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 your brain instantly shouted “10 cents!”, you are in very good company – most people give exactly that answer, including plenty of students at top universities. And it is wrong.
This little riddle is the most famous item on the Cognitive Reflection Test, a quiz developed by psychologist Shane Frederick to see whether people trust their first gut reaction or pause to check their reasoning. It has become a staple at institutions like Harvard and MIT because it is designed to trap fast, intuitive thinking. Read on to find the real answer – and learn a trick so you never fall for its cousins again.
Why Almost Everyone Says 10 Cents
The 10-cent answer feels right because $1.10 splits so neatly into $1.00 and $0.10. Your brain sees the total, grabs the simplest possible split, and happily moves on. Psychologists call this fast, automatic mode of thought “System 1”: quick, confident, and sometimes completely wrong.
But test that answer against the actual conditions. If the ball costs 10 cents and the bat costs $1.00 more than the ball, then the bat must cost $1.10. Add them together: $1.10 + $0.10 = $1.20. That is twenty cents too much. The intuitive answer collapses the moment you check it – which is precisely the lesson this puzzle is trying to teach.
The Rule: Name Your Unknowns
Whenever a word problem hands you a total and a difference between two things, stop guessing and turn it into algebra. Call the ball’s price x. Then the bat costs x + $1.00, because it is exactly one dollar more expensive than the ball. Together the two add up to $1.10. That is all you need.
Step-by-Step Solution
x + (x + 1.00) = 1.10
2x + 1.00 = 1.10
2x = 0.10
x = 0.05
The ball costs 5 cents and the bat costs $1.05. Now check the result: 0.05 + 1.05 = 1.10, and the bat ($1.05) is exactly $1.00 more than the ball ($0.05). Both conditions hold, so the answer is solid.
There is a handy shortcut hiding inside this algebra: the cheaper item always costs half the difference between the total and the gap. Here, (1.10 − 1.00) ÷ 2 = 0.05. Memorize that rule and you can solve any version of this puzzle in seconds. And if you want to double-check your arithmetic, try our free step-by-step calculators.
Practice Examples
1. A book and a pen cost $2.20 in total. The book costs $2.00 more than the pen. How much does the pen cost? Use the shortcut: (2.20 − 2.00) ÷ 2 = 0.10. Answer: 10 cents. If you said 20 cents, check it: 0.20 + 2.20 = 2.40. Too much!
2. A notebook and a pencil cost $5.50 together, and the notebook costs $5.00 more than the pencil. How much does the pencil cost? (5.50 − 5.00) ÷ 2 = 0.25. Answer: 25 cents. Check: 0.25 + 5.25 = 5.50, and 5.25 − 0.25 = 5.00. Correct.
3. If 5 machines take 5 minutes to make 5 widgets, how long do 100 machines take to make 100 widgets? This is a cousin of the same trap – the instinctive answer is 100 minutes. But each machine still makes one widget in 5 minutes, so 100 machines working in parallel finish 100 widgets in 5 minutes. Once again, the first answer that pops into your head is not the right one.