GB HOMEPAGE

4 3's

Posted By: CanukDenis

4 3's - 09/29/13 04:05 AM

These are allowed:
+ - / * ! ()

Make 100 using four 3's

...not easy!

Example:
3/.3 * 3/.3 = 100 (but . not allowed)




Posted By: BobH

Re: 4 3's - 09/30/13 01:36 AM

(((3!)!) - (((3!)!) / (3!))) / (3!)

= (720 - (720/6)) / 6

= (720 - 120) / 6

= 600 / 6

= 100

Some of the parentheses are not necessary if you assume standard precedence rules but I put them in to avoid possible ambiguity.

Here's what it would look like with standard precedence rules applied. It's more readable.

((3!)! - (3!)! / 3!) / 3!

smile
Posted By: CanukDenis

Re: 4 3's - 09/30/13 02:34 AM

Perfecto Bob!
Posted By: Lex

Re: 4 3's - 09/30/13 07:26 PM

I have not previously encountered ! as a mathematical symbol, and having considered this answer and googled I am not much the wiser: in layman's terms what does it denote? headscratch
Posted By: CanukDenis

Re: 4 3's - 09/30/13 08:43 PM

http://en.wikipedia.org/wiki/Factorial

Posted By: BobH

Re: 4 3's - 09/30/13 10:03 PM

Lex, so in the solution above

3! = 3*2*1 = 6

3!! = 6! = 6*5*4*3*2*1 = 720
Posted By: Lex

Re: 4 3's - 10/01/13 07:30 PM

Thanks to both: my head only hurts a little bit...! wink

Afterthought: if 9!! = 9*7*5*3*1 (as appears from wikipedia), how come 3!! includes the even number?
Posted By: BobH

Re: 4 3's - 10/01/13 09:00 PM

Interesing Lex! I had never seen that before. I guess I can't do away with so many parentheses after all.

I updated my simplified formula. Thanks for pointing that out. thumbsup
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