The bat and the ball

About this video

Answer quickly: a bat and a ball cost 1.10 dollars together. The bat costs 1.00 dollar more than the ball. How much does the ball cost? For most people the answer 10 cents jumps straight into their head, and it feels obvious. In 2005 the researcher Shane Frederick asked this question to thousands of students, and at some of the best universities in the United States about half of them gave that quick answer.

Put it back into the question and it falls apart. If the ball costs 10 cents, the bat costs 1.10, and together they cost 1.20, not 1.10. The ball costs 5 cents.

The puzzle shows the mind's two ways of thinking. Fast thinking happens by itself: you read the word STOP, you know that 2 + 2 is 4, you see an angry face as angry. Slow thinking is work: 17 × 24 in your head, or parking in a tight space. Keith Stanovich and Richard West named them System 1 and System 2 in 2000, and Daniel Kahneman made them famous in his book Thinking, Fast and Slow (2011).

Fast thinking is right most of the time, and it lets us read, talk and walk without thinking about every step. But slow thinking is a lazy checker: it usually accepts what fast thinking offers when the answer feels right. The habit that helps is small. When an answer comes easily and the question matters, check it once: put the answer back into the question and see whether it all adds up. Try the bat and the ball on a friend, and remember that nobody who falls for it should feel silly. This video explains fast and slow thinking on Knaph.

Transcript

1. 0:00A bat and a ball cost 1.10 together. The bat costs a dollar more.
2. 0:06Ten cents? About half the students at top universities said so.
3. 0:12Check it. Ten cents makes 1.20. The ball costs five cents.
4. 0:19Fast thinking is quick and automatic. Slow thinking is careful, and it takes work.
5. 0:25Slow thinking could have checked. But the answer felt right.
6. 0:31When it matters, put the answer back into the question.
7. 0:37Fast is usually right. Check it once.