123456789 = 100
© Copyright 2003, Jim LoyPuzzle: I received email asking me to make the numbers 123456789 add up to 100, by inserting any of these arithmetic operations (+ - * /) into the string of numbers (and keeping the numbers in the above order). I've seen this in a book somewhere, and I think the book gave only one solution. You might want to try it.
Solution: I found this solution by hand: 1+2+3-4+5+6+78+9, and my computer (with the standard computer rules of precendence, like 1/2*34 is 17) found all of these solutions:
1 123+45-67+8-9
2 123+4-5+67-89
3 123+4*5-6*7+8-9
4 123-45-67+89
5 123-4-5-6-7+8-9
6 12+34+5*6+7+8+9
7 12+34-5+6*7+8+9
8 12+34-5-6+7*8+9
9 12+34-5-6-7+8*9
10 12+3+4+5-6-7+89
11 12+3+4-56/7+89
12 12+3-4+5+67+8+9
13 12+3*45+6*7-89
14 12+3*4+5+6+7*8+9
15 12+3*4+5+6-7+8*9
16 12+3*4-5-6+78+9
17 12-3+4*5+6+7*8+9
18 12-3+4*5+6-7+8*9
19 12-3-4+5-6+7+89
20 12-3-4+5*6+7*8+9
21 12-3-4+5*6-7+8*9
22 12*3-4+5-6+78-9
23 12*3-4-5-6+7+8*9
24 12*3-4*5+67+8+9
25 12/3+4*5-6-7+89
26 12/3+4*5*6-7-8-9
27 12/3+4*5*6*7/8-9
28 12/3/4+5*6+78-9
29 1+234-56-7-8*9
30 1+234*5*6/78+9
31 1+234*5/6-7-89
32 1+23-4+56+7+8+9
33 1+23-4+56/7+8*9
34 1+23-4+5+6+78-9
35 1+23-4-5+6+7+8*9
36 1+23*4+56/7+8-9
37 1+23*4+5-6+7-8+9
38 1+23*4-5+6+7+8-9
39 1+2+34-5+67-8+9
40 1+2+34*5+6-7-8*9
41 1+2+3+4+5+6+7+8*9
42 1+2+3-45+67+8*9
43 1+2+3-4+5+6+78+9
44 1+2+3-4*5+6*7+8*9
45 1+2+3*4-5-6+7+89
46 1+2+3*4*56/7-8+9
47 1+2+3*4*5/6+78+9
48 1+2-3*4+5*6+7+8*9
49 1+2-3*4-5+6*7+8*9
50 1+2*34-56+78+9
51 1+2*3+4+5+67+8+9
52 1+2*3+4*5-6+7+8*9
53 1+2*3-4+56/7+89
54 1+2*3-4-5+6+7+89
55 1+2*3*4*5/6+7+8*9
56 1-23+4*5+6+7+89
57 1-23-4+5*6+7+89
58 1-23-4-5+6*7+89
59 1-2+3+45+6+7*8-9
60 1-2+3*4+5+67+8+9
61 1-2+3*4*5+6*7+8-9
62 1-2+3*4*5-6+7*8-9
63 1-2-34+56+7+8*9
64 1-2-3+45+6*7+8+9
65 1-2-3+45-6+7*8+9
66 1-2-3+45-6-7+8*9
67 1-2-3+4*56/7+8*9
68 1-2-3+4*5+67+8+9
69 1-2*3+4*5+6+7+8*9
70 1-2*3-4+5*6+7+8*9
71 1-2*3-4-5+6*7+8*9
72 1*234+5-67-8*9
73 1*23+4+56/7*8+9
74 1*23+4+5+67-8+9
75 1*23-4+5-6-7+89
76 1*23-4-56/7+89
77 1*23*4-56/7/8+9
78 1*2+34+56+7-8+9
79 1*2+34+5+6*7+8+9
80 1*2+34+5-6+7*8+9
81 1*2+34+5-6-7+8*9
82 1*2+34-56/7+8*9
83 1*2+3+45+67-8-9
84 1*2+3+4*5+6+78-9
85 1*2+3-4+5*6+78-9
86 1*2+3*4+5-6+78+9
87 1*2-3+4+56/7+89
88 1*2-3+4-5+6+7+89
89 1*2-3+4*5-6+78+9
90 1*2*34+56-7-8-9
91 1*2*3+4+5+6+7+8*9
92 1*2*3-45+67+8*9
93 1*2*3-4+5+6+78+9
94 1*2*3-4*5+6*7+8*9
95 1*2*3*4+5+6+7*8+9
96 1*2*3*4+5+6-7+8*9
97 1*2*3*4-5-6+78+9
98 1*2/3+4*5/6+7+89
99 1/2*34-5+6-7+89
100 1/2*3/4*56+7+8*9
101 1/2/3*456+7+8+9The shortest solution (fewest operations) is 123-45-67+89. There are 15 solutions with no two-digit or three-digit numbers. There are more solutions, if a negative sign (which is different from subtraction) is allowed. Allowing parentheses would produce a lot more solutions. There are quite a few longest solutions, with nine operations.Addendum:
A reader sent this email:
I send out a daily brainteaser to my group here at work and one of my co-workers came up with a new solution to your 123456789=100 puzzle. Just thought you'd like to know. 1 * 2 + 3 * 4 * 5 + 6 - 7 - 8 + 9 = 100!1*2+3*4*5+6-7-8+9 does not come out to 100, if it is viewed as a mathematical expression, because multiplication (or division) has precedence over addition or subtraction. We do the multiplication first, and then the addition and/or subtraction last. We mainly see this in algebra [where a+bc is a+(bc) and not (a+b)c] and in computer programming in BASIC and other languages (there are also languages with different kinds of precedence).
But this sequence of numbers and operations can also be viewed as a sequence of calculator key strokes, performed absolutely left to right, in which case it does come out to 100 (but not on my two scientific calculators). Most of my solutions above do not come out to 100 if done left to right. In my view, 1*2+3*4*5+6-7-8+9 does not indicate key strokes, but is a mathematical expression, and it requires a pair of parentheses to come out right: (1*2+3)*4*5+6-7-8+9 = 100.
With that warning about precedence, some people may still find some of my solutions confusing, like 1/2*3/4*56+7+8*9. Since multiplication and division have the same precedence, we evaluate them left to right, and so there is no problem. But some people may see the 2*3 as being a denominator. Similarly, with 1/2/3*456+7+8+9, some people may see the 2/3 as a denominator. But the most common standard is to do these divisions left to right.
A woman sent me this puzzle: _/_*_+_*_*_/_+_*_ = 100. Fill in the blanks with the digits 1 through 9 in any order. From the way it was described to me, ignore the rules of operator precedence, and just perform the operations from left to right. Thus, this works on the simplest of calculators, but will probably fail on some scientific calculators (unless you press = or ENTER after each digit). There are, of course, 362,880 ways to arrange these nine digits, and here are the 199 solutions:
1 1/2*7+5*3*6/9+8*4
2 1/2*7+5*6*3/9+8*4
3 1/2*8+5*3*6/9+7*4
4 1/2*8+5*6*3/9+7*4
5 1/3*6+5*2*8/7+9*4
6 1/3*6+5*8*2/7+9*4
7 1/3*6+7*2*8/9+4*5
8 1/3*6+7*8*2/9+4*5
9 1/3*8+9*2*6/7+5*4
10 1/3*8+9*6*2/7+5*4
11 1/3*9+4*2*6/7+8*5
12 1/3*9+4*6*2/7+8*5
13 1/4*7+2*3*6/9+5*8
14 1/4*7+2*6*3/9+5*8
15 1/4*8+7*3*6/9+2*5
16 1/4*8+7*6*3/9+2*5
17 1/6*2+5*3*9/8+7*4
18 1/6*2+5*9*3/8+7*4
19 1/6*2+7*3*4/8+9*5
20 1/6*2+7*4*3/8+9*5
21 1/6*8+2*3*9/5+7*4
22 1/6*8+2*9*3/5+7*4
23 1/9*3+2*6*8/7+4*5
24 1/9*3+2*8*6/7+4*5
25 1/9*5+8*3*4/7+2*6
26 1/9*5+8*4*3/7+2*6
27 1/9*6+8*2*3/4+7*5
28 1/9*6+8*3*2/4+7*5
29 1/9*7+5*2*3/4+8*6
30 1/9*7+5*3*2/4+8*6
31 1/9*8+2*3*6/4+7*5
32 1/9*8+2*6*3/4+7*5
33 2/3*5+6*8*9/7+4*1
34 2/3*5+6*9*8/7+4*1
35 2/4*8+1*3*7/9+5*6
36 2/4*8+1*7*3/9+5*6
37 2/6*1+5*3*9/8+7*4
38 2/6*1+5*9*3/8+7*4
39 2/6*1+7*3*4/8+9*5
40 2/6*1+7*4*3/8+9*5
41 2/6*7+1*3*8/5+9*4
42 2/6*7+1*8*3/5+9*4
43 2/6*7+3*1*9/4+8*5
44 2/6*7+3*9*1/4+8*5
45 2/6*9+7*1*3/4+5*8
46 2/6*9+7*3*1/4+5*8
47 2/8*9+5*1*4/3+7*6
48 2/8*9+5*4*1/3+7*6
49 2/9*3+8*1*6/4+7*5
50 2/9*3+8*6*1/4+7*5
51 3/2*5+8*4*9/6+7*1
52 3/2*5+8*9*4/6+7*1
53 3/2*6+5*1*8/7+9*4
54 3/2*6+5*8*1/7+9*4
55 3/4*9+2*1*6/7+5*8
56 3/4*9+2*6*1/7+5*8
57 3/6*7+2*1*8/4+9*5
58 3/6*7+2*8*1/4+9*5
59 3/6*8+1*2*9/5+7*4
60 3/6*8+1*9*2/5+7*4
61 3/6*9+2*1*8/4+7*5
62 3/6*9+2*8*1/4+7*5
63 3/9*1+2*6*8/7+4*5
64 3/9*1+2*8*6/7+4*5
65 3/9*2+8*1*6/4+7*5
66 3/9*2+8*6*1/4+7*5
67 3/9*5+2*1*6/4+7*8
68 3/9*5+2*6*1/4+7*8
69 3/9*6+5*7*8/4+2*1
70 3/9*6+5*8*7/4+2*1
71 3/9*6+7*1*8/4+2*5
72 3/9*6+7*8*1/4+2*5
73 3/9*7+5*1*8/4+2*6
74 3/9*7+5*8*1/4+2*6
75 4/2*7+8*1*3/6+9*5
76 4/2*7+8*3*1/6+9*5
77 4/2*9+8*1*3/6+7*5
78 4/2*9+8*3*1/6+7*5
79 4/3*9+2*1*6/7+8*5
80 4/3*9+2*6*1/7+8*5
81 4/8*7+2*1*6/3+9*5
82 4/8*7+2*6*1/3+9*5
83 4/8*9+2*1*6/3+7*5
84 4/8*9+2*6*1/3+7*5
85 5/2*3+8*4*9/6+7*1
86 5/2*3+8*9*4/6+7*1
87 5/3*2+6*8*9/7+4*1
88 5/3*2+6*9*8/7+4*1
89 5/3*9+7*1*8/4+6*2
90 5/3*9+7*8*1/4+6*2
91 5/4*6+8*2*9/3+7*1
92 5/4*6+8*9*2/3+7*1
93 5/4*7+1*2*3/9+6*8
94 5/4*7+1*3*2/9+6*8
95 5/6*7+1*3*8/4+9*2
96 5/6*7+1*8*3/4+9*2
97 5/6*9+3*2*8/7+1*4
98 5/6*9+3*8*2/7+1*4
99 5/6*9+8*3*4/2+7*1
100 5/6*9+8*4*3/2+7*1
101 5/9*1+8*3*4/7+2*6
102 5/9*1+8*4*3/7+2*6
103 5/9*3+2*1*6/4+7*8
104 5/9*3+2*6*1/4+7*8
105 6/2*3+5*1*8/7+9*4
106 6/2*3+5*8*1/7+9*4
107 6/2*9+7*1*4/8+3*5
108 6/2*9+7*4*1/8+3*5
109 6/3*1+5*2*8/7+9*4
110 6/3*1+5*8*2/7+9*4
111 6/3*1+7*2*8/9+4*5
112 6/3*1+7*8*2/9+4*5
113 6/3*7+8*1*2/4+9*5
114 6/3*7+8*2*1/4+9*5
115 6/3*9+8*1*2/4+7*5
116 6/3*9+8*2*1/4+7*5
117 6/4*5+8*2*9/3+7*1
118 6/4*5+8*9*2/3+7*1
119 6/9*1+8*2*3/4+7*5
120 6/9*1+8*3*2/4+7*5
121 6/9*3+5*7*8/4+2*1
122 6/9*3+5*8*7/4+2*1
123 6/9*3+7*1*8/4+2*5
124 6/9*3+7*8*1/4+2*5
125 7/2*1+5*3*6/9+8*4
126 7/2*1+5*6*3/9+8*4
127 7/2*4+8*1*3/6+9*5
128 7/2*4+8*3*1/6+9*5
129 7/2*8+5*1*6/9+3*4
130 7/2*8+5*6*1/9+3*4
131 7/3*6+8*1*2/4+9*5
132 7/3*6+8*2*1/4+9*5
133 7/4*1+2*3*6/9+5*8
134 7/4*1+2*6*3/9+5*8
135 7/4*5+1*2*3/9+6*8
136 7/4*5+1*3*2/9+6*8
137 7/4*9+8*2*6/3+5*1
138 7/4*9+8*6*2/3+5*1
139 7/6*2+1*3*8/5+9*4
140 7/6*2+1*8*3/5+9*4
141 7/6*2+3*1*9/4+8*5
142 7/6*2+3*9*1/4+8*5
143 7/6*3+2*1*8/4+9*5
144 7/6*3+2*8*1/4+9*5
145 7/6*5+1*8*3/4+9*2
146 7/8*4+2*1*6/3+9*5
147 7/8*4+2*6*1/3+9*5
148 7/9*1+5*2*3/4+8*6
149 7/9*1+5*3*2/4+8*6
150 7/9*3+5*1*8/4+2*6
151 7/9*3+5*8*1/4+2*6
152 8/2*1+5*3*6/9+7*4
153 8/2*1+5*6*3/9+7*4
154 8/2*7+5*1*6/9+3*4
155 8/2*7+5*6*1/9+3*4
156 8/3*1+9*2*6/7+5*4
157 8/3*1+9*6*2/7+5*4
158 8/4*1+7*3*6/9+2*5
159 8/4*1+7*6*3/9+2*5
160 8/4*2+1*3*7/9+5*6
161 8/4*2+1*7*3/9+5*6
162 8/4*9+3*1*6/7+2*5
163 8/4*9+3*6*1/7+2*5
164 8/6*1+2*3*9/5+7*4
165 8/6*1+2*9*3/5+7*4
166 8/6*3+1*2*9/5+7*4
167 8/6*3+1*9*2/5+7*4
168 8/9*1+2*3*6/4+7*5
169 8/9*1+2*6*3/4+7*5
170 9/2*4+8*1*3/6+7*5
171 9/2*4+8*3*1/6+7*5
172 9/2*6+7*1*4/8+3*5
173 9/2*6+7*4*1/8+3*5
174 9/3*1+4*2*6/7+8*5
175 9/3*1+4*6*2/7+8*5
176 9/3*4+2*1*6/7+8*5
177 9/3*4+2*6*1/7+8*5
178 9/3*5+7*1*8/4+6*2
179 9/3*5+7*8*1/4+6*2
180 9/3*6+8*1*2/4+7*5
181 9/3*6+8*2*1/4+7*5
182 9/4*3+2*1*6/7+5*8
183 9/4*3+2*6*1/7+5*8
184 9/4*7+8*2*6/3+5*1
185 9/4*7+8*6*2/3+5*1
186 9/4*8+3*1*6/7+2*5
187 9/4*8+3*6*1/7+2*5
188 9/6*2+7*1*3/4+5*8
189 9/6*2+7*3*1/4+5*8
190 9/6*3+2*1*8/4+7*5
191 9/6*3+2*8*1/4+7*5
192 9/6*5+3*2*8/7+1*4
193 9/6*5+3*8*2/7+1*4
194 9/6*5+8*3*4/2+7*1
195 9/6*5+8*4*3/2+7*1
196 9/8*2+5*1*4/3+7*6
197 9/8*2+5*4*1/3+7*6
198 9/8*4+2*1*6/3+7*5
199 9/8*4+2*6*1/3+7*5
No decent puzzle composer would poze a problem which has 199 solutions.I reported the above solutions to the above-mentioned woman, and she informed me that the rules of operator precendence DO apply to this puzzle, and then she became somewhat insulting (as seems to happen a lot on the Internet). Here are the 192 solutions, in that case, which I did not send to her:
1 1/2*6+5*7*8/4+3*9
2 1/2*6+5*7*8/4+9*3
3 1/2*6+5*8*7/4+3*9
4 1/2*6+5*8*7/4+9*3
5 1/2*6+7*5*8/4+3*9
6 1/2*6+7*5*8/4+9*3
7 1/2*6+7*8*5/4+3*9
8 1/2*6+7*8*5/4+9*3
9 1/2*6+8*5*7/4+3*9
10 1/2*6+8*5*7/4+9*3
11 1/2*6+8*7*5/4+3*9
12 1/2*6+8*7*5/4+9*3
13 4/1*8+2*3*5/6+7*9
14 4/1*8+2*3*5/6+9*7
15 4/1*8+2*5*3/6+7*9
16 4/1*8+2*5*3/6+9*7
17 4/1*8+3*2*5/6+7*9
18 4/1*8+3*2*5/6+9*7
19 4/1*8+3*5*2/6+7*9
20 4/1*8+3*5*2/6+9*7
21 4/1*8+5*2*3/6+7*9
22 4/1*8+5*2*3/6+9*7
23 4/1*8+5*3*2/6+7*9
24 4/1*8+5*3*2/6+9*7
25 4/6*9+2*5*7/1+3*8
26 4/6*9+2*5*7/1+8*3
27 4/6*9+2*7*5/1+3*8
28 4/6*9+2*7*5/1+8*3
29 4/6*9+5*2*7/1+3*8
30 4/6*9+5*2*7/1+8*3
31 4/6*9+5*7*2/1+3*8
32 4/6*9+5*7*2/1+8*3
33 4/6*9+7*2*5/1+3*8
34 4/6*9+7*2*5/1+8*3
35 4/6*9+7*5*2/1+3*8
36 4/6*9+7*5*2/1+8*3
37 4/8*6+2*5*7/1+3*9
38 4/8*6+2*5*7/1+9*3
39 4/8*6+2*7*5/1+3*9
40 4/8*6+2*7*5/1+9*3
41 4/8*6+5*2*7/1+3*9
42 4/8*6+5*2*7/1+9*3
43 4/8*6+5*7*2/1+3*9
44 4/8*6+5*7*2/1+9*3
45 4/8*6+7*2*5/1+3*9
46 4/8*6+7*2*5/1+9*3
47 4/8*6+7*5*2/1+3*9
48 4/8*6+7*5*2/1+9*3
49 6/2*1+5*7*8/4+3*9
50 6/2*1+5*7*8/4+9*3
51 6/2*1+5*8*7/4+3*9
52 6/2*1+5*8*7/4+9*3
53 6/2*1+7*5*8/4+3*9
54 6/2*1+7*5*8/4+9*3
55 6/2*1+7*8*5/4+3*9
56 6/2*1+7*8*5/4+9*3
57 6/2*1+8*5*7/4+3*9
58 6/2*1+8*5*7/4+9*3
59 6/2*1+8*7*5/4+3*9
60 6/2*1+8*7*5/4+9*3
61 6/2*9+5*7*8/4+1*3
62 6/2*9+5*7*8/4+3*1
63 6/2*9+5*8*7/4+1*3
64 6/2*9+5*8*7/4+3*1
65 6/2*9+7*5*8/4+1*3
66 6/2*9+7*5*8/4+3*1
67 6/2*9+7*8*5/4+1*3
68 6/2*9+7*8*5/4+3*1
69 6/2*9+8*5*7/4+1*3
70 6/2*9+8*5*7/4+3*1
71 6/2*9+8*7*5/4+1*3
72 6/2*9+8*7*5/4+3*1
73 6/8*4+2*5*7/1+3*9
74 6/8*4+2*5*7/1+9*3
75 6/8*4+2*7*5/1+3*9
76 6/8*4+2*7*5/1+9*3
77 6/8*4+5*2*7/1+3*9
78 6/8*4+5*2*7/1+9*3
79 6/8*4+5*7*2/1+3*9
80 6/8*4+5*7*2/1+9*3
81 6/8*4+7*2*5/1+3*9
82 6/8*4+7*2*5/1+9*3
83 6/8*4+7*5*2/1+3*9
84 6/8*4+7*5*2/1+9*3
85 7/1*9+2*3*5/6+4*8
86 7/1*9+2*3*5/6+8*4
87 7/1*9+2*5*3/6+4*8
88 7/1*9+2*5*3/6+8*4
89 7/1*9+3*2*5/6+4*8
90 7/1*9+3*2*5/6+8*4
91 7/1*9+3*5*2/6+4*8
92 7/1*9+3*5*2/6+8*4
93 7/1*9+5*2*3/6+4*8
94 7/1*9+5*2*3/6+8*4
95 7/1*9+5*3*2/6+4*8
96 7/1*9+5*3*2/6+8*4
97 7/4*8+3*6*9/2+1*5
98 7/4*8+3*6*9/2+5*1
99 7/4*8+3*9*6/2+1*5
100 7/4*8+3*9*6/2+5*1
101 7/4*8+6*3*9/2+1*5
102 7/4*8+6*3*9/2+5*1
103 7/4*8+6*9*3/2+1*5
104 7/4*8+6*9*3/2+5*1
105 7/4*8+9*3*6/2+1*5
106 7/4*8+9*3*6/2+5*1
107 7/4*8+9*6*3/2+1*5
108 7/4*8+9*6*3/2+5*1
109 8/1*4+2*3*5/6+7*9
110 8/1*4+2*3*5/6+9*7
111 8/1*4+2*5*3/6+7*9
112 8/1*4+2*5*3/6+9*7
113 8/1*4+3*2*5/6+7*9
114 8/1*4+3*2*5/6+9*7
115 8/1*4+3*5*2/6+7*9
116 8/1*4+3*5*2/6+9*7
117 8/1*4+5*2*3/6+7*9
118 8/1*4+5*2*3/6+9*7
119 8/1*4+5*3*2/6+7*9
120 8/1*4+5*3*2/6+9*7
121 8/3*9+4*5*7/2+1*6
122 8/3*9+4*5*7/2+6*1
123 8/3*9+4*7*5/2+1*6
124 8/3*9+4*7*5/2+6*1
125 8/3*9+5*4*7/2+1*6
126 8/3*9+5*4*7/2+6*1
127 8/3*9+5*7*4/2+1*6
128 8/3*9+5*7*4/2+6*1
129 8/3*9+7*4*5/2+1*6
130 8/3*9+7*4*5/2+6*1
131 8/3*9+7*5*4/2+1*6
132 8/3*9+7*5*4/2+6*1
133 8/4*7+3*6*9/2+1*5
134 8/4*7+3*6*9/2+5*1
135 8/4*7+3*9*6/2+1*5
136 8/4*7+3*9*6/2+5*1
137 8/4*7+6*3*9/2+1*5
138 8/4*7+6*3*9/2+5*1
139 8/4*7+6*9*3/2+1*5
140 8/4*7+6*9*3/2+5*1
141 8/4*7+9*3*6/2+1*5
142 8/4*7+9*3*6/2+5*1
143 8/4*7+9*6*3/2+1*5
144 8/4*7+9*6*3/2+5*1
145 9/1*7+2*3*5/6+4*8
146 9/1*7+2*3*5/6+8*4
147 9/1*7+2*5*3/6+4*8
148 9/1*7+2*5*3/6+8*4
149 9/1*7+3*2*5/6+4*8
150 9/1*7+3*2*5/6+8*4
151 9/1*7+3*5*2/6+4*8
152 9/1*7+3*5*2/6+8*4
153 9/1*7+5*2*3/6+4*8
154 9/1*7+5*2*3/6+8*4
155 9/1*7+5*3*2/6+4*8
156 9/1*7+5*3*2/6+8*4
157 9/2*6+5*7*8/4+1*3
158 9/2*6+5*7*8/4+3*1
159 9/2*6+5*8*7/4+1*3
160 9/2*6+5*8*7/4+3*1
161 9/2*6+7*5*8/4+1*3
162 9/2*6+7*5*8/4+3*1
163 9/2*6+7*8*5/4+1*3
164 9/2*6+7*8*5/4+3*1
165 9/2*6+8*5*7/4+1*3
166 9/2*6+8*5*7/4+3*1
167 9/2*6+8*7*5/4+1*3
168 9/2*6+8*7*5/4+3*1
169 9/3*8+4*5*7/2+1*6
170 9/3*8+4*5*7/2+6*1
171 9/3*8+4*7*5/2+1*6
172 9/3*8+4*7*5/2+6*1
173 9/3*8+5*4*7/2+1*6
174 9/3*8+5*4*7/2+6*1
175 9/3*8+5*7*4/2+1*6
176 9/3*8+5*7*4/2+6*1
177 9/3*8+7*4*5/2+1*6
178 9/3*8+7*4*5/2+6*1
179 9/3*8+7*5*4/2+1*6
180 9/3*8+7*5*4/2+6*1
181 9/6*4+2*5*7/1+3*8
182 9/6*4+2*5*7/1+8*3
183 9/6*4+2*7*5/1+3*8
184 9/6*4+2*7*5/1+8*3
185 9/6*4+5*2*7/1+3*8
186 9/6*4+5*2*7/1+8*3
187 9/6*4+5*7*2/1+3*8
188 9/6*4+5*7*2/1+8*3
189 9/6*4+7*2*5/1+3*8
190 9/6*4+7*2*5/1+8*3
191 9/6*4+7*5*2/1+3*8
192 9/6*4+7*5*2/1+8*3
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