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Old 2007-02-01, 19:47   #1
petrw1
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Default 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.....
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Old 2007-02-01, 20:39   #2
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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
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Old 2007-02-01, 21:30   #3
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Quote:
Originally Posted by Uncwilly View Post
(√9)! + (√9)! + (√9)! - 9 = 10
Great start only 79 to go.... have another look at 10.
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Old 2007-02-01, 23:01   #4
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Quote:
Originally Posted by petrw1 View Post
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
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Old 2007-02-02, 00:33   #5
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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
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Old 2007-02-02, 02:13   #6
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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
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Old 2007-02-02, 03:47   #7
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60 = (√9 + √9)*9/.9
32 = √ ( ((√9)!/ √9)^(9/.9) )
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Old 2007-02-02, 04:34   #8
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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
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Old 2007-02-02, 15:05   #9
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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
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Old 2007-02-02, 16:25   #10
petrw1
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Default 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
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Old 2007-02-02, 16:37   #11
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One minor mistake:
30 = 9 + 9 + (v9)! + (v9)! = 9 + 9 + 9 + (v9)!

last '!' should be gone
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