Full credit for this puzzle goes to my good friend Vahan who spent an evening puzzling our guild with it. I should also probably point out that to work it out, you only need the mathematical ability of a 13-year old (at least according to the English school system) so no excuses!

I’m now going to prove to you that 2 = 1. Your job is to work out why it doesn’t.

Take the ^ sign to mean ‘to the power of’, such that a^2 means ‘a to the power of two’ (or more commonly ‘a squared’).

Let a = b

a^2 = b^2

a^2 = ab

a^2 – b^2 = ab – b^2

(a + b)(a – b) = b(a – b)

a + b = b

b + b = b

2b = b

Which implies that 2 = 1.

You have until Friday!

Vel.

P.S. You don’t need to substitute numbers in to solve it.

Advertisements

January 4, 2010 at 12:29 pm

Much as I’d love to claim credit, this is quite well known. Oh and here’s a hint: a^2-b^2 does factorise to (a+b)(a-b). For some reason that’s where everyone in Imperial Guardsmen thought their was a mistake there, but I promise there isn’t!

January 4, 2010 at 3:04 pm

Well, you inspired me then.

And yes, anyone who doesn’t believe that can simply multiply out the brackets to check.

January 4, 2010 at 7:44 pm

“a = b”

…

“(a + b)(a – b) = b(a – b)”

(a – b) = 0 blows up everything.

January 5, 2010 at 6:36 am

Ah ha! Well spotted, you got it 😀