# Brain Teaser 5 ?

#### drag

Greetings !

What's all that stuff about (0! + 0! + 0! + 0!)! = 24 !?

Thanks !

Live long and prosper.

#### Greg Bernhardt

(0)! (pronounced as Zero -Factorial), is equal to 1. The factorial of the sum of the factorials of four zeros, each taken separately, giving 4!, which is equal to 24.

#### drag

Eeh... factorial ?

#### FZ+

Consider this:

4! = 4 * 3 * 2 * 1

So n!, where n is a natural number =

n * (n-1) * ... * 1

It can be mathematically proven that 0! = 1

Don't ask me how, because I forgot.

#### Hmmmm . . .

there is no 0! proof

actually there is no proof that 0! = 1. look at it from this perspective:

disregarding the order in which we choose, how many ways we can choose k objects from a set of n objects? when finding ways to choose we use the following: nCk = n!/(k!(n-k)!). since there is only one way that one can choose 0 objects, we define 0! = 1 so that n!/(0!(n-0)!) = n!/0!n! = 1/0! = 1.

bascially 0! = 1 is defined as such because we simply need it to be. try to choose k = 0 objects from a set of n objects if 0! = 0. now that's chaos.

i hope that helps.

#### drag

Re: there is no 0! proof

Aah...so 0! = 1 , in that case I knew what a factorial is but
I never heard of this equality so I thought this may be something else.

Thanks !

Live long and prosper.

#### Andy

4*3*2*1=24 how does that work?

#### dav2008

Gold Member
Originally posted by Andy
4*3*2*1=24 how does that work?
What do you mean? By definition 4!=4*3*2*1 which is 24. THats not the answer to the brain teaser, its just an example

#### Andy

What do you mean? By definition 4!=4*3*2*1 which is 24. THats not the answer to the brain teaser, its just an example
Sarcasm gets lost online.

#### dav2008

Gold Member
Originally posted by Andy
Sarcasm gets lost online.
What are you talking about?!?!?!...I was not being sarcastic. I was answering your question. If I didnt understand your question, that isnt my fault.

#### Andy

I was trying to be sarcastic, most probably just a piss poor attempt at sarcasm, but i was trying.

#### Imperial

Basically, (0! + 0! + 0! + 0!)! = (1 + 1 + 1 + 1)!, which equals 4! which evaluates to 24. That is all there is to it!

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