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Topic: mighty 4 fours
Replies: 3   Last Post: May 16, 2007 2:25 AM

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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 twenty-one 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 = 4-4+4-4
1 = (4/4)+4-4
2 = (4/4)+(4/4)
3 = (4+4+4)/4
4 = (4-4)x4+4
5 = [4+(4x4)]/4
6 = 4+[(4+4)/4]
7 = 4+4-(4/4)
8 = 4+4+4-4
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

Date Subject Author
8/27/06 math500
9/3/06 Oliver Stemforn
9/5/06 Jason Fahy
5/16/07 Parikshit