Brain Teaser 5: Solve 0! + 0! + 0! + 0! = 24

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Discussion Overview

The discussion revolves around the mathematical expression (0! + 0! + 0! + 0!)! and its evaluation to 24. Participants explore the concept of factorials, particularly the value of 0!, and engage in clarifying the reasoning behind the calculations involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that 0! is equal to 1, referencing the definition of factorials and the need for 0! to be defined this way for combinatorial purposes.
  • Others challenge the existence of a proof for 0! = 1, suggesting that it is defined for practical reasons in combinatorial contexts.
  • One participant explains that (0! + 0! + 0! + 0!)! simplifies to 4!, which equals 24, providing a breakdown of the factorial calculation.
  • There is a discussion about the nature of sarcasm in online communication, with participants expressing misunderstandings regarding tone and intent in their exchanges.

Areas of Agreement / Disagreement

Participants generally agree that 0! is defined as 1, but there is disagreement about the existence of a formal proof for this definition. The discussion remains unresolved regarding the clarity of communication and the interpretation of sarcasm.

Contextual Notes

Some participants express uncertainty about the definition of factorials and the implications of 0! = 1, indicating a potential gap in understanding the foundational concepts of combinatorial mathematics.

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Greetings !

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

Thanks ! :smile:

Live long and prosper.
 
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(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.
 
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 ! :smile:

Live long and prosper.
 
4*3*2*1=24 how does that work?
 
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.
 
  • #10
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 isn't my fault.
 
  • #11
I was trying to be sarcastic, most probably just a piss poor attempt at sarcasm, but i was trying.
 
  • #12
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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