# The Bat and Ball Problem

This is a famous cognitive reflection test question. Let me work through it carefully.

**Let:**
- Ball = x
- Bat = x + 1.00

**Equation:**
x + (x + 1.00) = 1.10
2x + 1.00 = 1.10
2x = 0.10

## **The ball costs $0.05 (5 cents)**

**Verification:** The bat costs $1.05, the ball costs $0.05
- Total: $1.05 + $0.05 = **$1.10** ✓
- Difference: $1.05 − $0.05 = **$1.00** ✓

> The intuitive (but wrong) answer that many people jump to is $0.10 — but if the ball cost $0.10, the bat would cost $1.10, making the total $1.20.
