# A bat and a ball cost $1.10 together. The bat costs $1.00 more than the ball. How much is the ball?

Source: https://silverapuzzles.com/riddles/a-bat-and-a-ball-cost-1-10-together-the-bat-costs-1-00-more-than-the

This question appears in research on quick thinking (the Cognitive Reflection Test) because a fast first guess is usually wrong. All you need is subtraction, but you have to slow down for a second.

**Answer:** 5 cents.

If the ball is 5 cents, the bat is $1.05: together $1.10, and the bat costs exactly $1.00 more.

Hint: It is not 10 cents.

## How to think about it

1. Write the two facts as equations: bat + ball = 1.10, and bat = ball + 1.00.
2. Test the instinctive answer, 10 cents. If the ball is 10 cents, the bat is 1.10, and together they cost 1.20. That is 10 cents too much, so 10 cents fails.
3. Substitute the second equation into the first: (ball + 1.00) + ball = 1.10, so 2 × ball = 0.10.
4. Divide by two. The ball costs 0.05, and the bat costs 1.05.

## Why “5 cents” is the answer

A ball at 5 cents and a bat at $1.05 add up to $1.10, and the gap between them is exactly $1.00, so both conditions hold at the same time. The 10-cent answer only satisfies the first condition. The riddle tempts you to split $1.10 into $1.00 and $0.10 because those numbers appear in the question, but the $1.00 is a difference, not a price.

## Common wrong answers

- **10 cents.** With a 10-cent ball the bat must be $1.10, and the pair would cost $1.20, not $1.10.
- **$1.00.** That is the difference between the two prices, not the cost of either item.