Talk:Sum to 100: Difference between revisions
(→extra credit: N largest sums doesn't seem to much affect the run-time, at least in the case of Haskell) |
(→extra credit: added a comment about including an "extra credit" (optional) requirement.) |
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: Seems fine as an additional task – I've just added it for Haskell and it doesn't seem to noticeably increase the interpreter run-time. [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 00:29, 5 January 2017 (UTC) |
: Seems fine as an additional task – I've just added it for Haskell and it doesn't seem to noticeably increase the interpreter run-time. [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 00:29, 5 January 2017 (UTC) |
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:: For interpreted languages, it may be problematic. Even so, I added an "extra credit" (optional) requirement. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 00:44, 5 January 2017 (UTC) |
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==complete list of solutions for '''9'''== |
==complete list of solutions for '''9'''== |
Revision as of 00:45, 5 January 2017
A 'sum' that can be shown but not expressed ?
Not sure that I have understood your third request. Something that can be 'shown' but not 'expressed' ? Sounds appeallingly ineffable and mysterious, but perhaps not entirely clear ...
Judging by your undo of my first suggestion, I guess that you are not simply looking for the first or lowest-valued integer than can't be expressed as a sum constructed in this way, but then I don't actually have any idea of what you are asking for. Perhaps some kind of example or concretisation might clarify ? Hout (talk) 01:42, 1 January 2017 (UTC)
- See the REXX's output to help understand what is required. I have changed the word first to lowest which is much clearer to what was intended (I knew what I meant, but it was somewhat unclear in this context). (Note that negative sums/integers are possible, these sums are just negative "versions" of the positive sums, so the requirement was worded to avoid looking for negative results.) Since the sums are integers (as there is no way to get a non-integer sum from additions and/or subtractions of decimal digits or whole numbers). I used the word "expressed" as it isn't necessary to have the expression "shown". The word "shown" (to me) seems to indicate to display, not necessarily to express (in this case, mathematically). To answer your question, yes, it is possible. Showing something doesn't mean that it is being expressed (in the sense that it is being understood). I believe it boils down to word choices. I was trying for a concise wording of the requirement without being unnecessarily wordy (or obtuse). It's a fine art. -- Gerard Schildberger (talk) 02:04, 1 January 2017 (UTC)
- I've also added a trailing phrase to the 3rd requirement that (I think) fits in more to what you originally addressed. -- Gerard Schildberger (talk) 02:09, 1 January 2017 (UTC)
- Would it be consistent with your meaning to replace the word 'sum' with 'integer' ? Also if you are looking for the lowest integer that is inexpressible in these terms, perhaps it would be helpful to give an example of a higher integer of this kind, and demonstrate/explain its inexpressibility within this system ? Hout (talk) 02:16, 1 January 2017 (UTC)
- I used the word sum because it was already used in the task's preamble and the word was also defined (in context). Introducing another word (integer) would, I think, just belabor the effort to have another version of the sum word. The next number (after 211) that can't be expressed within the rules is 219. Another example of a sum that can't be expressed is 5791. I'm not sure how to demonstrate/explain its inexpressibility other than to show (display) all the possible mathematical expressions that don't (can't) express the 5791 sum. This would be somewhat of a strange proof (and voluminous), but not unheard of. -- Gerard Schildberger (talk) 02:29, 1 January 2017 (UTC)
- FWIW my experience as a reader is that using the word 'sum' at that point certainly proved confusing at first reading, and even now feels distractingly odd. 211 is certainly a number – a member of the set of integers – but the point you are making about it seems to be precisely that it is not a sum (the result of an addition) within this system. Hout (talk) 02:38, 1 January 2017 (UTC)
- I'm not saying that 211 isn't an integer or a number --- just that it (the sum of 211) can't be expressed mathematically in the context of the rules for this puzzle as stated in the task's preamble. 211 is a sum (in particular, the lowest sum) of the set of sums that can't be expressed within the rules. -- Gerard Schildberger (talk) 02:56, 1 January 2017 (UTC)
- PS on the issue of an example; an existence proof would be fine – you could just give an example of a number like 5791, say that it can't be expressed by a sum that is restricted to these permutations of digits and signs, and ask for code that finds the lowest positive integer that shares this property. Hout (talk) 02:46, 1 January 2017 (UTC)
- That seems overly wordy just to ask for the lowest positive sum that can't be expressed (within the rules). In particular, the requirement was expressly worded to find that sum. However, I will add an example (i.e.: such as 5074). -- Gerard Schildberger (talk) 02:56, 1 January 2017 (UTC)
extra credit
I had initially thought to add an extra credit solution for the largest sum (except for the obvious 123456789). I'm not sure it would be a worthwhile (optional) requirement, it could be pretty CPU intensive. -- Gerard Schildberger (talk) 04:21, 1 January 2017 (UTC)
- Seems fine as an additional task – I've just added it for Haskell and it doesn't seem to noticeably increase the interpreter run-time. Hout (talk) 00:29, 5 January 2017 (UTC)
- For interpreted languages, it may be problematic. Even so, I added an "extra credit" (optional) requirement. -- Gerard Schildberger (talk) 00:44, 5 January 2017 (UTC)
complete list of solutions for 9
For those that are interested (or need a sanity check), the 46 solutions (for the sum of 9) are:
solution: 9 ◄───► -1+2+3+4+5+6+7-8-9 solution: 9 ◄───► -1+2+3-4+5-6-7+8+9 solution: 9 ◄───► -1+2+3-4-5+6+7-8+9 solution: 9 ◄───► -1+2+3-45+67-8-9 solution: 9 ◄───► -1+2+34+56+7-89 solution: 9 ◄───► -1+2-3+4+5-6+7-8+9 solution: 9 ◄───► -1+2-3+4-5+6+7+8-9 solution: 9 ◄───► -1+23+4+5+67-89 solution: 9 ◄───► -1+23+4-5-6-7-8+9 solution: 9 ◄───► -1+23-4+5-6-7+8-9 solution: 9 ◄───► -1+23-4-5+6+7-8-9 solution: 9 ◄───► -1-2+3+4+5+6-7-8+9 solution: 9 ◄───► -1-2+3+4+5-6+7+8-9 solution: 9 ◄───► -1-2+3-4-5-6+7+8+9 solution: 9 ◄───► -1-2+3-4-56+78-9 solution: 9 ◄───► -1-2-3+4-5+6-7+8+9 solution: 9 ◄───► -1-2-3+45-6-7-8-9 solution: 9 ◄───► -1-2-3-4+5+6+7-8+9 solution: 9 ◄───► -1-2-34+56+7-8-9 solution: 9 ◄───► -1-23+45-6-7-8+9 solution: 9 ◄───► -12+3-45-6+78-9 solution: 9 ◄───► -12+34+5+6-7-8-9 solution: 9 ◄───► -12+34+56-78+9 solution: 9 ◄───► -12-34+5+67-8-9 solution: 9 ◄───► 1+2+3+4-5-6-7+8+9 solution: 9 ◄───► 1+2+3-4+5-6+7-8+9 solution: 9 ◄───► 1+2+3-4-5+6+7+8-9 solution: 9 ◄───► 1+2-3+4+5+6-7-8+9 solution: 9 ◄───► 1+2-3+4+5-6+7+8-9 solution: 9 ◄───► 1+2-3-4-5-6+7+8+9 solution: 9 ◄───► 1+2-3-4-56+78-9 solution: 9 ◄───► 1+2-34-56+7+89 solution: 9 ◄───► 1+23+4-5-6-7+8-9 solution: 9 ◄───► 1+23-4+5-6+7-8-9 solution: 9 ◄───► 1+23-45+6+7+8+9 solution: 9 ◄───► 1-2+3+4+5+6-7+8-9 solution: 9 ◄───► 1-2+3-4-5+6-7+8+9 solution: 9 ◄───► 1-2-3+4+5-6-7+8+9 solution: 9 ◄───► 1-2-3+4-5+6+7-8+9 solution: 9 ◄───► 1-2-3-4+5+6+7+8-9 solution: 9 ◄───► 1-2-3-4-5-67+89 solution: 9 ◄───► 1-23+4+5-67+89 solution: 9 ◄───► 1-23+45-6-7+8-9 solution: 9 ◄───► 1-23-4+5+6+7+8+9 solution: 9 ◄───► 1-23-45-6-7+89 solution: 9 ◄───► 12-34-56+78+9 46 solutions found for 9
complete list of the number of solutions for zero ──► 300
For those that are interested in the density of solutions:
22 solutions found for 0 43 solutions found for 1 18 solutions found for 2 41 solutions found for 3 18 solutions found for 4 40 solutions found for 5 24 solutions found for 6 39 solutions found for 7 18 solutions found for 8 46 solutions found for 9 17 solutions found for 10 38 solutions found for 11 27 solutions found for 12 38 solutions found for 13 24 solutions found for 14 43 solutions found for 15 18 solutions found for 16 39 solutions found for 17 23 solutions found for 18 37 solutions found for 19 23 solutions found for 20 43 solutions found for 21 25 solutions found for 22 36 solutions found for 23 32 solutions found for 24 36 solutions found for 25 25 solutions found for 26 44 solutions found for 27 25 solutions found for 28 35 solutions found for 29 34 solutions found for 30 31 solutions found for 31 26 solutions found for 32 37 solutions found for 33 24 solutions found for 34 35 solutions found for 35 32 solutions found for 36 32 solutions found for 37 27 solutions found for 38 37 solutions found for 39 31 solutions found for 40 26 solutions found for 41 34 solutions found for 42 34 solutions found for 43 29 solutions found for 44 42 solutions found for 45 27 solutions found for 46 27 solutions found for 47 35 solutions found for 48 26 solutions found for 49 28 solutions found for 50 35 solutions found for 51 29 solutions found for 52 33 solutions found for 53 30 solutions found for 54 26 solutions found for 55 23 solutions found for 56 29 solutions found for 57 32 solutions found for 58 25 solutions found for 59 33 solutions found for 60 30 solutions found for 61 24 solutions found for 62 34 solutions found for 63 22 solutions found for 64 26 solutions found for 65 32 solutions found for 66 30 solutions found for 67 25 solutions found for 68 29 solutions found for 69 22 solutions found for 70 25 solutions found for 71 26 solutions found for 72 24 solutions found for 73 22 solutions found for 74 26 solutions found for 75 25 solutions found for 76 22 solutions found for 77 24 solutions found for 78 25 solutions found for 79 19 solutions found for 80 31 solutions found for 81 20 solutions found for 82 23 solutions found for 83 25 solutions found for 84 21 solutions found for 85 18 solutions found for 86 23 solutions found for 87 17 solutions found for 88 24 solutions found for 89 21 solutions found for 90 22 solutions found for 91 21 solutions found for 92 23 solutions found for 93 17 solutions found for 94 17 solutions found for 95 19 solutions found for 96 21 solutions found for 97 15 solutions found for 98 25 solutions found for 99 12 solutions found for 100 18 solutions found for 101 19 solutions found for 102 14 solutions found for 103 14 solutions found for 104 18 solutions found for 105 18 solutions found for 106 17 solutions found for 107 19 solutions found for 108 12 solutions found for 109 14 solutions found for 110 19 solutions found for 111 13 solutions found for 112 12 solutions found for 113 17 solutions found for 114 15 solutions found for 115 14 solutions found for 116 20 solutions found for 117 13 solutions found for 118 11 solutions found for 119 18 solutions found for 120 10 solutions found for 121 9 solutions found for 122 13 solutions found for 123 12 solutions found for 124 12 solutions found for 125 19 solutions found for 126 8 solutions found for 127 12 solutions found for 128 12 solutions found for 129 13 solutions found for 130 7 solutions found for 131 15 solutions found for 132 14 solutions found for 133 8 solutions found for 134 16 solutions found for 135 10 solutions found for 136 5 solutions found for 137 15 solutions found for 138 7 solutions found for 139 10 solutions found for 140 10 solutions found for 141 10 solutions found for 142 9 solutions found for 143 14 solutions found for 144 8 solutions found for 145 8 solutions found for 146 11 solutions found for 147 9 solutions found for 148 6 solutions found for 149 10 solutions found for 150 9 solutions found for 151 6 solutions found for 152 13 solutions found for 153 9 solutions found for 154 6 solutions found for 155 10 solutions found for 156 8 solutions found for 157 4 solutions found for 158 8 solutions found for 159 5 solutions found for 160 4 solutions found for 161 11 solutions found for 162 5 solutions found for 163 6 solutions found for 164 7 solutions found for 165 4 solutions found for 166 5 solutions found for 167 3 solutions found for 168 8 solutions found for 169 4 solutions found for 170 10 solutions found for 171 6 solutions found for 172 4 solutions found for 173 5 solutions found for 174 3 solutions found for 175 1 solution found for 176 6 solutions found for 177 3 solutions found for 178 3 solutions found for 179 7 solutions found for 180 2 solutions found for 181 4 solutions found for 182 4 solutions found for 183 3 solutions found for 184 5 solutions found for 185 4 solutions found for 186 5 solutions found for 187 4 solutions found for 188 6 solutions found for 189 6 solutions found for 190 1 solution found for 191 4 solutions found for 192 2 solutions found for 193 1 solution found for 194 4 solutions found for 195 1 solution found for 196 3 solutions found for 197 7 solutions found for 198 3 solutions found for 199 3 solutions found for 200 4 solutions found for 201 2 solutions found for 202 3 solutions found for 203 2 solutions found for 204 2 solutions found for 205 2 solutions found for 206 6 solutions found for 207 4 solutions found for 208 1 solution found for 209 5 solutions found for 210 no solutions found for 211 4 solutions found for 212 1 solution found for 213 3 solutions found for 214 1 solution found for 215 6 solutions found for 216 1 solution found for 217 3 solutions found for 218 no solutions found for 219 3 solutions found for 220 no solutions found for 221 4 solutions found for 222 1 solution found for 223 4 solutions found for 224 2 solutions found for 225 5 solutions found for 226 no solutions found for 227 4 solutions found for 228 no solutions found for 229 3 solutions found for 230 2 solutions found for 231 2 solutions found for 232 no solutions found for 233 5 solutions found for 234 no solutions found for 235 3 solutions found for 236 1 solution found for 237 3 solutions found for 238 no solutions found for 239 6 solutions found for 240 no solutions found for 241 5 solutions found for 242 3 solutions found for 243 6 solutions found for 244 2 solutions found for 245 5 solutions found for 246 no solutions found for 247 2 solutions found for 248 3 solutions found for 249 2 solutions found for 250 2 solutions found for 251 7 solutions found for 252 1 solution found for 253 4 solutions found for 254 2 solutions found for 255 5 solutions found for 256 2 solutions found for 257 7 solutions found for 258 1 solution found for 259 4 solutions found for 260 3 solutions found for 261 3 solutions found for 262 1 solution found for 263 4 solutions found for 264 4 solutions found for 265 2 solutions found for 266 5 solutions found for 267 2 solutions found for 268 2 solutions found for 269 6 solutions found for 270 2 solutions found for 271 1 solution found for 272 3 solutions found for 273 1 solution found for 274 1 solution found for 275 3 solutions found for 276 no solutions found for 277 4 solutions found for 278 3 solutions found for 279 4 solutions found for 280 4 solutions found for 281 2 solutions found for 282 4 solutions found for 283 no solutions found for 284 2 solutions found for 285 no solutions found for 286 no solutions found for 287 2 solutions found for 288 1 solution found for 289 1 solution found for 290 2 solutions found for 291 1 solution found for 292 1 solution found for 293 3 solutions found for 294 1 solution found for 295 3 solutions found for 296 2 solutions found for 297 2 solutions found for 298 2 solutions found for 299 no solutions found for 300 sum of 9 has the maximum number of solutions: 46 sums of 211 219 221 227 229 233 235 239 241 247 277 284 286 287 300 have the minimum number of solutions: 0