20070131, 18:33  #1 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
1000111001010_{2} Posts 
Four Fours
I don't know if this a new one for some of you OR as old as Mersenne himself
The Four 4's Puzzle: For you Disney fans this puzzle is also known as: "The 101 Damn Calculations". Using four 4's and standard mathematical operations formulate equations with the answer being each of the numbers from 0 to 100. All 101 (a prime number!!!) are possible. Every calculation MUST use exactly four 4's and no other digits. The allowable operations are: · Addition: 4 + 4 = 8 · Subtraction: 4 – 4 = 0 · Multiplication: 4 * 4 = 16 · Division: 4 / 4 = 1 · Parenthesis: (4 + 4) / 4 = 2 · Factorial: 4! = 24 · Exponential: 4^4 = 256 · Squareroot: √4 = 2 · Concatenation: 44 · Decimal Point: .4 · Repeating Decimal .4 (uses one 4) repeating is equal to 4/9 Examples: 4+444 = 0 4!*4*(4/4)= 100 
20070131, 19:07  #2 
Oct 2006
73 Posts 

20070131, 19:16  #3 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
10712_{8} Posts 

20070201, 00:54  #4 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
We already did this one
Please see thread 4756

20070201, 05:30  #5 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2×3^{2}×11×23 Posts 

20070201, 05:58  #6 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{3}×1,171 Posts 
Here is that thread easy style:
http://www.mersenneforum.org/showthread.php?t=4756 Notice the form of the url, the t= is the thread number. If it were p= , that would be a post number. 
20070201, 17:57  #7  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
T and P
Quote:
Thank you Unwilly for the info as I often wondered about this too. But where do you get t=4756 from? Is it from the archives? Mally 

20070201, 19:34  #8 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2×3^{2}×11×23 Posts 
OKAY...I concede. I was reminded that this puzzle ran a couple years ago....albeit with slightly different parameters....so watch for a companion posting of the Four Nines puzzle....

20070203, 10:42  #9 
Oct 2004
Austria
2·17·73 Posts 
This was not the same. In thread 4756, it was allowed to use less than four fours, the "square" operator was allowed (but no SQRT, no exponent)
Here you have to use EXACTLY four fours and a different set of allowed operators. It would be fun to see how far we could complete the list according to the rules in this thread. (a number of things used in thread 4756 would not work here) Note: squaring seems to be still allowed using x^2 = x^(√4) let's start with a somewhat "unusual" 1: 1=(4!4)^(44) 3=44^(44) 5=4+4^(44) 
20070203, 11:32  #10 
Jun 2003
The Texas Hill Country
441_{16} Posts 
And just to keep it "interesting", no skipping around. :)
You have to wait to post "7" until someone posts a solution for 6", etc. Posting "better" solutions for smaller numbers is fine. And, since this is abour 4's, no more than 4 additions before you give others a chance to play. 0 = 4 + 4  4  4 1 = (4+4)^(44) 2 = 4/4 + 4/4 3 = 44^(44) (from Andi47) 4 = 4*4^(44) 5 = 4+4^(44) (from Andi47) Last fiddled with by Wacky on 20070203 at 11:36 Reason: More "rules" 
20070203, 13:49  #11 
Oct 2006
73 Posts 
Well, as the rules are subtly different, I'll join in.
6 = 4 + ((4 + 4) / 4) 7 = 4 + 4  (4 / 4) 8 = 4 * 4  4  4 9 = 4 + 4 + (4 / 4) I appreciate that some of the brackets are redundant, but I believe in making things as clear to comprehend as possible. Last fiddled with by DJones on 20070203 at 13:50 Reason: Typing error 