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#916056 - 09/28/13 11:05 PM 4 3's
CanukDenis Offline
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Registered: 11/26/00
Posts: 15342
Loc: Ottawa Ontario Canada
These are allowed:
+ - / * ! ()

Make 100 using four 3's

...not easy!

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




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#916173 - 09/29/13 08:36 PM Re: 4 3's [Re: CanukDenis]
BobH Offline
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Registered: 10/14/11
Posts: 1911
Loc: 47.79N, 122.24W
(((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


Edited by BobH (10/01/13 03:59 PM)
Edit Reason: corrected unintentional double factorial
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#916180 - 09/29/13 09:34 PM Re: 4 3's [Re: CanukDenis]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 15342
Loc: Ottawa Ontario Canada
Perfecto Bob!
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#916302 - 09/30/13 02:26 PM Re: 4 3's [Re: CanukDenis]
Lex Offline
BAAG Specialist

Registered: 03/07/04
Posts: 5199
Loc: Isle of Man
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
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#916312 - 09/30/13 03:43 PM Re: 4 3's [Re: CanukDenis]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 15342
Loc: Ottawa Ontario Canada
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#916322 - 09/30/13 05:03 PM Re: 4 3's [Re: CanukDenis]
BobH Offline
Addicted Boomer

Registered: 10/14/11
Posts: 1911
Loc: 47.79N, 122.24W
Lex, so in the solution above

3! = 3*2*1 = 6

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


Edited by BobH (09/30/13 05:57 PM)
Edit Reason: expanded a bit more
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Bob
I've learned that if you're too busy to help a friend, you're too busy.

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#916476 - 10/01/13 02:30 PM Re: 4 3's [Re: CanukDenis]
Lex Offline
BAAG Specialist

Registered: 03/07/04
Posts: 5199
Loc: Isle of Man
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?


Edited by Lex (10/01/13 02:37 PM)
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#916502 - 10/01/13 04:00 PM Re: 4 3's [Re: CanukDenis]
BobH Offline
Addicted Boomer

Registered: 10/14/11
Posts: 1911
Loc: 47.79N, 122.24W
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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