Overview
This one-line problem from the Cognitive Reflection Test famously fools most people, because a fast, intuitive answer springs to mind before the arithmetic is checked.
How to solve The Bat and Ball
- Let the ball cost x. Then the bat costs x + $1.00.
- Together they cost x + (x + 1.00) = 1.10, so 2x = 0.10.
- Therefore x = $0.05 — the ball is 5 cents and the bat is $1.05.
The key insight
The gut answer of 10 cents ignores the word 'more'. Writing the difference as an equation forces the split to be $1.00, not the total.
Variations & echoes
- It's the flagship item of Kahneman's 'System 1 vs System 2' thinking.
- Any 'sum and difference' word problem yields to the same two-equation setup.
Frequently asked questions
Why is 10 cents wrong?
If the ball were $0.10 the bat would be $1.10, and together that's $1.20 — not $1.10. The gap would be only $1.00 at $0.05.