Classic problem: Four 4's

[grandpascorpion]

75 = (4sqsq+44)/4
86 = 4!/(.4sq)-4*4sq
122= 4!/(.4sq)-4!-4

[grandpascorpion]

133 = (4!-.4sq)/(.4sq)-4sq

[Orgasmic Troll]

pi = (-4/(4+4))!sq

:D

[S80780]

Originally Posted by Wacky

Where is "75" ?

Oops! forgot to post:
75 = (4!+4!/4)/.4

So, we're down to 13.

[Wacky]

Ken,

Thanks for the "puzzle". Perhaps you will now disclose which of the remaining numbers are those that you have not yet solved.

As for the "Scoreboard", I haven't found a way to get a message to the top of the thread.

So, for the next thread for this kind of puzzle, let me suggest that the original author set up the top of the thread by posting two or three messages.

(1) The statement of the problem (to be edited if clarification is required)
(2) A placeholder for the Scoreboard
(3) The original statement of the problem (and author's comments)

That way, we can have the "executive overview" of the puzzle and scoreboard at the head and the rest of the thread can develop in a normal fashion.

[Ken_g6]

Thanks, GrandpaScorpion! That subtract-from-256 trick solved one I hadn't gotten (113), and helped me get two others. So now there's only one less than 160 that I haven't gotten. I'd rather not disclose it just yet, as it might discourage you from finding a solution for it!

Trying numbers up around 256, it looks to me like it might be fruitful to expand the range up to 300, though I wouldn't expect to find solutions for all numbers in that range.

Wacky, can't you just edit your first message (the 3rd in the list) this time?

[rogue]

I think the solution to 73 is incorrect. Try this:

73 = ((4! + 4)/4)sq + 4!

And two more:

79 = (4sqsq - 4)/4 + 4sq
87 = (4sqsq - 4)/4 + 4!

[grandpascorpion]

73 = (4sqsq+(4!/4)sq)/4 is valid
= (256 + 6^2)/4 = 73

Is it me or did some solutions disappear (like 79 and 87 earlier)?

And Ken, glad that helped. I'm game for increasing finding solutions thru 300.

[rogue]

Originally Posted by grandpascorpion

73 = (4sqsq+(4!/4)sq)/4 is valid
= (256 + 6^2)/4 = 73

You are correct and I noticed that right after I posted.

[grandpascorpion]

Thanks

[rogue]

Here is the current list. I have removed duplicates and solutions which use more fours than other solutions for the same number.

0 = 4 - 4
1 = 4/4
2 = (4 + 4)/4
3 = 4 - 4/4
4 = 4
5 = 4 + 4/4
6 = 4!/4
7 = (4! + 4)/4
8 = 4 + 4
9 = (4 - .4)/.4
10 = 4 / .4
10 = 4/.4
11 = 44 / 4
12 = 4sq - 4
13 = 4sq - 4 + 4/4
14 = 4sq - (4 + 4)/4
15 = 4sq - 4/4
16 = 4sq
17 = 4sq + 4/4
18 = 4/.4 + 4 + 4
18 = 4sq + (4 + 4)/4
19 = (4 + 4 - .4)/.4
19 = 4! - 4 - 4/4
20 = 4! - 4
21 = (4 + 4.4)/.4
21 = 4! - 4 + 4/4
22 = 4! - (4 + 4)/4
23 = 4! - 4/4
24 = 4!
25 = 4! + 4/4
26 = 4sq + 4/.4
27 = 4! + 4 - 4/4
28 = 4! + 4
29 = 4! + 4 + 4/4
30 = (4 + 4/4)!/4
31 = 4sq + 4sq - 4/4
32 = 4sq + 4sq
33 = 4sq + 4sq + 4/4
34 = 4! + 4/.4
35 = 4! + 44/4
36 = (4!/4)sq
36 = 4!sq / 4sq
37 = (4!/4)sq + 4/4
37 = 4!sq / 4sq + 4/4
38 = (4sq - .4 - .4)/.4
38 = 4! + 4/.4 + 4
39 = (4sq - .4)/.4
40 = 4! + 4sq
40 = 4sq/.4
41 = (4sq + .4)/.4
41 = 4! + 4sq + 4/4
42 = (4sq + .4 + .4)/.4
42 = 4! + 4! - 4!/4
43 = 44 - 4/4
44 = 44
45 = 44 + 4/4
46 = (4! - 4)/.4 - 4
46 = (4sq + 4)/.4 - 4
47 = 4! + 4! - 4/4
48 = 4! + 4!
49 = ((4! + 4)/4)sq
50 = (4! - 4)/.4
50 = (4sq + 4)/.4
51 = (4! - 4 + .4)/.4
51 = (4sq + 4 + .4)/.4
52 = 4! + 4! + 4
52 = 44 + 4 + 4
53 = ((4! + 4)/4)sq + 4
54 = (4sq + 4)/.4 + 4
54 = 4! + 4! + 4!/4
54 = 4!/.4 - 4!/4
54 = 4!/4 + 4! + 4!
55 = (4! - .4)/.4 - 4
56 = 4!/.4 - 4
57 = (4! + .4)/.4 - 4
58 = (4! - .4 - .4)/.4
58 = 4! + 4! + 4/.4
59 = (4! - .4)/.4
60 = 4!/.4
61 = (4! + .4)/.4
61 = 4!/.4 + 4/4
62 = (4! + .4 + .4)/.4
63 = 4sq * 4 - 4/4
64 = (4 + 4)sq
64 = 4sq * 4
65 = 4sq * 4 + 4/4
66 = (4! + 4)/.4 - 4
66 = 4!/.4 + 4!/4
67 = (4sqsq - 4)/4 + 4
68 = 4! + 44
68 = 4sq * 4 + 4
69 = (4! + 4 - .4)/.4
70 = (4! + 4)/.4
71 = (4! + 4.4)/.4
72 = 4! * 4 - 4!
72 = 4! + 4! + 4!
73 = ((4! + 4)/4)sq + 4!
74 = (4! + 4)/.4 + 4
75 = (4! + 4!/4)/.4
76 = 4! + 4! + 4! + 4
77 = (4 - 4/4)sqsq - 4
79 = (4sqsq - 4)/4 + 4sq
80 = 4*(4! - 4)
80 = 4sq * 4 + 4sq
81 = ((4 - .4)/.4)sq
81 = ((4 - 4/4)sq)sq
84 = 4!/.4 + 4!
84 = 4*(4sq + 4) + 4
85 = (4 - 4/4)sqsq + 4
85 = (4! + .4)/.4 + 4!
85 = (4! + 4/.4)/.4
86 = 4!/(.4sq) - 4sq * 4
87 = (4sqsq - 4)/4 + 4!
88 = 4! + 4! + 4! + 4sq
89 = ((4!/4)sq - .4)/.4
90 = (4!/4)sq/.4
91 = ((4!/4)sq + .4)/.4
92 = 4! * 4 - 4
94 = (4 / .4)sq - 4!/4
94 = (4/.4)sq - 4!/4
95 = (4! * 4sq - 4)/4
95 = 4! * 4 - 4/4
96 = 4! * 4
97 = (4! * 4sq + 4)/4
97 = 4! * 4 + 4/4
99 = (4 / .4)sq - 4/4
99 = (4/.4)sq - 4/4
100 = (4/.4)sq
101 = (4/.4)sq + 4/4
102 = 4! * 4 + 4!/4
104 = (4/.4)sq + 4
105 = (4 - 4/4)sqsq + 4!
105 = (44/4)sq - 4sq
106 = (4/.4)sq + 4!/4
106 = 44/.4 - 4
108 = (4/.4)sq + 4 + 4
109 = (44 - .4)/.4
110 = 44/.4
111 = 444/4
112 = 4 * (4! + 4)
112 = 4! * 4 + 4sq
113 = 4sqsq - (4!sq - 4)/4
114 = 44/.4 + 4
116 = (4/.4)sq + 4sq
117 = (44/4)sq - 4
118 = 4sqsq - (4!sq - 4!)/4
119 = (4! + 4! - .4)/.4
120 = (4 + 4/4)!
120 = (4! + 4!)/.4
121 = (44/4)sq
122 = 4!/(.4sq)-4! - 4
124 = (4 + 4/4)! + 4
124 = (4sq - 4)sq - 4sq - 4
125 = (44/4)sq + 4
125 = (4! - 4)/(.4)sq
126 = (4!sq + 4!)/4 - 4!
127 = (4!sq - 4)/4 - 4sq
128 = (4sq - 4)sq - 4sq
128 = 4!sq/4 - 4sq
128 = 4sq * 4 + 4sq * 4
129 = (4!sq + 4)/4 - 4sq
130 = (4! + 4! + 4)/.4
132 = (4/.4)sq + 4sq + 4sq
132 = (4sq - 4)sq - 4sq + 4
132 = 4!sq/4 - 4sq + 4
133 = (4! - .4sq)/(.4sq)-4sq
134 = (4!sq + 4!)/4 - 4sq
135 = 4sqsq - (44/4)sq
136 = (4sq - 4)sq - 4 - 4
136 = 4!sq/4 - 4 - 4
137 = (4!sq - 4! - 4)/4
137 = (44/4)sq + 4sq
138 = (4!sq - 4!)/4
139 = (4!sq - 4)/4 - 4
140 = (4sq - 4)sq - 4
140 = 4!sq/4 - 4
141 = (4!sq - 4sq + 4)/4
142 = (4!sq - 4 - 4)/4
143 = (4!sq - 4)/4
143 = 4!sq/4 - 4/4
144 = (4sq - 4)sq
144 = 4!sq/4
144 = 4!sq/4 + 4/4
145 = (4!sq + 4)/4
146 = (4!sq + 4 + 4)/4
147 = (4!sq - 4)/4 + 4
148 = (4sq - 4)sq + 4
149 = (4!-(.4)sq)/(.4)sq
150 = 4!/(.4)sq
151 = (4!+(.4)sq)/(.4)sq
152 = (4sq - 4)sq + 4 + 4
152 = 4 * 44 - 4!
153 = 4+(4!-(.4)sq)/(.4)sq
154 = 4 + 4!/(.4)sq
155 = 4+(4!+(.4)sq)/(.4)sq
156 = 4sqsq - (4/.4)sq
158 = 4!/(.4)sq + 4 + 4
159 = (4!sq - 4)/4 + 4sq
160 = (4sq - 4)sq + 4sq
256 = 4sqsq