# Brain Teaser 5 ?

Greetings !

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

Thanks !

Live long and prosper.

(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.

Eeh... factorial ?

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.

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.

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

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.

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!