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Jason Fahy
Posts:
15
From:
Edmonton, AB
Registered:
9/5/06


Re: mighty 4 fours
Posted:
Sep 5, 2006 4:28 PM


It doesn't appear that all values are possible. Here's some work I did for our math department a few years ago, hopefully the formatting isn't too bad:
I decided to put the matter to rest and work out every possible permutation of this question, so we'd know once and for all which ones are possible.
There are 4^3 ways to put four operators in three spaces, so 64 operation sequences. There are ten ways to arrange the brackets. Including no brackets at all, they are:
4 4 4 4
(4 4) 4 4 4 (4 4) 4 4 4 (4 4)
(4 4 4) 4 4 (4 4 4)
[(4 4) 4] 4 4 [(4 4) 4]
[4 (4 4)] 4 4 [4 (4 4)]
Edit, May 2006: The configuration (4 4) (4 4) wasn't tested originally. I just did it; it didn't generate any new values.
So, with 64 operation sequences and 10 bracket configurations, we get 640 possibilities. Some work in Excel with flood fill and copy/paste soon yielded twenty pages of expressions, which took a little under an hour to evaluate. The result: fifteen of the twentyone values are gettable. They are listed below, along with a single example to prove that they're possible. (Many of the brackets are superfluous, but I hope they will improve the readability.)
0 = 44+44 1 = (4/4)+44 2 = (4/4)+(4/4) 3 = (4+4+4)/4 4 = (44)x4+4 5 = [4+(4x4)]/4 6 = 4+[(4+4)/4] 7 = 4+4(4/4) 8 = 4+4+44 9 = 4+4+(4/4)
12 = [4(4/4)]x4
15 = (4x4)(4/4) 16 = 4+4+4+4 17 = (4x4)+(4/4)
20 = [(4/4)+4]x4
Message was edited by: Jason Fahy
Message was edited by: Jason Fahy



