Brain Teaser 5 ?

1. Jul 3, 2003

drag

Greetings !

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

Thanks !

Live long and prosper.

2. Jul 3, 2003

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.

3. Jul 3, 2003

drag

Eeh... factorial ?

4. Jul 3, 2003

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.

5. Jul 3, 2003

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.

6. Jul 4, 2003

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.

7. Jul 4, 2003

Andy

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

8. Jul 5, 2003

dav2008

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

9. Jul 5, 2003

Andy

Sarcasm gets lost online.

10. Jul 5, 2003

dav2008

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.

11. Jul 5, 2003

Andy

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

12. Jul 7, 2003

Imperial

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