You've probably seen it on a Facebook feed or tucked into a LinkedIn "thought leader" post. It looks like a second-grade math problem. Honestly, it’s so simple it feels insulting.
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?
If you’re like the vast majority of people—including students at Harvard, MIT, and Princeton—the number "10 cents" just flashed in your mind like a neon sign. It’s a clean answer. It feels right.
But it’s wrong.
If the ball costs 10 cents and the bat is a dollar more, the bat would be $1.10. Add those together, and you're at $1.20. The math doesn't check out. The actual answer is 5 cents.
So why does a room full of the world's brightest engineers and future CEOs consistently trip over a nickel?
The Cognitive Reflection Test: Not Just a Riddle
This isn't just a bar bet or a "gotcha" question. It’s officially known as the first item of the Cognitive Reflection Test (CRT). Shane Frederick, a professor then at MIT (now at Yale), published this in 2005. He wanted to measure a very specific human trait: the ability to resist the first "gut" answer that pops into your head.
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Frederick's research was groundbreaking because it showed that intelligence and "reflection" are two different things. You can have a sky-high IQ and still be a "cognitive miser." That’s the term psychologists use for people who take the path of least mental resistance.
Basically, our brains are lazy. Evolutionarily speaking, this makes sense. If you’re being chased by a predator, you don't want to sit down and solve simultaneous equations. You need System 1 thinking—fast, intuitive, and automatic.
System 1 vs. System 2: The War in Your Head
Nobel Prize winner Daniel Kahneman made the ball and bat cost 1.10 problem famous in his book Thinking, Fast and Slow. He uses it to illustrate the friction between two mental "operating systems."
- System 1: This is your "fast" brain. It handles things like recognizing your mother's face or knowing that 2+2=4. It’s the part of you that shouted "10 cents!" before you even finished reading the sentence.
- System 2: This is the "slow" brain. It’s effortful. It’s what you use when you’re filling out tax forms or trying to remember where you parked in a massive airport garage.
The problem with the ball and bat cost 1.10 puzzle is that it specifically targets System 1. The numbers $1.10 and $1.00 "separate naturally" into $1.00 and $0.10. Your brain sees the pattern and stops looking for the logic.
To get to 5 cents, you have to manually "kick" System 2 into gear. You have to stop, ignore the 10-cent impulse, and actually run the numbers.
$$x + (x + 1.00) = 1.10$$
$$2x + 1.00 = 1.10$$
$$2x = 0.10$$
$$x = 0.05$$
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Most people find that level of effort "mildly unpleasant," according to Frederick's original paper. We’d rather be wrong and comfortable than right and exhausted.
Why Does This Matter in the Real World?
You might think, "Okay, so I got a riddle wrong. Big deal."
But the implications are actually kinda terrifying. Researchers have found that your score on the CRT—how well you handle the ball and bat problem—correlates with some heavy-duty life choices.
- Financial Decisions: People who get this wrong are statistically more likely to be "impatient" with money. They prefer a smaller reward now over a larger one later. They struggle with delayed gratification.
- Belief Systems: A study by Gordon Pennycook found that people who score low on the CRT are more susceptible to "pseudo-profound bullshit"—those deep-sounding but meaningless quotes—and are more likely to believe fake news.
- Gambling and Risk: If your System 1 is always in the driver's seat, you're more likely to fall for the "gambler's fallacy." This is the belief that if a coin flips heads five times in a row, it’s "due" to be tails next.
The "Harvard" Factor
One of the most cited statistics from Frederick’s 2005 paper is that even at elite universities, the error rate was staggering. At Harvard, only about 50% of students got all three CRT questions right. At less selective colleges, that number dropped to below 20%.
This proves that being "smart" doesn't mean you're a "reflective" thinker.
In fact, being highly intelligent can sometimes make you more prone to these errors because you’ve spent your whole life trusting your quick-fire intuitions. You’re used to being right immediately. When a problem like the ball and bat cost 1.10 comes along, your confidence becomes your biggest liability.
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Can You Train Yourself to Be Less "Miserly"?
The good news is that cognitive reflection is a muscle. Sorta.
Recent studies have shown that simply being told "this is a trick question" or "most people get this wrong" significantly increases the number of people who find the 5-cent answer. Awareness is the first step.
When you feel that "click" of an easy answer, learn to treat it with suspicion. Ask yourself: "Is this the answer, or is this just the first thing I thought of?"
If you want to test your progress, try to solve the other two classic CRT questions without jumping to conclusions:
- If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? (Intuitive answer: 100. Correct answer: 5.)
- 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? (Intuitive answer: 24. Correct answer: 47.)
Actionable Steps for Better Thinking
Next time you’re faced with a decision—whether it’s a math puzzle or a major purchase—try these three things to bypass your "lazy" brain:
- Write it down. Physically seeing the numbers $0.05 + $1.05 = $1.10 makes the error of "10 cents" obvious.
- The "Pre-Mortem" Technique. Assume your first instinct is wrong. Now, try to figure out why it would be wrong. This forces System 2 to start looking for flaws.
- Wait 10 seconds. For simple puzzles, just a few seconds of silence can be enough to let the "slow" brain catch up to the "fast" one.
The ball and bat cost 1.10 problem isn't about math. It's a mirror. It shows us that even in 2026, with all our technology, our biological hardware is still prone to the same shortcuts it used thousands of years ago. Recognizing that glitch is the only way to fix it.
To improve your own decision-making today, take the most "obvious" conclusion you’ve reached this week—perhaps about a work project or a personal relationship—and apply the $1.05 + $0.05 logic to it. Check if the "sum" of your assumptions actually adds up to the reality of the situation.