The Bat and the Ball

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

Ten cents jumps into nearly everyone’s head. It feels right. It is also wrong, because a ten cent ball means a $1.10 bat and a total of $1.20.

Doing it slowly

Call the ball b. The bat is b + 1.00. Together they make 2b + 1.00 = 1.10, so 2b = 0.10 and the ball costs 5 cents. The bat costs $1.05, and the total is $1.10.

Why the wrong answer feels so right

The numbers split neatly into 1.00 and 0.10, and the brain loves a neat split. Quick intuition is wonderful for catching a ball or reading a face. It is less reliable with anything that has a twist in its wording.

A cheap habit

Before you trust a fast answer, spend ten seconds plugging it back into the problem. Almost every wrong answer to this puzzle would be caught by that one step. It is the same reason accountants add a column twice.