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 Add down to One (Posted on 2003-05-21)
The numbers 0-9 are lined up in a row, like this:

0 1 2 3 4 5 6 7 8 9

You have to put in + and - signs in the blanks, so that in the end it will all equal 1.

Also, if possible, try to make expressions resulting in 0 and -1.

 See The Solution Submitted by Jonathan Waltz Rating: 2.5000 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Solution plus | Comment 11 of 16 |
(In reply to Solution plus by Bryan)

Following your allowing of the removal of spaces in addition to replacement of others by + or -, and to answer your question on the first positive integer that can't be produced in that manner, the answer is 211.

0 = 0- 1 - 2 + 34 + 56 - 78 - 9
(32 others)
1 = 0- 1 - 2 - 3 - 4 - 5 + 6 - 7 + 8 + 9
(68 others)
2 = 0- 1 + 2 - 34 + 5 + 6 + 7 + 8 + 9
(28 others)
3 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 7 + 8 + 9
(58 others)
4 = 0- 1 - 2 + 34 - 5 + 67 - 89
(25 others)
5 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 8 - 9
(60 others)
6 = 0- 1 - 2 + 34 + 5 - 6 - 7 - 8 - 9
(35 others)
7 = 0- 1 - 2 - 3 - 4 - 5 - 67 + 89
(55 others)
8 = 0- 1 - 2 - 34 - 5 + 67 - 8 - 9
(25 others)
9 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 - 8 + 9
(67 others)
10 = 0- 1 - 2 + 34 - 5 - 6 + 7 - 8 - 9
(28 others)
11 = 0- 1 - 2 - 3 - 4 + 5 + 6 - 7 + 8 + 9
(58 others)
12 = 0- 1 - 2 - 3 - 45 - 6 + 78 - 9
(37 others)
13 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 7 + 8 + 9
(53 others)
14 = 0- 1 - 2 + 34 - 5 - 6 - 7 - 8 + 9
(38 others)
15 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 7 + 8 + 9
(62 others)
16 = 0- 1 - 2 - 3 - 4 - 56 - 7 + 89
(25 others)
17 = 0- 1 - 2 - 3 - 4 + 5 - 67 + 89
(55 others)
18 = 0- 1 - 2 - 34 + 5 + 67 - 8 - 9
(33 others)
19 = 0- 1 - 2 - 3 + 4 + 5 + 6 - 7 + 8 + 9
(56 others)
20 = 0- 1 - 2 + 34 + 5 - 6 + 7 - 8 - 9
(37 others)
21 = 0- 1 - 2 - 3 - 4 - 56 + 78 + 9
(58 others)
22 = 0- 1 - 2 - 3 - 4 + 56 - 7 - 8 - 9
(35 others)
23 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 8 + 9
(58 others)
24 = 0- 1 - 2 - 3 - 45 + 6 + 78 - 9
(49 others)
25 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 + 8 + 9
(48 others)
26 = 0- 1 - 2 - 34 - 5 + 67 - 8 + 9
(38 others)
27 = 0- 1 - 2 - 3 + 45 - 6 - 7 - 8 + 9
(64 others)
28 = 0- 1 - 2 + 3 - 4 + 56 - 7 - 8 - 9
(39 others)
29 = 0- 1 - 2 - 3 + 4 - 56 + 78 + 9
(53 others)
30 = 0- 1 - 2 - 3 - 4 - 56 + 7 + 89
(50 others)
31 = 0- 1 - 2 - 34 + 5 - 6 + 78 - 9
(44 others)
32 = 0- 1 - 2 + 34 + 5 + 6 + 7 - 8 - 9
(44 others)
33 = 0- 1 - 2 - 3 - 45 + 67 + 8 + 9
(55 others)
34 = 0- 1 - 2 - 34 - 5 - 6 - 7 + 89
(30 others)
35 = 0- 1 - 2 - 3 - 4 - 5 + 67 - 8 - 9
(48 others)
36 = 0- 1 - 2 - 3 - 4 + 56 + 7 - 8 - 9
(50 others)
37 = 0- 1 - 2 - 3 - 45 + 6 - 7 + 89
(50 others)
38 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 8 - 9
(43 others)
39 = 0- 1 - 2 - 3 - 45 - 6 + 7 + 89
(54 others)
40 = 0- 1 - 2 - 3 - 4 + 56 - 7 - 8 + 9
(46 others)
41 = 0- 1 - 2 - 3 + 45 - 6 + 7 - 8 + 9
(42 others)
42 = 0- 1 - 2 - 3 - 45 + 6 + 78 + 9
(51 others)
43 = 0- 1 - 2 - 3 + 4 - 5 + 67 - 8 - 9
(43 others)
44 = 0- 1 - 2 - 3 + 4 + 56 + 7 - 8 - 9
(43 others)
45 = 0- 1 - 2 - 3 - 4 + 5 + 67 - 8 - 9
(67 others)
46 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 8 - 9
(44 others)
47 = 0- 1 - 2 + 3 + 45 - 6 + 7 - 8 + 9
(41 others)
48 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 78 - 9
(50 others)
49 = 0- 1 - 2 - 34 + 5 - 6 + 78 + 9
(37 others)
50 = 0- 1 - 2 + 3 + 4 + 56 + 7 - 8 - 9
(44 others)
51 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 8 - 9
(53 others)
52 = 0- 1 - 2 - 3 - 4 + 56 + 7 + 8 - 9
(37 others)
53 = 0- 1 - 2 - 3 - 4 - 5 + 67 - 8 + 9
(49 others)
54 = 0- 1 - 2 - 3 - 4 + 56 + 7 - 8 + 9
(50 others)
55 = 0- 1 - 2 - 3 + 45 + 6 - 7 + 8 + 9
(41 others)
56 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 8 + 9
(35 others)
57 = 0- 1 - 2 - 3 + 45 - 6 + 7 + 8 + 9
(42 others)
58 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 78 - 9
(47 others)
59 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 8 - 9
(41 others)
60 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 78 - 9
(49 others)
61 = 0- 1 - 2 - 3 - 4 - 5 - 6 - 7 + 89
(40 others)
62 = 0- 1 - 2 - 3 + 4 + 56 + 7 - 8 + 9
(36 others)
63 = 0- 1 - 2 - 3 - 4 + 5 + 67 - 8 + 9
(55 others)
64 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 8 + 9
(35 others)
65 = 0- 1 - 2 + 3 + 4 - 5 + 67 + 8 - 9
(38 others)
66 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 78 + 9
(46 others)
67 = 0- 1 - 2 + 3 - 4 - 5 - 6 - 7 + 89
(44 others)
68 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 78 - 9
(39 others)
69 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 8 + 9
(45 others)
70 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 78 - 9
(28 others)
71 = 0- 1 - 2 - 3 - 4 + 5 - 6 - 7 + 89
(38 others)
72 = 0- 1 - 2 + 3 - 4 - 5 - 6 + 78 + 9
(42 others)
73 = 0- 1 - 2 - 3 - 4 - 5 + 6 - 7 + 89
(38 others)
74 = 0- 1 - 2 - 3 + 4 - 5 - 6 + 78 + 9
(33 others)
75 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 7 + 89
(38 others)
76 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 78 + 9
(38 others)
77 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 8 + 9
(35 others)
78 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 78 + 9
(37 others)
79 = 0- 1 - 2 - 3 - 4 + 5 + 67 + 8 + 9
(34 others)
80 = 0- 1 - 2 + 3 + 4 - 5 - 6 + 78 + 9
(27 others)
81 = 0- 1 - 2 - 3 + 4 - 5 + 6 - 7 + 89
(49 others)
82 = 0- 1 - 2 + 3 - 4 + 5 - 6 + 78 + 9
(31 others)
83 = 0- 1 - 2 - 3 - 4 + 5 + 6 - 7 + 89
(35 others)
84 = 0- 1 - 2 - 3 + 4 + 5 - 6 + 78 + 9
(37 others)
85 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 7 + 89
(32 others)
86 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 78 + 9
(28 others)
87 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 7 + 89
(34 others)
88 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 78 + 9
(22 others)
89 = 0- 1 - 2 - 3 + 45 + 67 - 8 - 9
(35 others)
90 = 0- 1 - 2 + 3 + 4 + 5 - 6 + 78 + 9
(34 others)
91 = 0- 1 - 2 - 3 + 4 + 5 + 6 - 7 + 89
(37 others)
92 = 0- 1 - 2 + 3 + 4 - 5 + 6 + 78 + 9
(33 others)
93 = 0- 1 - 2 - 3 + 4 + 5 - 6 + 7 + 89
(33 others)
94 = 0- 1 - 2 + 3 - 4 + 5 + 6 + 78 + 9
(27 others)
95 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 89
(26 others)
96 = 0- 1 - 2 - 3 + 4 + 5 + 6 + 78 + 9
(29 others)
97 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 + 89
(27 others)
98 = 0- 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9
(23 others)
99 = 0- 1 - 2 + 3 + 4 + 5 - 6 + 7 + 89
(41 others)
100 = 0- 1 + 2 - 3 + 4 + 5 + 6 + 78 + 9
(22 others)
101 = 0- 1 - 2 - 34 + 56 - 7 + 89
(27 others)
102 = 0- 1 - 2 - 3 + 45 - 6 + 78 - 9
(26 others)
103 = 0- 1 - 2 + 3 - 4 + 5 + 6 + 7 + 89
(22 others)
104 = 0- 1 - 2 + 34 + 5 + 67 - 8 + 9
(24 others)
105 = 0- 1 - 2 - 3 - 45 + 67 + 89
(23 others)
106 = 0- 1 - 2 - 34 + 56 + 78 + 9
(24 others)
107 = 0- 1 - 2 - 3 + 45 + 67 - 8 + 9
(27 others)
108 = 0- 1 - 2 + 3 + 45 - 6 + 78 - 9
(33 others)
109 = 0- 1 - 23 + 45 + 6 - 7 + 89
(18 others)
110 = 0- 1 - 2 + 34 - 5 + 67 + 8 + 9
(23 others)
111 = 0- 1 - 2 + 3 - 45 + 67 + 89
(24 others)
112 = 0- 1 - 2 + 34 + 5 - 6 - 7 + 89
(20 others)
113 = 0- 1 - 2 + 3 + 45 + 67 - 8 + 9
(21 others)
114 = 0- 1 - 2 - 3 + 45 + 6 + 78 - 9
(25 others)
115 = 0- 1 - 2 - 3 - 4 + 56 + 78 - 9
(16 others)
116 = 0- 1 - 2 + 34 - 5 - 6 + 7 + 89
(24 others)
117 = 0- 1 - 2 + 34 + 5 - 6 + 78 + 9
(34 others)
118 = 0- 1 - 23 + 4 + 56 - 7 + 89
(20 others)
119 = 0- 1 - 2 + 34 - 5 + 6 + 78 + 9
(14 others)
120 = 0- 1 - 2 - 3 + 45 - 6 + 78 + 9
(27 others)
121 = 0- 1 - 2 + 3 - 4 + 56 + 78 - 9
(15 others)
122 = 0+ 1 - 2 - 3 + 45 - 6 + 78 + 9
(17 others)
123 = 0- 1 - 2 - 3 + 4 + 56 + 78 - 9
(17 others)
124 = 0- 1 - 2 - 34 + 5 + 67 + 89
(14 others)
125 = 0- 1 + 2 + 3 - 4 + 56 + 78 - 9
(19 others)
126 = 0- 1 - 2 + 3 + 45 - 6 + 78 + 9
(33 others)
127 = 0- 1 - 2 - 3 + 45 + 6 - 7 + 89
(11 others)
128 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 89
(19 others)
129 = 0- 1 - 2 - 3 + 45 - 6 + 7 + 89
(17 others)
130 = 0- 1 + 2 + 3 + 45 - 6 + 78 + 9
(21 others)
131 = 0- 1 - 23 + 4 - 5 + 67 + 89
(11 others)
132 = 0- 1 - 2 - 3 + 45 + 6 + 78 + 9
(22 others)
133 = 0- 1 - 2 - 3 - 4 + 56 + 78 + 9
(15 others)
134 = 0- 1 - 2 + 3 - 4 + 56 - 7 + 89
(14 others)
135 = 0- 1 - 2 + 3 + 45 - 6 + 7 + 89
(28 others)
136 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 89
(16 others)
137 = 0- 1 + 2 - 3 - 4 + 56 + 78 + 9
(7 others)
138 = 0- 1 - 2 + 3 + 45 + 6 + 78 + 9
(22 others)
139 = 0- 1 - 2 + 3 - 4 + 56 + 78 + 9
(10 others)
140 = 0- 1 + 2 - 3 + 4 + 56 - 7 + 89
(16 others)
141 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 89
(14 others)
142 = 0- 1 - 2 - 3 - 4 + 56 + 7 + 89
(13 others)
143 = 0- 1 + 2 + 3 - 4 + 56 + 78 + 9
(14 others)
144 = 0- 1 + 234 - 5 - 67 - 8 - 9
(26 others)
145 = 0- 1 + 2 - 3 - 4 - 5 + 67 + 89
(11 others)
146 = 0- 1 + 2 - 3 - 4 + 56 + 7 + 89
(12 others)
147 = 0- 1 - 2 + 3 - 4 - 5 + 67 + 89
(15 others)
148 = 0- 1 - 2 + 3 - 4 + 56 + 7 + 89
(13 others)
149 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 89
(10 others)
150 = 0- 1 - 2 - 3 + 4 + 56 + 7 + 89
(16 others)
151 = 0- 1 - 2 - 3 - 4 + 5 + 67 + 89
(11 others)
152 = 0- 1 + 2 + 3 - 4 + 56 + 7 + 89
(9 others)
153 = 0- 1 + 2 - 3 + 4 - 5 + 67 + 89
(22 others)
154 = 0- 1 + 2 - 3 + 4 + 56 + 7 + 89
(15 others)
155 = 0- 1 - 2 + 3 + 4 - 5 + 67 + 89
(8 others)
156 = 0- 1 - 2 + 3 + 4 + 56 + 7 + 89
(15 others)
157 = 0- 1 - 2 + 3 - 4 + 5 + 67 + 89
(12 others)
158 = 0+ 1 - 2 + 3 + 4 + 56 + 7 + 89
(7 others)
159 = 0- 1 - 2 - 3 + 4 + 5 + 67 + 89
(13 others)
160 = 0- 1 + 2 + 3 + 4 + 56 + 7 + 89
(4 others)
161 = 0- 1 + 2 + 3 - 4 + 5 + 67 + 89
(5 others)
162 = 0- 1 + 234 - 5 - 67 - 8 + 9
(19 others)
163 = 0- 1 + 2 - 3 + 4 + 5 + 67 + 89
(7 others)
164 = 0- 1 + 23 + 4 + 56 - 7 + 89
(10 others)
165 = 0- 1 - 2 + 3 + 4 + 5 + 67 + 89
(10 others)
166 = 0+ 1 + 23 + 4 + 56 - 7 + 89
(7 others)
167 = 0- 1 + 234 - 56 + 7 - 8 - 9
(8 others)
168 = 0+ 123 - 45 - 6 + 7 + 89
(5 others)
169 = 0- 1 - 2 + 34 + 56 - 7 + 89
(9 others)
170 = 0- 1 + 23 - 4 + 56 + 7 + 89
(5 others)
171 = 0- 1 + 234 - 56 - 7 - 8 + 9
(18 others)
172 = 0- 1 + 234 + 5 - 67 - 8 + 9
(10 others)
173 = 0- 1 + 2 + 34 + 56 - 7 + 89
(5 others)
174 = 0- 1 - 2 + 34 + 56 + 78 + 9
(7 others)
175 = 0- 1 + 234 + 5 + 6 - 78 + 9
(4 others)
176 = 0+ 1 - 2 + 34 + 56 + 78 + 9
(1 other)
177 = 0- 1 - 23 + 45 + 67 + 89
(8 others)
178 = 0- 1 + 2 + 34 + 56 + 78 + 9
(2 others)
179 = 0- 1 + 23 - 4 + 5 + 67 + 89
(4 others)
180 = 0+ 1 + 2 + 34 + 56 + 78 + 9
(13 others)
181 = 0+ 1 + 23 - 4 + 5 + 67 + 89
(3 others)
182 = 0- 1 - 2 + 34 - 5 + 67 + 89
(6 others)
183 = 0- 1 - 2 + 34 + 56 + 7 + 89
(4 others)
184 = 0+ 1 - 2 + 34 - 5 + 67 + 89
(5 others)
185 = 0- 1 + 234 - 56 + 7 - 8 + 9
(8 others)
186 = 0- 1 - 2 + 345 - 67 - 89
(4 others)
187 = 0- 1 + 2 + 34 + 56 + 7 + 89
(6 others)
188 = 0- 1 + 234 + 5 - 67 + 8 + 9
(6 others)
189 = 0+ 1 + 2 + 34 + 56 + 7 + 89
(11 others)
190 = 0- 1 + 2 + 345 - 67 - 89
(10 others)
191 = 0+ 123 + 4 + 56 + 7 - 8 + 9
(1 other)
192 = 0- 1 - 2 + 34 + 5 + 67 + 89
(5 others)
193 = 0- 1 + 234 + 56 - 7 - 89
(2 others)
194 = 0+ 1 - 2 + 34 + 5 + 67 + 89
(1 other)
195 = 0- 1 - 2 - 3 + 45 + 67 + 89
(6 others)
196 = 0- 1 + 2 + 34 + 5 + 67 + 89
197 = 0+ 1 - 2 - 3 + 45 + 67 + 89
(5 others)
198 = 0- 1 + 234 - 5 - 6 - 7 - 8 - 9
(12 others)
199 = 0- 1 + 2 - 3 + 45 + 67 + 89
(4 others)
200 = 0+ 1 + 234 - 5 - 6 - 7 - 8 - 9
(5 others)
201 = 0- 1 - 2 + 3 + 45 + 67 + 89
(5 others)
202 = 0- 1 + 234 + 56 - 78 - 9
(2 others)
203 = 0+ 1 - 2 + 3 + 45 + 67 + 89
(5 others)
204 = 0+ 1 + 234 + 56 - 78 - 9
(3 others)
205 = 0- 1 + 2 + 3 + 45 + 67 + 89
(2 others)
206 = 0- 1 + 234 - 5 + 67 - 89
(2 others)
207 = 0- 1 + 234 + 56 + 7 - 89
(10 others)
208 = 0- 1 + 234 + 5 - 6 - 7 - 8 - 9
(6 others)
209 = 0+ 1 + 234 + 56 + 7 - 89
(1 other)
210 = 0- 1 + 234 - 5 + 6 - 7 - 8 - 9
(7 others)
Skip 1
212 = 0- 1 + 234 - 5 - 6 + 7 - 8 - 9
(6 others)
213 = 0+ 123 + 4 + 5 - 6 + 78 + 9
(1 other)
214 = 0- 1 + 234 - 5 - 6 - 7 + 8 - 9
(4 others)
215 = 0+ 123 + 4 - 5 + 6 + 78 + 9
(1 other)
216 = 0- 1 + 234 - 5 - 6 - 7 - 8 + 9
(9 others)
217 = 0+ 123 - 4 + 5 + 6 + 78 + 9
(1 other)
218 = 0+ 1 + 234 - 5 - 6 - 7 - 8 + 9
(5 others)
Skip 1
220 = 0- 1 + 234 + 5 + 6 - 7 - 8 - 9
(3 others)
Skip 1
222 = 0- 1 + 234 + 5 - 6 + 7 - 8 - 9
(6 others)
223 = 0- 1 + 23 + 45 + 67 + 89
224 = 0- 1 + 234 - 5 + 6 + 7 - 8 - 9
(5 others)
225 = 0+ 1 + 23 + 45 + 67 + 89
(3 others)
226 = 0- 1 + 234 - 5 + 6 - 7 + 8 - 9
(7 others)
Skip 1
228 = 0- 1 + 234 - 5 - 6 + 7 + 8 - 9
(5 others)
Skip 1
230 = 0- 1 + 234 - 5 - 6 + 7 - 8 + 9

 Posted by Charlie on 2003-05-22 06:52:24

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