The Fours / Nines Puzzle

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Kevin_P86
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Re: The Fours / Nines Puzzle (0)

Maurog wrote:
Here you go, rechecked with calculator.

Looks good to me! Some of them are a lot more clever than the ones I found!

Once again, I split up the +10 between your two posts in this thread.

Casebier wrote:
After doing a little research... Try finding 113 with only 4 4's.

That was the first one my program didn't find, although it certainly doesn't try everything.

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02-07-2007 at 11:21 PM

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levelthirteen
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Re: The Fours / Nines Puzzle (0)

Casebier wrote:
After doing a little research... Try finding 113 with only 4 4's.

An exhaustive search revealed
sqrt( (4! ^ 4) / (sqrt(4) + 4!) ) = 112.9628

Is that close enough?

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03-11-2007 at 07:32 AM

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Kevin_P86
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Re: The Fours / Nines Puzzle (0)

levelthirteen wrote:

Casebier wrote:
After doing a little research... Try finding 113 with only 4 4's.

An exhaustive search revealed
sqrt( (4! ^ 4) / (sqrt(4) + 4!) ) = 112.9628

Is that close enough?

Well, no. The idea is to get EXACTLY each number, so nothing is close enough except exactly 113

.

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03-11-2007 at 10:10 PM

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Casebier
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Re: The Fours / Nines Puzzle (0)

A not-so-exhaustive search shows that any number can be made if you include the ability to use Log functions.

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Revisiting old Project: ZelDROD 1 / ZelDROD RPG (If I can ever find the custom graphic files that I made for it.)

03-12-2007 at 03:27 AM

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Kevin_P86
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Re: The Fours / Nines Puzzle (0)

Casebier wrote:
A not-so-exhaustive search shows that any number can be made if you include the ability to use Log functions.

Yes, of course if you include the appropriate operations everything becomes possible. I once found a site that had the solutions up to 40,000 with the help of a rather large list of operations.

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03-12-2007 at 04:36 AM

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halyavin
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Re: The Fours / Nines Puzzle (0)

Very strange - we are playing the same game in our labaratory in MSU (we use others starting sequences of digits). So I wrote program long ago. Here is the result for 4444 (the most strange ways to obtain small numbers you ever see!):

Click here to view the secret text

0=.4-s(s(((-s(.4*.4))^4))))
1=.4/s(s(((-s(.4*.4))^4)))
2=s(s(s(s(((s(4)*s(4))^(4*s(4)))))))
3=4!/s((s(4)^((s(4)/s(.(4)))!)))
4=s(s(s(((s(4)*s(4))^(4*s(4))))))
5=s(s(s(.(4))/(((-0.4)^4)/4!)))
6=s(s((.(4)*((-.(4))/4!^(-s(4))))))
7=s((4!*(s(4)+s(((-4!)^(-s(4)))))))
8=s(((-s(4))^s(s(4!/.(4)/4!))))
9=((-.(4))+(.(4)+4/.(4)))
10=(.(4)*s((((-.(4))+.4)^(-s(4)))))
11=(s(4)+s((s(.(4)/4)^(-4))))
12=s(s(((-s(4))/4!^(-(s(4)*s(4))))))
13=(s(.(4))+(4!+s(.(4)))/s(4))
14=s(s((s(4)/(4+4!)^(-4))))
15=s(4!/s(.(4)/((-.4)^(-4))))
16=s(s(((s(4)*s(4))^(4*s(4)))))
17=s(((4!^s(4))+s(4))/s(4))
18=s(4)/s(s((4/.(4)^(-4))))
19=s((((-4!)+s(4)/.4)^s(4)))
20=(.4*(4!+(s(4)+4!)))
21=(4!+(-s(s((s(.(4)/4)^(-4))))))
22=s(.(4))/s(.(4))/((-s(4))+4!)
23=(4!+(-((-4)+(s(4)*s(4)))!))
24=s((4!^s(((-s(4))^(4+(-s(4)))))))
25=s(s(.(4))/((-.4)^4)/4!)
26=s(((-(s(4)+4!))^(4+(-s(4)))))
27=s(4)/.(4)/s(4)/s(.(4))!
28=s(((4+4!)^(4+(-s(4)))))
29=s((((-4!)+(-s(4))/.4)^s(4)))
30=s(.(4))/((-.4)+.(4))/s(4)
31=((-s(4))+(4!+4/.(4)))
32=s(.(4)/((4!+4!)^(-s(4))))
33=s(.(4))/.(4)/((-s(4))+4!)
34=(4*(4+s(4)/.(4)))
35=s((((-s(.(4)))+4!)^s(4))/.(4))
36=s((.(4)*((-.(4))/4!^(-s(4)))))
37=s(.(4))/.(4)/(4!+s(.(4)))
38=s((s(4)*(s(4)/s(.(4))!!+s(4))))
39=(s(4)+(4!+s(.(4)))/s(.(4)))
40=4/s((4/.4^(-s(4))))
41=s((4!+(4*s(4))!)/4!)
42=s(((-((-s(4))+44))^s(4)))
43=(s(4)*(4!+(-s((.4^(-s(4)))))))
44=s((44^(4+(-s(4)))))
45=(4!*s(4)/(s(.(4))+.4))
46=((-s(.(4)))+(s(4)*((-s(.(4)))+4!)))
47=(s(4)*((-s(s((4^(-s(4))))))+4!))
48=(4!*s(((-s(4))^(4+(-s(4))))))
49=(4!*(s(4)+s(((-4!)^(-s(4))))))
50=s(4)/s(((-.4/s(4))^4))
51=(4!+(s(4)/s(.(4))+4!))
52=s(4/((-(s(4)+4!))^(-s(4))))
53=s(((4!+(-.(4)))/.(4)^s(4)))
54=(.4*4!/(.4*.(4)))
55=(s(4)+(4!+(-.(4)))/.(4))
56=s(4)/s(((-(4+4!))^(-s(4))))
57=((-4)+(.4+4!)/.4)
58=(4!+(4!+4/.4))
59=((-4)+(4+4!)/.(4))
60=s(s(4)/.4/s(4)/s(.(4))!!)
61=(.4+4!)/s(s(((-.4)^4)))
62=s(((s(4)+4!/.4)^s(4)))
63=(4!+(s(4)+4!)/s(.(4)))
64=((-s(4))^s(s(4!/.(4)/4!)))
65=(s(4)+4!)/s((.4*.4))
66=s(.(4))/.(4)/44
67=(4+(4+4!)/.(4))
68=(s(4)*(4!+4/.4))
69=(4!/.4+4/.(4))
70=s(((-(4+4!)/.4)^s(4)))
71=(4!+(4+.4))/.4
72=(4*((-4)+((-s(4))+4!)))
73=(s(.(4))+(4!+4!))/s(.(4))
74=s(4)/s(.(4))/(4!+s(.(4)))
75=4!/s(4)/(.4^(-s(4)))
76=(4*((-s(4))/.4+4!))
77=(4!+(4!+(-.(4)))/.(4))
78=s(4)/s(.(4))/(s(4)+4!)
79=(4!+((-s(4))+4!)/.4)
80=(4*s((((-4!)+4)^s(4))))
81=4!/s(.(4))/(s(.(4))^(-s(4)))
82=(4!+((-s(4))+4!/.4))
83=(4!+((-.4)+4!)/.4)
84=s(4)/s(.(4))/(4+4!)
85=(4!+4/.4)/.4
86=(4!+(s(4)+4!/.4))
87=(4*(4!+(-(s(.(4))^(-s(4))))))
88=s(((4*((-s(4))+4!))^s(4)))
89=(4!+(s(4)+4!)/.4)
90=s((.4/4!/s(.(4))^(-s(4))))
91=(s(.(4))+4!/.4)/s(.(4))
92=s(((-((4*4!)+(-4)))^s(4)))
93=((-s(4)/s(.(4)))+(4*4!))
94=s(((-((4*4!)+(-s(4))))^s(4)))
95=(4*((-s((4^(-s(4)))))+4!))
96=s(4/((4!+4!)^(-s(4))))
97=((4*4!)+(s(4)+(-s(4)))!)
98=s(((s(4)+(4*4!))^s(4)))
99=s(((-44)/.(4)^s(4)))
100=s((.4/4^(-(s(4)*s(4)))))
101=(s(4)/.4+(4*4!))
102=(4*(s((s(.(4))^(-s(4))))+4!))
103=(4+44/.(4))
104=s((((-4)*(s(4)+4!))^s(4)))
105=s(4)/.(4)/((-s(.(4)))+4!)
106=((-s(4))+s(4)/.(4)/4!)
107=((-.(4))+(4!+4!))/.(4)
108=s(4)/.(4)/(s(4)*s(4))!
109=(4!+(.(4)+4!))/.(4)
110=s((44/.4^s(4)))
111=s(4)/.(4)/(4!+s(.(4)))
112=s((((-4!)*(s(.(4))+4))^s(4)))
113=?
114=(4*(4!+s(4)/.(4)))
115=(s(4)/.4!+(-s(4))/.4)
116=(4*(4!+s(4)/.4))
117=s(4)/.(4)/(s(4)+4!)
118=s(4)/.4/((-.4)+4!)
119=((-4)/4+s(4)/.4!)
120=s(s(s(.(4))/((-.4)^4)/4!))!
121=(s(4)/.4!+(s(4)+(-s(4)))!)
122=s(4)/.4/(.4+4!)
123=(s(4)/.4!+s(4)/s(.(4)))
124=s(((s(4)/.4!+4)^s(4)))
125=s(((-.4/s(4))^(-s(4)/s(.(4))!)))
126=(s(4)*(4+4!)/.(4))
127=((-s(4))+((-4)^4))/s(4)
128=(4!*s((.(4)+(4+4!))))
129=(4/.(4)+s(4)/.4!)
130=(s(4)+4!)/.4/s(4)
131=(4!/(.4*.(4))+(-4))
132=(4!*((-s(4))+4!)/4)
133=(4!/(.4*.(4))+(-s(4)))
134=(4!*((.4^(-s(4)))+(-s(.(4)))))
135=s(((-.(4)/4!/.4)^(-s(4))))
136=(4*(4!+4/.4))
137=(4!/(.4*.(4))+s(4))
138=((-4!)+(4!^s(4)))/4
139=(4+4!/(.4*.(4)))
140=s(4)/.4/(4+4!)
141=((4*4!)+(-s(4)))/s(.(4))
142=((-s(4))+(4!+s(4)/.4!))
143=((4!^s(4))+(-4))/4
144=s(((-s(4))/4!^(-(s(4)*s(4)))))
145=((4!^s(4))+4)/4
146=((s(4)/.4!+s(4))+4!)
147=(s(4)+(4*4!))/s(.(4))
148=4!/4/(4!+s(.(4)))
149=(4!/.4+(-.4))/.4
150=4!/((-.4)^(4+(-s(4))))
151=(.4+4!/.4)/.4
152=(4*(s(4)+4!/s(.(4))))
153=(4!+44)/.(4)
154=(4+4!/(.4*.4))
155=(s(4)+4!/.4)/.4
156=(s(4)*(4!/.(4)+4!))

(Sometimes you have to guess the order of operations

)
It haven't found 113 and 157. And I know only 1 case when my program missed variant (it was 9!/7! trick which uses too large intermediate numbers).
Result for 9999:

Click here to view the secret text

0=(s(9)+(-s(9))/.9/.9)
1=s(9)/s(s(9)!!/s(9)!!/9)
2=s(s(((-s(9))+(9+9/.9))))
3=s(s(((-s(9))^s((s(9)!+9/.9)))))
4=s(((-s(9))+(9+9/.9)))
5=s((9/.9+(9+s(9)!)))
6=s(s(((-s(9))^s((s(9)!+9/.9)))))!
7=s(9)/.9/(s(9)+(-.9))
8=s(s((9/(s(9)!*s(9)!)^(-s(9)!))))
9=s(((-s(9))^s((s(9)!+9/.9))))
10=9/s((.9*s((.9*.9))))
11=(9+s(9)/9/s(9)!)
12=s(9)!/9/s(9)!/s(9)
13=s(((s(9)!!+s(9)!!)/9+9))
14=(s(9)+9.9/.9)
15=s((9+(s(9)!^s(s((9*9))))))
16=((-s(9))+(9+9/.9))
17=s(9)/.9/(s(9)!+(-.9))
18=s(9/s((s(9)!^(-s(9)))/s(9)!))
19=(s(9)*(s(9)+s(9)/.9))
20=9/s(9)/s(9)!/.9
21=9/.9/(s(9)+(-.9))
22=s((s(9)!*(s(9)!!+s(9)!)/9))
23=(s(9)/.9*(s(9)!+.9))
24=s(((-s(9))+(9+9/.9)))!
25=(9/.9+(9+s(9)!))
26=s(9)!/.9/(s(9)+.9)
27=.9/.9/s((9+s(9)!!))
28=(9+(9+9/.9))
29=s((s(9)!!+(s(9)!!+s(9)!)/s(9)!))
30=s(.9/(9/.9^(-s(9))))
31=s((s(9)!!+(s(9)!!+s(9))/s(9)))
32=(s(9)!*(s(9)!+(-s(9)!)/9))
33=s(9/s(9)!/(s(9)!!+s(9)!))
34=(s(9)!*(s(9)!+(-s(9)/9)))
35=((-.9/.9)+(s(9)!*s(9)!))
36=.9/s(.9/(s(9)!!+s(9)!!))
37=((-s(9))+s((s(9)!!+s(9)!!)/.9))
38=(s(9)!/s(9)+(s(9)!*s(9)!))
39=9/.9/(s(9)+.9)
40=s(9)!/.9/s(s((9*9)))!
41=(.9+(s(9)!*s(9)!))/.9
42=(s(9)!*(.9/.9+s(9)!))
43=(s((s(9)!!+s(9)!!)/.9)+s(9))
44=(s(9)!!/9+(-(s(9)!*s(9)!)))
45=s(9)!!/(s(9)!+9/.9)
46=s(9)!/.9/(s(9)!+.9)
47=((9+s(9)!/.9)*s(9))
48=s(9)!!/s(((s(9)!^s(9))+9))
49=s(((s(9)!!*s(9))+.9)/.9)
50=(s(9)!*((-s(9)!)/9+9))
51=(9*(s(9)!+(-s(9)/9)))
52=((-s(9)!)/s(9)+(9*s(9)!))
53=((-.9/.9)+(9*s(9)!))
54=s(9)!/s(s(((-s(9))^(-s(9)!))/9))
55=((-9)+((-s(9)!)/s(9)^s(9)!))
56=((9*s(9)!)+s(9)!/s(9))
57=(s(9)!*(9+s(9)/s(9)!))
58=(s(9)!*(9+s(9)!/9))
59=((9*s(9)!)+(-.9))/.9
60=s(9)!/((-.9)+.9/.9)
61=((9*s(9)!)+.9)/.9
62=((-9)+(s(9)!!/9+(-9)))
63=(s(9)!*(9+9/s(9)!))
64=s((9/(s(9)!*s(9)!)^(-s(9)!)))
65=(((-s(9)!)+(-9))+s(9)!!/9)
66=s(9)!/s(s(9)!/(s(9)!!+s(9)!))
67=(s(9)+((-s(9)!)/s(9)^s(9)!))
68=((-s(9))+(s(9)!!/9+(-9)))
69=9/.9/(s(9)!+.9)
70=((-9/.9)+s(9)!!/9)
71=((-9)+s(9)!!/s((9*9)))
72=s(9)!/s(9)/s(9)!/s(9)!
73=((-s(9)!)+(s(9)!!+(-9))/9)
74=(s(9)!*(9+s(9)/.9))
75=(9+s((s(9)!*(s(9)!!+s(9)!))))
76=((s(9)!!+(-9))/9+(-s(9)))
77=(s(9)+(s(9)!!/9+(-s(9)!)))
78=(s(9)!!+((-(.9*s(9)!!))+s(9)!))
79=(s(9)!!+(-9))/s((9*9))
80=.9/9/s(9)!!/.9
81=((-s(9))^s((s(9)!+9/.9)))
82=((s(9)!!+(-9))/9+s(9))
83=(s(s((9*9)))+s(9)!!/9)
84=((-9)+(99+(-s(9)!)))
85=((s(9)!!+(-9))/9+s(9)!)
86=(9+((-s(9))+s(9)!!/9))
87=((-s(9))+9/.9/9)
88=((s(9)!!+(-9))/9+9)
89=(s(9)!+(s(9)!!/9+s(9)))
90=s(9)!!/(9+(-.9/.9))
91=(99+s(9)!!)/9
92=((s(9)+9)+s(9)!!/9)
93=((-s(9))+(99+(-s(9))))
94=(s(9)!*(9+s(9)!/.9))
95=((9+s(9)!)+s(9)!!/9)
96=s(9)!!/((-9)/s(9)!+9)
97=(99+(-s(9)!)/s(9))
98=(s(9)!!/9+(s(9)!*s(9)))
99=s((99*99))
100=((-.9)/9^(-s(9)!)/s(9))
101=(s(9)!/s(9)+99)
102=((-9)+(s(9)!!/s(9)!+(-9)))
103=?
104=((-s(9)!)+99/.9)
105=((-s(9))+.9/s(9)!/s(9)!!)
106=?
107=((-s(9))+99/.9)
108=s(9/(s(9)!^(-s(9)))/s(9)!)
109=(99+9/.9)
110=99/s((.9*.9))
111=(9*(9+s(9)/.9))
112=((s(9)!!+s(9)!)/s(9)!+(-9))
113=((-s(9)!)+((-s(9)!)+s(9)!!)/s(9)!)
114=s((s(9)!*(s(9)!+(s(9)!!*s(9)))))
115=((-s(9)!)+(s(9)!!+s(9)!)/s(9)!)
116=(((-s(9)!)+s(9)!!)/s(9)!+(-s(9)))
117=(s(9)*((s(9)!*s(9)!)+s(9)))
118=((s(9)!!+s(9)!)/s(9)!+(-s(9)))
119=((-.9/.9)+s(9)!!/s(9)!)
120=s((9/.9+(9+s(9)!)))!
121=(s(9)!!+s(9)!)/s(s((9*9)))!
122=(s(9)!!/s(9)!+s(9)!/s(9))
123=((-s(9)!)+(9+s(9)!!/s(9)!))
124=((s(9)!!+s(9)!)/s(9)!+s(9))
125=(s(9)!+((-s(9)!)+s(9)!!)/s(9)!)
126=(s(9)!*((-s(9)!)+s((9+s(9)!!))))
127=(s(9)!+(s(9)!!+s(9)!)/s(9)!)
128=(((-s(9)!)+s(9)!!)/s(9)!+9)
129=(9+s(9)!!/s(s((9*9)))!)
130=(s(9)!!/s(9)!+9/.9)

It haven't found 103 and 106.
BTW, here is some others games we are playing:
New Year game.
Try to obtain current year from only zeros, ones, twos, and so on. You should use as minimal digits as possible. Your result is total number of digits. Person with the least number wins.
Bus game.
Try to obtain current year using the 6-digit number on the bus ticket.
Bus pyramid game.
Try to create pyramid (f denotes expression):
1=f(2,3,4,5,6)
12=f(3,4,5,6)
123=f(4,5,6)
f(1,2,3)=456
f(1,2,3,4)=56
f(1,2,3,4,5)=6
Where 123456 is a the 6-digit number on the bus ticket.

03-12-2007 at 07:29 AM

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