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 2007-02-01, 19:47 #1 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 10010000111102 Posts Four Nines I don't know if this a new one for some of you OR as old as Mersenne himself and I hope I am not told again that it has been done. None of the links to other websites from the four-fours types of puzzle that I have seen yet have dealt with four-nines. The Four 9's Puzzle: For you Disney fans this puzzle is also known as: "The 101 Damn Calculations". Using four 9'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 9's and no other digits. The allowable operations are: · Addition: 9 + 9 = 18 · Subtraction: 9 – 9 = 0 · Multiplication: 9 * 9 = 81 · Division: 9 / 9 = 1 · Parenthesis: (9 + 9) / 9 = 2 · Square-root: √9 = 3 · Factorial: √(9!) = 6 · Exponential: √9^√9 = 27 · Concatenation: 99 · Decimal Point: .9 OR 9 . Some puzzles of this form allow the use of repeating decimals, my version does not required or allow it: I think using .9 repeating as 1 makes this puzzle too easy. . Other versions allow the percent operator (i.e. √9% = .3). Again it is not necessary for this puzzle but if you have to use it.....
 2007-02-01, 20:39 #2 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 225518 Posts 9 + 9 - 9 - 9 = 0 99/99 = 1 9/9 + 9/9 = 2 (or 99/9 - 9) 9/(√9) + 9 - 9 = 3 9/(√9) + 9/9 = 4 √9 + √9 - 9/9 = 5 √9 + √9 - 9 + 9 = 6 9 - √9 + 9/9 = 7 99/9 - √9 = 8 (√9 * √9) + 9 - 9 = 9 (√9)! + (√9)! + (√9)! - 9 = 10 9 + (9 + 9)/9 = 11 √9 + √9 + √9 + √9 = 12 9 + √9 + 9/9 = 13 99/9 + √9 = 14 √9 * √9 + √9 + √9 = 15 (√9)! + 9 + 9/9 = 16 9 + 9 - 9/9 = 17 9 + 9 + 9 - 9 = 18 9 + 9 + 9/9 = 19 99/9 + 9 = 20 ((√9)!)*√9) + (√9)! - √9 = 21 Last fiddled with by Uncwilly on 2007-02-01 at 21:00 Reason: added 0, 10 - 21
2007-02-01, 21:30   #3
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

2×3×773 Posts

Quote:
 Originally Posted by Uncwilly (√9)! + (√9)! + (√9)! - 9 = 10
Great start only 79 to go.... have another look at 10.

2007-02-01, 23:01   #4
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

100101011010012 Posts

Quote:
 Originally Posted by petrw1 Great start only 79 to go.... have another look at 10.
(√9 * √9) + 9/9 = 10
((√9)! * (√9)!) - 9 -√9) = 22

Last fiddled with by Uncwilly on 2007-02-01 at 23:07

 2007-02-02, 00:33 #5 Wacky     Jun 2003 The Texas Hill Country 32×112 Posts Starting at the top and working down: 99/.9 - 9 = 101 99 + 9/9 = 9/.9 * 9/.9 =100 99 + 9 - 9 = 99 99 - 9/9 = 98
 2007-02-02, 02:13 #6 grandpascorpion     Jan 2005 Transdniestr 1F716 Posts Some more 97 = 99 - (√9)!/(√9) 96 = 99-9/√9 = 99 + √9 - (√9)! = 9/.9 + √9 + √9 93 = 99- √9 - √9 91 = 9*9 + 9/.9 90 = 99 - √9 - (√9)! 89 = 99 - 9/.9 87 = 99 -(√9)! -(√9)! 84 = 99 -(√9)! -9 83 = 9*9 + (√9)!/(√9) 82 = 9*9 + 9/9 81 = 99 -9 -9 = 9 * 9 + 9 - 9 = 9 = (√9)^(9-9/9) 80 = 9*9 - 9/9 79 = 9*9 - (√9)!/(√9) 73 = ((√9)!/(√9))^((√9)!) + 9 72 = 99 - (√9) * 9 71 = 9*9 - 9/.9 70 = ((√9)!/(√9))^((√9)!) + (√9)! 67 = ((√9)!/(√9))^((√9)!) + √9 66 = (√9)! * (9 + (√9)!/(√9) ) 65 = 9! / (9*((√9)!)!) +9 64 =(√9 + 9/9)^(√9) = (√9 - 9/9) ^ ( (√9)!) 63 = 99 - (√9)! * (√9)! 62= 9! / (9*((√9)!)!) +(√9)! 61 = ((√9)!/(√9))^((√9)!) - √9 59= 9! / (9*((√9)!)!) +√9 58 = ((√9)!/(√9))^((√9)!) - (√9)! 57 = (9 + 9/.9) * √9 56 = (9-9/9)! / ((√9)!)!) 55 = ((√9)!/(√9))^((√9)!) - 9 54 = (9 + (√9)!) * √9 + 9 53 = 9! / (9*((√9)!)!) - √9 51 = (9 + (√9)!) * √9 + (√9)! 50 = 9! / (9*((√9)!)!) - (√9)! 48 = (9 + (√9)!) * √9 + (√9) 47 = 9! / (9*((√9)!)!) - 9 46 = (√9)! * (√9)! + 9/.9 45 = 99 - 9 * (√9)! 44 = 9 * (√9)! - 9/.9 42 = (√9)! * (9 - (√9)!/(√9) ) 40 = ((√9)!-9/9)!/√9 39 = 9/.9 * √9 + 9 38 = (√9)! * (√9)! + (√9)!/(√9) 37 = (√9)! * (√9)! + 9/9 36 = 9 + 9 + 9 + 9 35 = (√9)! * (√9)! - 9/9 34 = (√9)! * (√9)! - (√9)!/(√9) 33 = 9/.9 * √9 + √9 30 = 9 + 9 + (√9)! + (√9)! = 9 + 9 + 9 + (√9)! 29 = (√9)^(√9) + (√9)!/(√9) 28 = (√9)^(√9) + 9/9 27 = 9 + 9 + (√9)! + √9 26 = (√9)! * (√9)! - 9/.9 25 = (√9)^(√9) - (√9)!/(√9) 24 = 9 + 9 + √9 + √9 21 = (√9)^(√9) - (√9) - (√9) 10 = 99 / 9.9 Last fiddled with by grandpascorpion on 2007-02-02 at 03:10
 2007-02-02, 03:47 #7 grandpascorpion     Jan 2005 Transdniestr 503 Posts 60 = (√9 + √9)*9/.9 32 = √ ( ((√9)!/ √9)^(9/.9) )
 2007-02-02, 04:34 #8 grandpascorpion     Jan 2005 Transdniestr 50310 Posts 95 = ((√9)!)!/9 + 9 + (√9)! 94 = ? 92 = ((√9)!)!/9 + 9 + √9 88 = ( ((√9)!)! - 9)/9 + 9 86 = ( ((√9)!)! + 9*(√9)! )/9 85 = ( ((√9)!)! - 9)/9 + (√9)! 78 = ( ((√9)!)! + 9)/9 - (√9) 77 = ( ((√9)!)! - (√9)^ (√9) )/9 76 = ( ((√9)!)! - (√9)!*(√9)! )/9 75 = ( ((√9)!)! + 9)/9 - (√9)! 74 = ( ((√9)!)! - 9*(√9)! )/9 69 = (√9)!*9/.9 + 9 68 = ? 52 = ? 49 = ? 43 = ? 41 = ? 31 = ? 23 = ( ((√9)!)^(√9)- 9)/9 Last fiddled with by grandpascorpion on 2007-02-02 at 04:36 Reason: add question marks
 2007-02-02, 15:05 #9 grandpascorpion     Jan 2005 Transdniestr 503 Posts 94 = ? 68 = ((√9)!)!/9 - 9 - (√9) 52 = ? 49 = ? 43 = ? 41 = (((√9)!)^√9) / 9 + 9 31 = ( ((√9)!)^√9-9 ) / 9 Last fiddled with by grandpascorpion on 2007-02-02 at 15:50 Reason: More results
 2007-02-02, 16:25 #10 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 2·3·773 Posts The complete list as of 02 Feb 07 10:05 AM - grandscorpion Only 4 to go.....43, 49, 52, 94. My answer for 52 is relatively basic, the other 3 are more complex, but not as complex as some you collectively have found below. For the record when my friends and I last worked on this a few years ago we got all but 4: 76, 85, 88, 94. At the time I surmised they had NO solution ... that is until a few days ago when my son wrote a program to solve this puzzle and found MY 4 missing answers. Your answers for 76, 85 and 88 match his program's ... I tip my hat. P.S. I didn't double check them all yet. 0 = 9 + 9 - 9 - 9 1 = 99/99 2 = 9/9 + 9/9 OR 99/9 - 9 3 = 9/(v9) + 9 - 9 4 = 9/(v9) + 9/9 5 = v9 + v9 - 9/9 6 = v9 + v9 - 9 + 9 7 = 9 - v9 + 9/9 8 = 99/9 - v9 9 = (v9 * v9) + 9 - 9 10 = (v9 * v9) + 9/9 OR 99 / 9.9 11 = 9 + (9 + 9)/9 12 = v9 + v9 + v9 + v9 13 = 9 + v9 + 9/9 14 = 99/9 + v9 15 = v9 * v9 + v9 + v9 16 = (v9)! + 9 + 9/9 17 = 9 + 9 - 9/9 18 = 9 + 9 + 9 - 9 19 = 9 + 9 + 9/9 20 = 99/9 + 9 21 = ((v9)!)*v9) + (v9)! - v9 OR (v9)^(v9) - (v9) - (v9) 22 = ((v9)! * (v9)!) - 9 -v9) 23 = ( ((v9)!)^(v9)- 9)/9 24 = 9 + 9 + v9 + v9 25 = (v9)^(v9) - (v9)!/(v9) 26 = (v9)! * (v9)! - 9/.9 27 = 9 + 9 + (v9)! + v9 28 = (v9)^(v9) + 9/9 29 = (v9)^(v9) + (v9)!/(v9) 30 = 9 + 9 + (v9)! + (v9)! = 9 + 9 + 9 + (v9)! 31 = ( ((v9)!)^v9-9 ) / 9 32 = v ( ((v9)!/ v9)^(9/.9) ) 33 = 9/.9 * v9 + v9 34 = (v9)! * (v9)! - (v9)!/(v9) 35 = (v9)! * (v9)! - 9/9 36 = 9 + 9 + 9 + 9 37 = (v9)! * (v9)! + 9/9 38 = (v9)! * (v9)! + (v9)!/(v9) 39 = 9/.9 * v9 + 9 40 = ((v9)!-9/9)!/v9 41 = (((√9)!)^√9) / 9 + 9 42 = (v9)! * (9 - (v9)!/(v9) ) 43 = 44 = 9 * (v9)! - 9/.9 45 = 99 - 9 * (v9)! 46 = (v9)! * (v9)! + 9/.9 47 = 9! / (9*((v9)!)!) - 9 48 = (9 + (v9)!) * v9 + (v9) 49 = 50 = 9! / (9*((v9)!)!) - (v9)! 51 = (9 + (v9)!) * v9 + (v9)! 52 = 53 = 9! / (9*((v9)!)!) - v9 54 = (9 + (v9)!) * v9 + 9 55 = ((v9)!/(v9))^((v9)!) - 9 56 = (9-9/9)! / ((v9)!)!) 57 = (9 + 9/.9) * v9 58 = ((v9)!/(v9))^((v9)!) - (v9)! 59= 9! / (9*((v9)!)!) +v9 60 = (v9 + v9)*9/.9 61 = ((v9)!/(v9))^((v9)!) - v9 62= 9! / (9*((v9)!)!) +(v9)! 63 = 99 - (v9)! * (v9)! 64 =(v9 + 9/9)^(v9) OR (v9 - 9/9) ^ ( (v9)!) 65 = 9! / (9*((v9)!)!) +9 66 = (v9)! * (9 + (v9)!/(v9) ) 67 = ((v9)!/(v9))^((v9)!) + v9 68 = ((v9)!)!/9 - 9 - (v9) 69 = (v9)!*9/.9 + 9 70 = ((v9)!/(v9))^((v9)!) + (v9)! 71 = 9*9 - 9/.9 72 = 99 - (v9) * 9 73 = ((v9)!/(v9))^((v9)!) + 9 74 = ( ((v9)!)! - 9*(v9)! )/9 75 = ( ((v9)!)! + 9)/9 - (v9)! 76 = ( ((v9)!)! - (v9)!*(v9)! )/9 77 = ( ((v9)!)! - (v9)^ (v9) )/9 78 = ( ((v9)!)! + 9)/9 - (v9) 79 = 9*9 - (v9)!/(v9) 80 = 9*9 - 9/9 81 = 99 -9 -9 OR 9 * 9 + 9 - 9 OR (v9)^(v9+9/9) 82 = 9*9 + 9/9 83 = 9*9 + (v9)!/(v9) 84 = 99 -(v9)! -9 85 = ( ((v9)!)! - 9)/9 + (v9)! 86 = ( ((v9)!)! + 9*(v9)! )/9 87 = 99 -(v9)! -(v9)! 88 = ( ((v9)!)! - 9)/9 + 9 89 = 99 - 9/.9 90 = 99 - v9 - (v9)! 91 = 9*9 + 9/.9 92 = ((v9)!)!/9 + 9 + v9 93 = 99- v9 - v9 94 = 95 = ((v9)!)!/9 + 9 + (v9)! 96 = 99-9/v9 = 99 + v9 - (v9)! = 9/.9 + v9 + v9 97 = 99 - (v9)!/(v9) 98 = 99 - 9/9 99 = 99 + 9 - 9 100 = 99 + 9/9 = 9/.9 * 9/.9 101 = 99/.9 - 9
 2007-02-02, 16:37 #11 michaf     Jan 2005 479 Posts One minor mistake: 30 = 9 + 9 + (v9)! + (v9)! = 9 + 9 + 9 + (v9)! last '!' should be gone