Given four digits 1,2,3 & 4 you are asked to create all integer numbers from 1 to 150 using some or all of those digits and the following operations: concatenation (numbers only), +-/*^! and sqrt plus any amount of brackets. No other operators, no subfactorials, no double factorials, logs etc
For any correct result score +1 point.
If for a certain number no answer was found the penalty
is -6 points if the the missing answer is between two valid solutions
or -8 otherwise.
Partial results accepted and the final answer will be the updated list.
Examples: 123 = 123; 6= 3!; 88=(43+1)*2.
REM1: Use software only for difficult cases, most of the work is easily done by hand
REM2: If facing several valid choices ,- choose the simplest.
Have fun !
I modified a program I've used for similar previous puzzles on this site to produce the below list.
The list appears below using Reverse Polish Notation (the first column after the column for n). Only six are missing, each between valid solutions, so 144 - 6*6 = 108 is the score.
The below have been simplified as far as possible (the shortest representation in RPN). I've manually translated the RPN into algebraic:
n RPN algebraic
1 1 1
2 2 2
3 3 3
4 4 4
5 1,4+ 1+4
6 3! 3!
7 3,4+ 3+4
8 2,3^ 2^3
9 3,2^ 3^2
10 3!,4+ 3!+4
11 13,2- 13-2
12 12 12
13 13 13
14 14 14
15 13,2+ 13+2
16 2,4^ 2^4
17 13,4+ 13+4
18 324v sqrt(324)
19 23,4- 23-4
20 14,3!+ 14+3!
21 21 21
22 23,1- 23-1
23 23 23
24 24 24
25 1,24+ 1+24
26 13,2* 13*2
27 23,4+ 23+4
28 14,2* 14*2
29 31,2- 31-2
30 24,3!+ 24+3!
31 31 31
32 32 32
33 1,32+ 1+32
34 34 34
35 1,34+ 1+34
36 2,34+ 2+34
37 13,24+ 13+24
38 41,3- 41-3
39 41,2- 41-2
40 1,3-,42+ 1-3+42
41 41 41
42 42 42
43 43 43
44 1,43+ 1+43
45 2,43+ 2+43
46 14,32+ 14+32
47 23,4!+ 23+4!
48 12,4* 12*4
49 3,4+,2^ (3+4)^2
50 13,4*,2- 13*4-2
51 12,4*,3+ 12*4+3
52 13,4* 13*4
53 2,3!*,41+ 2*3!+41
54 13,4*,2+ 13*4+2
55 12,43+ 12+43
56 32,4!+ 32+4!
57 1,32+,4!+ 1+32+4!
58 2,31*,4- 2*31-4
59 21,3*,4- 21*3-4
60 3!!,12/ (3!)!/12
61 13,2,4!*+ 13+2*4!
62 2,31* 2*31
63 21,3* 21*3
64 4,3^ 4^2
65 1,4,3^+ 1+4^3
66 132,4v/ 132/sqrt(4)
67 134,2/ 134/2
68 2,34* 2*34
69 1,34,2*+ 1+34*2
70 1,34+,2* (1+34)*2
71 24,3*,1- 24*3-1
72 24,3* 24*3
73 31,42+ 31+42
74 2,3,4!*+ 2+3*4!
75 1,24+,3* (1+24)*3
76 12,4,3^+ 12+4^3
77 3!,2^,41+ (3!)^2+41
78 312,4/ 312/4
79 3,4^,2- 3^4-2
80 3,4^,1- 3^4-1
81 3,4^ 3^4
82 2,41* 2*41
83 2,3,4^+ 2+3^4
84 21,4* 21*4
85 21,4,3^+ 21+4^3
86 2,43* 2*43
87 1,2,43*+ 1+2*43
88 1,43+,2* (1+43)*2
89 1,4!+,2,3!^+ 1+4!+2^(3!)
90 21,4*,3!+ 21*4+3!
91 23,4*,1- 23*4-1
92 23,4* 23*4
93 1,4,23*+ 1+4*23
94 2,3!,41+* 2*(3!+41)
95 2,4^,3!*,1- (2^4)*3!-1
96 1,3+,24* (1+3)*24
97 1,4+!,23- (1+4)!-23
98 1,3+!,4*,2+ ((1+3)!)*4+2
99 123,4!- 123-4!
100 3!,4+,2^ (3!+4)^2
101 1,3!,4+,2^+ 1+(3!+4)^2
102 2,1+,34* (2+1)*34
103
104 13,2*,4* 13*2*4
105 21,3,4v+* 21*(3+sqrt(4))
106 2,3+!,14- (2+3)!-14
107
108 132,4!- 132-4!
109
110 2,31,4!+* 2*(31+4!)
111 1,4+!,3,2^- (1+4)!-3^2
112 14,2,3^* 14*2^3
113
114 1,4+!,3!- (1+4)!-3!
115 1,4+,23* (1+4)*23
116 2,3+!,4- (2+3)!-4
117 1,4+!,3- (1+4)!-3
118 124,3!- 124-3!
119 123,4- 123-4
120 1,4+! (1+4)!
121 124,3- 124-3
122 1,4+!,2+ (1+4)!+2
123 123 123
124 124 124
125 1,4+,3^ (1+4)^3
126 3,42* 3*42
127 124,3+ 124+3
128 32,4* 32*4
129 1,2+,43* (1+2)*43
130 124,3!+ 124+3!
131 2,14^v,3+ sqrt(2^14)+3
132 132 132
133 1,2,4!-,3!*- 1-(2-4!)*3!
134 134 134
135 21,4!+,3* (21+4!)*3
136 132,4+ 132+4
137
138 23,4,1-!* 23*(4-1)!
139 142,3- 142-3
140 3!,2^,1-,4* ((3!)^2-1)*4
141 143,2- 143-2
142 142 142
143 143 143
144 12,4v^ 12^sqrt(4)
145 142,3+ 142+3
146 2,3!,4!*+ 2+3!*4!
147 4!,123+ 4!+123
148 142,3!+ 142+3!
149
150 1,24+,3!* (1+24)*3!
103, 107, 109, 113, 137 and 149 remain unsolved.
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Posted by Charlie
on 2023-01-03 21:15:24 |
computer solution (spoiler)
