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4 3's #916056
09/28/13 11:05 PM
09/28/13 11:05 PM
Joined: Nov 2000
Posts: 18,719
Ottawa Ontario Canada
CanukDenis Offline OP
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CanukDenis  Offline OP
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These are allowed:
+ - / * ! ()

Make 100 using four 3's

...not easy!

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






I'm a man of few words, BUT I use 'em often!!
Re: 4 3's [Re: CanukDenis] #916173
09/29/13 08:36 PM
09/29/13 08:36 PM
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47.79N, 122.24W
BobH Offline
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(((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

Last edited by BobH; 10/01/13 03:59 PM. Reason: corrected unintentional double factorial

Bob
As I've grown older, I've found that my memory is not as good as I used to think it was.
Re: 4 3's [Re: CanukDenis] #916180
09/29/13 09:34 PM
09/29/13 09:34 PM
Joined: Nov 2000
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Ottawa Ontario Canada
CanukDenis Offline OP
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Perfecto Bob!


I'm a man of few words, BUT I use 'em often!!
Re: 4 3's [Re: CanukDenis] #916302
09/30/13 02:26 PM
09/30/13 02:26 PM
Joined: Mar 2004
Posts: 11,846
Isle of Man
Lex Offline
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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


Life is what happens while you're making other plans.

Re: 4 3's [Re: CanukDenis] #916312
09/30/13 03:43 PM
09/30/13 03:43 PM
Joined: Nov 2000
Posts: 18,719
Ottawa Ontario Canada
CanukDenis Offline OP
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CanukDenis  Offline OP
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I'm a man of few words, BUT I use 'em often!!
Re: 4 3's [Re: CanukDenis] #916322
09/30/13 05:03 PM
09/30/13 05:03 PM
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BobH Offline
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Lex, so in the solution above

3! = 3*2*1 = 6

3!! = 6! = 6*5*4*3*2*1 = 720

Last edited by BobH; 09/30/13 05:57 PM. Reason: expanded a bit more

Bob
As I've grown older, I've found that my memory is not as good as I used to think it was.
Re: 4 3's [Re: CanukDenis] #916476
10/01/13 02:30 PM
10/01/13 02:30 PM
Joined: Mar 2004
Posts: 11,846
Isle of Man
Lex Offline
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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?

Last edited by Lex; 10/01/13 02:37 PM.

Life is what happens while you're making other plans.

Re: 4 3's [Re: CanukDenis] #916502
10/01/13 04:00 PM
10/01/13 04:00 PM
Joined: Oct 2011
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BobH Offline
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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


Bob
As I've grown older, I've found that my memory is not as good as I used to think it was.
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