Does 2 Equal 1? A Classic Algebra Puzzle

Does 2 equal 1? You tell me! Here is the proof (unfiltered by rational arguments):

1. Let a and b be equal non-zero quantities: a = b
2. Multiply through by a: a² = ab
3. Subtract b²: a² − b² = ab − b²
4. Factor both sides: (a − b)(a + b) = b(a − b)
5. Divide out (a − b): a + b = b
6. Observing that a = b: b + b = b
7. Combine like terms on the left: 2b = b
8. Divide by the non-zero b: 2 = 1

Well, can you spot the mistake?

Puzzles like this are a fun way to sharpen your algebra. For more practice, see our math review sheet.