, reflection helps students understand their approach and improve their mathematical reasoning.
Assumptions – Statements accepted as true without proof, serving as a starting point for further reasoning. – In geometry, assumptions about the properties of shapes are often used to prove theorems.
Analytical – Relating to or using analysis or logical reasoning. – An analytical approach to mathematics involves breaking down complex problems into simpler parts.
Intuitive – Based on what one feels to be true without conscious reasoning. – Some mathematical concepts, like symmetry, can be understood through an intuitive grasp of patterns.
Challenge – A task or problem that tests a person’s abilities and skills. – Solving advanced calculus problems is a challenge that requires both analytical and creative thinking.
Students – Individuals who are engaged in learning, especially at a school or university. – University students often collaborate to tackle complex mathematical problems and share diverse perspectives.
