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Challenges The holeyest base

Given a positive integer as input, indicate which base from 2 to 16 gives the most holes in the representation of the input in that base. The digits used are 0123456789ABCDEF. Note that these incl...

6 answers  ·  posted 2y ago by trichoplax‭  ·  last activity 2y ago by Razetime‭

Question code-golf base
#3: Post edited by user avatar trichoplax‭ · 2022-09-30T01:40:45Z (about 2 years ago)
Add note to multiple valid outputs test cases
  • Given a positive integer as input, indicate which base from 2 to 16 gives the most holes in the representation of the input in that base.
  • The digits used are 0123456789ABCDEF. Note that these include upper case letters (the number of holes would be different for lower case letters).
  • Different fonts have different numbers of holes per character, so the number of holes per digit is as follows for this challenge (in the format `digit : number of holes`):
  • ```text
  • 0 : 1
  • 1 : 0
  • 2 : 0
  • 3 : 0
  • 4 : 1
  • 5 : 0
  • 6 : 1
  • 7 : 0
  • 8 : 2
  • 9 : 1
  • A : 1
  • B : 2
  • C : 0
  • D : 1
  • E : 0
  • F : 0
  • ```
  • ## Input
  • - A positive integer
  • ## Output
  • - A single integer from 2 to 16
  • - The output indicates which base gives the representation with the most holes (being the sum of the number of holes in each digit when represented in that base)
  • - For the purposes of counting holes:
  • - Each representation will have no leading zeroes
  • - The base indicator characters used by some languages, such as a leading `0b` or `0x` are not included in the counting
  • - If more than one base has the highest number of holes, any such base is a valid output, but you must only output one of them
  • ## Example
  • For input `123` the representation in each of the bases from 2 to 16, and the associated number of holes, is as follows (in the format `base : representation : holes`):
  • ```text
  • 2 : 1111011 : 0 + 0 + 0 + 0 + 1 + 0 + 0 = 1
  • 3 : 11120 : 0 + 0 + 0 + 0 + 1 = 1
  • 4 : 1323 : 0 + 0 + 0 + 0 = 0
  • 5 : 443 : 1 + 1 + 0 = 2
  • 6 : 323 : 0 + 0 + 0 = 0
  • 7 : 234 : 0 + 0 + 1 = 1
  • 8 : 173 : 0 + 0 + 0 = 0
  • 9 : 146 : 0 + 1 + 1 = 2
  • 10 : 123 : 0 + 0 + 0 = 0
  • 11 : 102 : 0 + 1 + 0 = 1
  • 12 : A3 : 1 + 0 = 1
  • 13 : 96 : 1 + 1 = 2
  • 14 : 8B : 2 + 2 = 4
  • 15 : 83 : 2 + 0 = 2
  • 16 : 7B : 0 + 2 = 2
  • ```
  • The highest number of holes is 4, and this only occurs when the base is 14. So the only valid output is 14.
  • ## Test cases
  • ### Test cases with only 1 valid output
  • These test cases are in the format `input : output`.
  • ```text
  • 2 : 2
  • 3 : 3
  • 4 : 2
  • 7 : 7
  • 8 : 2
  • 10 : 2
  • 12 : 2
  • 16 : 2
  • 17 : 2
  • 18 : 2
  • 20 : 2
  • 24 : 2
  • 27 : 3
  • 32 : 2
  • 33 : 2
  • 34 : 2
  • 35 : 2
  • 36 : 2
  • 37 : 2
  • 38 : 2
  • 40 : 2
  • 41 : 2
  • 42 : 2
  • 48 : 2
  • 49 : 2
  • 50 : 2
  • 51 : 2
  • 54 : 3
  • 59 : 12
  • 60 : 13
  • 61 : 13
  • 62 : 9
  • 63 : 13
  • 64 : 2
  • 65 : 2
  • 66 : 2
  • 67 : 2
  • 68 : 2
  • 69 : 2
  • 70 : 2
  • 72 : 2
  • 73 : 2
  • 74 : 2
  • 76 : 2
  • 77 : 2
  • 80 : 2
  • 82 : 2
  • 84 : 2
  • 85 : 2
  • 87 : 3
  • 94 : 11
  • 95 : 14
  • 96 : 2
  • 97 : 2
  • 98 : 2
  • 123 : 14
  • ```
  • ### Test cases including some with multiple valid outputs
  • These test cases are in the format `input : [comma separated outputs]` where any of the listed outputs would be valid. These also include all of the single valid output test cases listed above.
  • ```text
  • 0 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 1 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 2 : [2]
  • 3 : [3]
  • 4 : [2]
  • 5 : [2, 5]
  • 6 : [2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 7 : [7]
  • 8 : [2]
  • 9 : [2, 3]
  • 10 : [2]
  • 11 : [12, 13, 14, 15, 16]
  • 12 : [2]
  • 13 : [2, 7, 9, 13, 14, 15, 16]
  • 14 : [2, 5, 7, 8, 10, 14]
  • 15 : [3, 5, 9, 11, 15]
  • 16 : [2]
  • 17 : [2]
  • 18 : [2]
  • 19 : [2, 11]
  • 20 : [2]
  • 21 : [2, 13]
  • 22 : [2, 14]
  • 23 : [12, 15]
  • 24 : [2]
  • 25 : [2, 5, 14]
  • 26 : [2, 9, 15]
  • 27 : [3]
  • 28 : [2, 3, 6, 7, 10]
  • 29 : [3, 5]
  • 30 : [3, 11]
  • 31 : [3, 7, 9, 11]
  • 32 : [2]
  • 33 : [2]
  • 34 : [2]
  • 35 : [2]
  • 36 : [2]
  • 37 : [2]
  • 38 : [2]
  • 39 : [2, 14]
  • 40 : [2]
  • 41 : [2]
  • 42 : [2]
  • 43 : [2, 16]
  • 44 : [2, 9]
  • 45 : [2, 3, 5]
  • 46 : [2, 7, 10]
  • 47 : [12, 13]
  • 48 : [2]
  • 49 : [2]
  • 50 : [2]
  • 51 : [2]
  • 52 : [2, 11]
  • 53 : [2, 7, 9, 11, 14, 15]
  • 54 : [3]
  • 55 : [3, 7]
  • 56 : [2, 12]
  • 57 : [2, 3, 12]
  • 58 : [2, 9, 10, 12, 13]
  • 59 : [12]
  • 60 : [13]
  • 61 : [13]
  • 62 : [9]
  • 63 : [13]
  • 64 : [2]
  • 65 : [2]
  • 66 : [2]
  • 67 : [2]
  • 68 : [2]
  • 69 : [2]
  • 70 : [2]
  • 71 : [2, 15]
  • 72 : [2]
  • 73 : [2]
  • 74 : [2]
  • 75 : [2, 16]
  • 76 : [2]
  • 77 : [2]
  • 78 : [2, 9]
  • 79 : [2, 5, 9]
  • 80 : [2]
  • 81 : [2, 3]
  • 82 : [2]
  • 83 : [2, 3, 12]
  • 84 : [2]
  • 85 : [2]
  • 86 : [2, 10, 13]
  • 87 : [3]
  • 88 : [2, 10]
  • 89 : [2, 9, 10, 13]
  • 90 : [2, 3]
  • 91 : [2, 3, 7, 11, 16]
  • 92 : [2, 11, 14]
  • 93 : [2, 3, 11, 14]
  • 94 : [11]
  • 95 : [14]
  • 96 : [2]
  • 97 : [2]
  • 98 : [2]
  • 99 : [2, 3]
  • 123 : [14]
  • 1200 : [2]
  • 1201 : [2]
  • 1202 : [2]
  • 1203 : [2]
  • 1204 : [2]
  • 1205 : [2]
  • 1206 : [2]
  • 1207 : [2, 11]
  • 1208 : [2]
  • 1209 : [2]
  • 1210 : [2]
  • 1211 : [12, 16]
  • 1212 : [2]
  • 1213 : [2, 16]
  • 1214 : [2, 9]
  • 1215 : [3]
  • 1216 : [2]
  • 1217 : [2]
  • 1218 : [2]
  • 1219 : [2]
  • 1220 : [2]
  • 1221 : [2]
  • 1222 : [2]
  • 1223 : [2]
  • 1224 : [2]
  • 1225 : [2]
  • 1226 : [2]
  • 1227 : [2]
  • 1228 : [2]
  • 1229 : [2]
  • 1230 : [2]
  • 1231 : [2]
  • 1232 : [2]
  • 1233 : [2]
  • 1234 : [2]
  • 1235 : [2, 12]
  • 1236 : [2]
  • 1237 : [2]
  • 1238 : [2]
  • 1239 : [2]
  • 1240 : [2]
  • 1241 : [2]
  • 1242 : [2]
  • 1243 : [2, 14, 16]
  • 1244 : [2]
  • 1245 : [2, 5]
  • 1246 : [2]
  • 1247 : [12]
  • 1248 : [2]
  • 1249 : [2]
  • 1250 : [2]
  • 1251 : [2]
  • 1252 : [2]
  • 1253 : [2]
  • 1254 : [2, 12]
  • 1255 : [2, 12]
  • 1256 : [2, 12]
  • 1257 : [2, 12]
  • 1258 : [2, 12]
  • 1259 : [12]
  • 1260 : [2]
  • 1261 : [2]
  • 1262 : [2, 11]
  • 1263 : [2, 11, 12]
  • 1264 : [2]
  • 1265 : [2]
  • 1266 : [2]
  • 1267 : [2]
  • 1268 : [2, 12]
  • 1269 : [2, 3, 12]
  • 1270 : [2, 5, 12]
  • 1271 : [12]
  • 1272 : [2]
  • 1273 : [2]
  • 1274 : [2, 5]
  • 1275 : [2, 3, 5, 9, 12, 16]
  • 1276 : [2, 12]
  • 1277 : [9]
  • 1278 : [12]
  • 1279 : [5, 12]
  • 1280 : [2]
  • 1281 : [2]
  • 1282 : [2]
  • 1283 : [2]
  • 1284 : [2]
  • 1285 : [2]
  • 1286 : [2]
  • 1287 : [2]
  • 1288 : [2]
  • 1289 : [2]
  • 1290 : [2]
  • 1291 : [2]
  • 1292 : [2]
  • 1293 : [2]
  • 1294 : [2]
  • 1295 : [12]
  • 1296 : [2]
  • 1297 : [2]
  • 1298 : [2]
  • 1299 : [2]
  • ```
  • > Explanations in answers are optional, but I'm more likely to upvote answers that have one.
  • Given a positive integer as input, indicate which base from 2 to 16 gives the most holes in the representation of the input in that base.
  • The digits used are 0123456789ABCDEF. Note that these include upper case letters (the number of holes would be different for lower case letters).
  • Different fonts have different numbers of holes per character, so the number of holes per digit is as follows for this challenge (in the format `digit : number of holes`):
  • ```text
  • 0 : 1
  • 1 : 0
  • 2 : 0
  • 3 : 0
  • 4 : 1
  • 5 : 0
  • 6 : 1
  • 7 : 0
  • 8 : 2
  • 9 : 1
  • A : 1
  • B : 2
  • C : 0
  • D : 1
  • E : 0
  • F : 0
  • ```
  • ## Input
  • - A positive integer
  • ## Output
  • - A single integer from 2 to 16
  • - The output indicates which base gives the representation with the most holes (being the sum of the number of holes in each digit when represented in that base)
  • - For the purposes of counting holes:
  • - Each representation will have no leading zeroes
  • - The base indicator characters used by some languages, such as a leading `0b` or `0x` are not included in the counting
  • - If more than one base has the highest number of holes, any such base is a valid output, but you must only output one of them
  • ## Example
  • For input `123` the representation in each of the bases from 2 to 16, and the associated number of holes, is as follows (in the format `base : representation : holes`):
  • ```text
  • 2 : 1111011 : 0 + 0 + 0 + 0 + 1 + 0 + 0 = 1
  • 3 : 11120 : 0 + 0 + 0 + 0 + 1 = 1
  • 4 : 1323 : 0 + 0 + 0 + 0 = 0
  • 5 : 443 : 1 + 1 + 0 = 2
  • 6 : 323 : 0 + 0 + 0 = 0
  • 7 : 234 : 0 + 0 + 1 = 1
  • 8 : 173 : 0 + 0 + 0 = 0
  • 9 : 146 : 0 + 1 + 1 = 2
  • 10 : 123 : 0 + 0 + 0 = 0
  • 11 : 102 : 0 + 1 + 0 = 1
  • 12 : A3 : 1 + 0 = 1
  • 13 : 96 : 1 + 1 = 2
  • 14 : 8B : 2 + 2 = 4
  • 15 : 83 : 2 + 0 = 2
  • 16 : 7B : 0 + 2 = 2
  • ```
  • The highest number of holes is 4, and this only occurs when the base is 14. So the only valid output is 14.
  • ## Test cases
  • ### Test cases with only 1 valid output
  • These test cases are in the format `input : output`.
  • ```text
  • 2 : 2
  • 3 : 3
  • 4 : 2
  • 7 : 7
  • 8 : 2
  • 10 : 2
  • 12 : 2
  • 16 : 2
  • 17 : 2
  • 18 : 2
  • 20 : 2
  • 24 : 2
  • 27 : 3
  • 32 : 2
  • 33 : 2
  • 34 : 2
  • 35 : 2
  • 36 : 2
  • 37 : 2
  • 38 : 2
  • 40 : 2
  • 41 : 2
  • 42 : 2
  • 48 : 2
  • 49 : 2
  • 50 : 2
  • 51 : 2
  • 54 : 3
  • 59 : 12
  • 60 : 13
  • 61 : 13
  • 62 : 9
  • 63 : 13
  • 64 : 2
  • 65 : 2
  • 66 : 2
  • 67 : 2
  • 68 : 2
  • 69 : 2
  • 70 : 2
  • 72 : 2
  • 73 : 2
  • 74 : 2
  • 76 : 2
  • 77 : 2
  • 80 : 2
  • 82 : 2
  • 84 : 2
  • 85 : 2
  • 87 : 3
  • 94 : 11
  • 95 : 14
  • 96 : 2
  • 97 : 2
  • 98 : 2
  • 123 : 14
  • ```
  • ### Test cases including some with multiple valid outputs
  • These test cases are in the format `input : [comma separated potential outputs]` where any one of the listed outputs would be valid. These also include all of the single valid output test cases listed above.
  • *Note that the output can be any one, but must be only one, of the potential outputs listed.*
  • ```text
  • 0 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 1 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 2 : [2]
  • 3 : [3]
  • 4 : [2]
  • 5 : [2, 5]
  • 6 : [2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 7 : [7]
  • 8 : [2]
  • 9 : [2, 3]
  • 10 : [2]
  • 11 : [12, 13, 14, 15, 16]
  • 12 : [2]
  • 13 : [2, 7, 9, 13, 14, 15, 16]
  • 14 : [2, 5, 7, 8, 10, 14]
  • 15 : [3, 5, 9, 11, 15]
  • 16 : [2]
  • 17 : [2]
  • 18 : [2]
  • 19 : [2, 11]
  • 20 : [2]
  • 21 : [2, 13]
  • 22 : [2, 14]
  • 23 : [12, 15]
  • 24 : [2]
  • 25 : [2, 5, 14]
  • 26 : [2, 9, 15]
  • 27 : [3]
  • 28 : [2, 3, 6, 7, 10]
  • 29 : [3, 5]
  • 30 : [3, 11]
  • 31 : [3, 7, 9, 11]
  • 32 : [2]
  • 33 : [2]
  • 34 : [2]
  • 35 : [2]
  • 36 : [2]
  • 37 : [2]
  • 38 : [2]
  • 39 : [2, 14]
  • 40 : [2]
  • 41 : [2]
  • 42 : [2]
  • 43 : [2, 16]
  • 44 : [2, 9]
  • 45 : [2, 3, 5]
  • 46 : [2, 7, 10]
  • 47 : [12, 13]
  • 48 : [2]
  • 49 : [2]
  • 50 : [2]
  • 51 : [2]
  • 52 : [2, 11]
  • 53 : [2, 7, 9, 11, 14, 15]
  • 54 : [3]
  • 55 : [3, 7]
  • 56 : [2, 12]
  • 57 : [2, 3, 12]
  • 58 : [2, 9, 10, 12, 13]
  • 59 : [12]
  • 60 : [13]
  • 61 : [13]
  • 62 : [9]
  • 63 : [13]
  • 64 : [2]
  • 65 : [2]
  • 66 : [2]
  • 67 : [2]
  • 68 : [2]
  • 69 : [2]
  • 70 : [2]
  • 71 : [2, 15]
  • 72 : [2]
  • 73 : [2]
  • 74 : [2]
  • 75 : [2, 16]
  • 76 : [2]
  • 77 : [2]
  • 78 : [2, 9]
  • 79 : [2, 5, 9]
  • 80 : [2]
  • 81 : [2, 3]
  • 82 : [2]
  • 83 : [2, 3, 12]
  • 84 : [2]
  • 85 : [2]
  • 86 : [2, 10, 13]
  • 87 : [3]
  • 88 : [2, 10]
  • 89 : [2, 9, 10, 13]
  • 90 : [2, 3]
  • 91 : [2, 3, 7, 11, 16]
  • 92 : [2, 11, 14]
  • 93 : [2, 3, 11, 14]
  • 94 : [11]
  • 95 : [14]
  • 96 : [2]
  • 97 : [2]
  • 98 : [2]
  • 99 : [2, 3]
  • 123 : [14]
  • 1200 : [2]
  • 1201 : [2]
  • 1202 : [2]
  • 1203 : [2]
  • 1204 : [2]
  • 1205 : [2]
  • 1206 : [2]
  • 1207 : [2, 11]
  • 1208 : [2]
  • 1209 : [2]
  • 1210 : [2]
  • 1211 : [12, 16]
  • 1212 : [2]
  • 1213 : [2, 16]
  • 1214 : [2, 9]
  • 1215 : [3]
  • 1216 : [2]
  • 1217 : [2]
  • 1218 : [2]
  • 1219 : [2]
  • 1220 : [2]
  • 1221 : [2]
  • 1222 : [2]
  • 1223 : [2]
  • 1224 : [2]
  • 1225 : [2]
  • 1226 : [2]
  • 1227 : [2]
  • 1228 : [2]
  • 1229 : [2]
  • 1230 : [2]
  • 1231 : [2]
  • 1232 : [2]
  • 1233 : [2]
  • 1234 : [2]
  • 1235 : [2, 12]
  • 1236 : [2]
  • 1237 : [2]
  • 1238 : [2]
  • 1239 : [2]
  • 1240 : [2]
  • 1241 : [2]
  • 1242 : [2]
  • 1243 : [2, 14, 16]
  • 1244 : [2]
  • 1245 : [2, 5]
  • 1246 : [2]
  • 1247 : [12]
  • 1248 : [2]
  • 1249 : [2]
  • 1250 : [2]
  • 1251 : [2]
  • 1252 : [2]
  • 1253 : [2]
  • 1254 : [2, 12]
  • 1255 : [2, 12]
  • 1256 : [2, 12]
  • 1257 : [2, 12]
  • 1258 : [2, 12]
  • 1259 : [12]
  • 1260 : [2]
  • 1261 : [2]
  • 1262 : [2, 11]
  • 1263 : [2, 11, 12]
  • 1264 : [2]
  • 1265 : [2]
  • 1266 : [2]
  • 1267 : [2]
  • 1268 : [2, 12]
  • 1269 : [2, 3, 12]
  • 1270 : [2, 5, 12]
  • 1271 : [12]
  • 1272 : [2]
  • 1273 : [2]
  • 1274 : [2, 5]
  • 1275 : [2, 3, 5, 9, 12, 16]
  • 1276 : [2, 12]
  • 1277 : [9]
  • 1278 : [12]
  • 1279 : [5, 12]
  • 1280 : [2]
  • 1281 : [2]
  • 1282 : [2]
  • 1283 : [2]
  • 1284 : [2]
  • 1285 : [2]
  • 1286 : [2]
  • 1287 : [2]
  • 1288 : [2]
  • 1289 : [2]
  • 1290 : [2]
  • 1291 : [2]
  • 1292 : [2]
  • 1293 : [2]
  • 1294 : [2]
  • 1295 : [12]
  • 1296 : [2]
  • 1297 : [2]
  • 1298 : [2]
  • 1299 : [2]
  • ```
  • > Explanations in answers are optional, but I'm more likely to upvote answers that have one.
#2: Post edited by user avatar trichoplax‭ · 2022-09-30T01:34:22Z (about 2 years ago)
Change requirement for a single integer from implicit to explicit
  • Given a positive integer as input, indicate which base from 2 to 16 gives the most holes in the representation of the input in that base.
  • The digits used are 0123456789ABCDEF. Note that these include upper case letters (the number of holes would be different for lower case letters).
  • Different fonts have different numbers of holes per character, so the number of holes per digit is as follows for this challenge (in the format `digit : number of holes`):
  • ```text
  • 0 : 1
  • 1 : 0
  • 2 : 0
  • 3 : 0
  • 4 : 1
  • 5 : 0
  • 6 : 1
  • 7 : 0
  • 8 : 2
  • 9 : 1
  • A : 1
  • B : 2
  • C : 0
  • D : 1
  • E : 0
  • F : 0
  • ```
  • ## Input
  • - A positive integer
  • ## Output
  • - An integer from 2 to 16
  • - The output indicates which base gives the representation with the most holes (being the sum of the number of holes in each digit when represented in that base)
  • - For the purposes of counting holes:
  • - Each representation will have no leading zeroes
  • - The base indicator characters used by some languages, such as a leading `0b` or `0x` are not included in the counting
  • - If more than one base has the highest number of holes, any such base is a valid output
  • ## Example
  • For input `123` the representation in each of the bases from 2 to 16, and the associated number of holes, is as follows (in the format `base : representation : holes`):
  • ```text
  • 2 : 1111011 : 0 + 0 + 0 + 0 + 1 + 0 + 0 = 1
  • 3 : 11120 : 0 + 0 + 0 + 0 + 1 = 1
  • 4 : 1323 : 0 + 0 + 0 + 0 = 0
  • 5 : 443 : 1 + 1 + 0 = 2
  • 6 : 323 : 0 + 0 + 0 = 0
  • 7 : 234 : 0 + 0 + 1 = 1
  • 8 : 173 : 0 + 0 + 0 = 0
  • 9 : 146 : 0 + 1 + 1 = 2
  • 10 : 123 : 0 + 0 + 0 = 0
  • 11 : 102 : 0 + 1 + 0 = 1
  • 12 : A3 : 1 + 0 = 1
  • 13 : 96 : 1 + 1 = 2
  • 14 : 8B : 2 + 2 = 4
  • 15 : 83 : 2 + 0 = 2
  • 16 : 7B : 0 + 2 = 2
  • ```
  • The highest number of holes is 4, and this only occurs when the base is 14. So the only valid output is 14.
  • ## Test cases
  • ### Test cases with only 1 valid output
  • These test cases are in the format `input : output`.
  • ```text
  • 2 : 2
  • 3 : 3
  • 4 : 2
  • 7 : 7
  • 8 : 2
  • 10 : 2
  • 12 : 2
  • 16 : 2
  • 17 : 2
  • 18 : 2
  • 20 : 2
  • 24 : 2
  • 27 : 3
  • 32 : 2
  • 33 : 2
  • 34 : 2
  • 35 : 2
  • 36 : 2
  • 37 : 2
  • 38 : 2
  • 40 : 2
  • 41 : 2
  • 42 : 2
  • 48 : 2
  • 49 : 2
  • 50 : 2
  • 51 : 2
  • 54 : 3
  • 59 : 12
  • 60 : 13
  • 61 : 13
  • 62 : 9
  • 63 : 13
  • 64 : 2
  • 65 : 2
  • 66 : 2
  • 67 : 2
  • 68 : 2
  • 69 : 2
  • 70 : 2
  • 72 : 2
  • 73 : 2
  • 74 : 2
  • 76 : 2
  • 77 : 2
  • 80 : 2
  • 82 : 2
  • 84 : 2
  • 85 : 2
  • 87 : 3
  • 94 : 11
  • 95 : 14
  • 96 : 2
  • 97 : 2
  • 98 : 2
  • 123 : 14
  • ```
  • ### Test cases including some with multiple valid outputs
  • These test cases are in the format `input : [comma separated outputs]` where any of the listed outputs would be valid. These also include all of the single valid output test cases listed above.
  • ```text
  • 0 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 1 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 2 : [2]
  • 3 : [3]
  • 4 : [2]
  • 5 : [2, 5]
  • 6 : [2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 7 : [7]
  • 8 : [2]
  • 9 : [2, 3]
  • 10 : [2]
  • 11 : [12, 13, 14, 15, 16]
  • 12 : [2]
  • 13 : [2, 7, 9, 13, 14, 15, 16]
  • 14 : [2, 5, 7, 8, 10, 14]
  • 15 : [3, 5, 9, 11, 15]
  • 16 : [2]
  • 17 : [2]
  • 18 : [2]
  • 19 : [2, 11]
  • 20 : [2]
  • 21 : [2, 13]
  • 22 : [2, 14]
  • 23 : [12, 15]
  • 24 : [2]
  • 25 : [2, 5, 14]
  • 26 : [2, 9, 15]
  • 27 : [3]
  • 28 : [2, 3, 6, 7, 10]
  • 29 : [3, 5]
  • 30 : [3, 11]
  • 31 : [3, 7, 9, 11]
  • 32 : [2]
  • 33 : [2]
  • 34 : [2]
  • 35 : [2]
  • 36 : [2]
  • 37 : [2]
  • 38 : [2]
  • 39 : [2, 14]
  • 40 : [2]
  • 41 : [2]
  • 42 : [2]
  • 43 : [2, 16]
  • 44 : [2, 9]
  • 45 : [2, 3, 5]
  • 46 : [2, 7, 10]
  • 47 : [12, 13]
  • 48 : [2]
  • 49 : [2]
  • 50 : [2]
  • 51 : [2]
  • 52 : [2, 11]
  • 53 : [2, 7, 9, 11, 14, 15]
  • 54 : [3]
  • 55 : [3, 7]
  • 56 : [2, 12]
  • 57 : [2, 3, 12]
  • 58 : [2, 9, 10, 12, 13]
  • 59 : [12]
  • 60 : [13]
  • 61 : [13]
  • 62 : [9]
  • 63 : [13]
  • 64 : [2]
  • 65 : [2]
  • 66 : [2]
  • 67 : [2]
  • 68 : [2]
  • 69 : [2]
  • 70 : [2]
  • 71 : [2, 15]
  • 72 : [2]
  • 73 : [2]
  • 74 : [2]
  • 75 : [2, 16]
  • 76 : [2]
  • 77 : [2]
  • 78 : [2, 9]
  • 79 : [2, 5, 9]
  • 80 : [2]
  • 81 : [2, 3]
  • 82 : [2]
  • 83 : [2, 3, 12]
  • 84 : [2]
  • 85 : [2]
  • 86 : [2, 10, 13]
  • 87 : [3]
  • 88 : [2, 10]
  • 89 : [2, 9, 10, 13]
  • 90 : [2, 3]
  • 91 : [2, 3, 7, 11, 16]
  • 92 : [2, 11, 14]
  • 93 : [2, 3, 11, 14]
  • 94 : [11]
  • 95 : [14]
  • 96 : [2]
  • 97 : [2]
  • 98 : [2]
  • 99 : [2, 3]
  • 123 : [14]
  • 1200 : [2]
  • 1201 : [2]
  • 1202 : [2]
  • 1203 : [2]
  • 1204 : [2]
  • 1205 : [2]
  • 1206 : [2]
  • 1207 : [2, 11]
  • 1208 : [2]
  • 1209 : [2]
  • 1210 : [2]
  • 1211 : [12, 16]
  • 1212 : [2]
  • 1213 : [2, 16]
  • 1214 : [2, 9]
  • 1215 : [3]
  • 1216 : [2]
  • 1217 : [2]
  • 1218 : [2]
  • 1219 : [2]
  • 1220 : [2]
  • 1221 : [2]
  • 1222 : [2]
  • 1223 : [2]
  • 1224 : [2]
  • 1225 : [2]
  • 1226 : [2]
  • 1227 : [2]
  • 1228 : [2]
  • 1229 : [2]
  • 1230 : [2]
  • 1231 : [2]
  • 1232 : [2]
  • 1233 : [2]
  • 1234 : [2]
  • 1235 : [2, 12]
  • 1236 : [2]
  • 1237 : [2]
  • 1238 : [2]
  • 1239 : [2]
  • 1240 : [2]
  • 1241 : [2]
  • 1242 : [2]
  • 1243 : [2, 14, 16]
  • 1244 : [2]
  • 1245 : [2, 5]
  • 1246 : [2]
  • 1247 : [12]
  • 1248 : [2]
  • 1249 : [2]
  • 1250 : [2]
  • 1251 : [2]
  • 1252 : [2]
  • 1253 : [2]
  • 1254 : [2, 12]
  • 1255 : [2, 12]
  • 1256 : [2, 12]
  • 1257 : [2, 12]
  • 1258 : [2, 12]
  • 1259 : [12]
  • 1260 : [2]
  • 1261 : [2]
  • 1262 : [2, 11]
  • 1263 : [2, 11, 12]
  • 1264 : [2]
  • 1265 : [2]
  • 1266 : [2]
  • 1267 : [2]
  • 1268 : [2, 12]
  • 1269 : [2, 3, 12]
  • 1270 : [2, 5, 12]
  • 1271 : [12]
  • 1272 : [2]
  • 1273 : [2]
  • 1274 : [2, 5]
  • 1275 : [2, 3, 5, 9, 12, 16]
  • 1276 : [2, 12]
  • 1277 : [9]
  • 1278 : [12]
  • 1279 : [5, 12]
  • 1280 : [2]
  • 1281 : [2]
  • 1282 : [2]
  • 1283 : [2]
  • 1284 : [2]
  • 1285 : [2]
  • 1286 : [2]
  • 1287 : [2]
  • 1288 : [2]
  • 1289 : [2]
  • 1290 : [2]
  • 1291 : [2]
  • 1292 : [2]
  • 1293 : [2]
  • 1294 : [2]
  • 1295 : [12]
  • 1296 : [2]
  • 1297 : [2]
  • 1298 : [2]
  • 1299 : [2]
  • ```
  • > Explanations in answers are optional, but I'm more likely to upvote answers that have one.
  • Given a positive integer as input, indicate which base from 2 to 16 gives the most holes in the representation of the input in that base.
  • The digits used are 0123456789ABCDEF. Note that these include upper case letters (the number of holes would be different for lower case letters).
  • Different fonts have different numbers of holes per character, so the number of holes per digit is as follows for this challenge (in the format `digit : number of holes`):
  • ```text
  • 0 : 1
  • 1 : 0
  • 2 : 0
  • 3 : 0
  • 4 : 1
  • 5 : 0
  • 6 : 1
  • 7 : 0
  • 8 : 2
  • 9 : 1
  • A : 1
  • B : 2
  • C : 0
  • D : 1
  • E : 0
  • F : 0
  • ```
  • ## Input
  • - A positive integer
  • ## Output
  • - A single integer from 2 to 16
  • - The output indicates which base gives the representation with the most holes (being the sum of the number of holes in each digit when represented in that base)
  • - For the purposes of counting holes:
  • - Each representation will have no leading zeroes
  • - The base indicator characters used by some languages, such as a leading `0b` or `0x` are not included in the counting
  • - If more than one base has the highest number of holes, any such base is a valid output, but you must only output one of them
  • ## Example
  • For input `123` the representation in each of the bases from 2 to 16, and the associated number of holes, is as follows (in the format `base : representation : holes`):
  • ```text
  • 2 : 1111011 : 0 + 0 + 0 + 0 + 1 + 0 + 0 = 1
  • 3 : 11120 : 0 + 0 + 0 + 0 + 1 = 1
  • 4 : 1323 : 0 + 0 + 0 + 0 = 0
  • 5 : 443 : 1 + 1 + 0 = 2
  • 6 : 323 : 0 + 0 + 0 = 0
  • 7 : 234 : 0 + 0 + 1 = 1
  • 8 : 173 : 0 + 0 + 0 = 0
  • 9 : 146 : 0 + 1 + 1 = 2
  • 10 : 123 : 0 + 0 + 0 = 0
  • 11 : 102 : 0 + 1 + 0 = 1
  • 12 : A3 : 1 + 0 = 1
  • 13 : 96 : 1 + 1 = 2
  • 14 : 8B : 2 + 2 = 4
  • 15 : 83 : 2 + 0 = 2
  • 16 : 7B : 0 + 2 = 2
  • ```
  • The highest number of holes is 4, and this only occurs when the base is 14. So the only valid output is 14.
  • ## Test cases
  • ### Test cases with only 1 valid output
  • These test cases are in the format `input : output`.
  • ```text
  • 2 : 2
  • 3 : 3
  • 4 : 2
  • 7 : 7
  • 8 : 2
  • 10 : 2
  • 12 : 2
  • 16 : 2
  • 17 : 2
  • 18 : 2
  • 20 : 2
  • 24 : 2
  • 27 : 3
  • 32 : 2
  • 33 : 2
  • 34 : 2
  • 35 : 2
  • 36 : 2
  • 37 : 2
  • 38 : 2
  • 40 : 2
  • 41 : 2
  • 42 : 2
  • 48 : 2
  • 49 : 2
  • 50 : 2
  • 51 : 2
  • 54 : 3
  • 59 : 12
  • 60 : 13
  • 61 : 13
  • 62 : 9
  • 63 : 13
  • 64 : 2
  • 65 : 2
  • 66 : 2
  • 67 : 2
  • 68 : 2
  • 69 : 2
  • 70 : 2
  • 72 : 2
  • 73 : 2
  • 74 : 2
  • 76 : 2
  • 77 : 2
  • 80 : 2
  • 82 : 2
  • 84 : 2
  • 85 : 2
  • 87 : 3
  • 94 : 11
  • 95 : 14
  • 96 : 2
  • 97 : 2
  • 98 : 2
  • 123 : 14
  • ```
  • ### Test cases including some with multiple valid outputs
  • These test cases are in the format `input : [comma separated outputs]` where any of the listed outputs would be valid. These also include all of the single valid output test cases listed above.
  • ```text
  • 0 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 1 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 2 : [2]
  • 3 : [3]
  • 4 : [2]
  • 5 : [2, 5]
  • 6 : [2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
  • 7 : [7]
  • 8 : [2]
  • 9 : [2, 3]
  • 10 : [2]
  • 11 : [12, 13, 14, 15, 16]
  • 12 : [2]
  • 13 : [2, 7, 9, 13, 14, 15, 16]
  • 14 : [2, 5, 7, 8, 10, 14]
  • 15 : [3, 5, 9, 11, 15]
  • 16 : [2]
  • 17 : [2]
  • 18 : [2]
  • 19 : [2, 11]
  • 20 : [2]
  • 21 : [2, 13]
  • 22 : [2, 14]
  • 23 : [12, 15]
  • 24 : [2]
  • 25 : [2, 5, 14]
  • 26 : [2, 9, 15]
  • 27 : [3]
  • 28 : [2, 3, 6, 7, 10]
  • 29 : [3, 5]
  • 30 : [3, 11]
  • 31 : [3, 7, 9, 11]
  • 32 : [2]
  • 33 : [2]
  • 34 : [2]
  • 35 : [2]
  • 36 : [2]
  • 37 : [2]
  • 38 : [2]
  • 39 : [2, 14]
  • 40 : [2]
  • 41 : [2]
  • 42 : [2]
  • 43 : [2, 16]
  • 44 : [2, 9]
  • 45 : [2, 3, 5]
  • 46 : [2, 7, 10]
  • 47 : [12, 13]
  • 48 : [2]
  • 49 : [2]
  • 50 : [2]
  • 51 : [2]
  • 52 : [2, 11]
  • 53 : [2, 7, 9, 11, 14, 15]
  • 54 : [3]
  • 55 : [3, 7]
  • 56 : [2, 12]
  • 57 : [2, 3, 12]
  • 58 : [2, 9, 10, 12, 13]
  • 59 : [12]
  • 60 : [13]
  • 61 : [13]
  • 62 : [9]
  • 63 : [13]
  • 64 : [2]
  • 65 : [2]
  • 66 : [2]
  • 67 : [2]
  • 68 : [2]
  • 69 : [2]
  • 70 : [2]
  • 71 : [2, 15]
  • 72 : [2]
  • 73 : [2]
  • 74 : [2]
  • 75 : [2, 16]
  • 76 : [2]
  • 77 : [2]
  • 78 : [2, 9]
  • 79 : [2, 5, 9]
  • 80 : [2]
  • 81 : [2, 3]
  • 82 : [2]
  • 83 : [2, 3, 12]
  • 84 : [2]
  • 85 : [2]
  • 86 : [2, 10, 13]
  • 87 : [3]
  • 88 : [2, 10]
  • 89 : [2, 9, 10, 13]
  • 90 : [2, 3]
  • 91 : [2, 3, 7, 11, 16]
  • 92 : [2, 11, 14]
  • 93 : [2, 3, 11, 14]
  • 94 : [11]
  • 95 : [14]
  • 96 : [2]
  • 97 : [2]
  • 98 : [2]
  • 99 : [2, 3]
  • 123 : [14]
  • 1200 : [2]
  • 1201 : [2]
  • 1202 : [2]
  • 1203 : [2]
  • 1204 : [2]
  • 1205 : [2]
  • 1206 : [2]
  • 1207 : [2, 11]
  • 1208 : [2]
  • 1209 : [2]
  • 1210 : [2]
  • 1211 : [12, 16]
  • 1212 : [2]
  • 1213 : [2, 16]
  • 1214 : [2, 9]
  • 1215 : [3]
  • 1216 : [2]
  • 1217 : [2]
  • 1218 : [2]
  • 1219 : [2]
  • 1220 : [2]
  • 1221 : [2]
  • 1222 : [2]
  • 1223 : [2]
  • 1224 : [2]
  • 1225 : [2]
  • 1226 : [2]
  • 1227 : [2]
  • 1228 : [2]
  • 1229 : [2]
  • 1230 : [2]
  • 1231 : [2]
  • 1232 : [2]
  • 1233 : [2]
  • 1234 : [2]
  • 1235 : [2, 12]
  • 1236 : [2]
  • 1237 : [2]
  • 1238 : [2]
  • 1239 : [2]
  • 1240 : [2]
  • 1241 : [2]
  • 1242 : [2]
  • 1243 : [2, 14, 16]
  • 1244 : [2]
  • 1245 : [2, 5]
  • 1246 : [2]
  • 1247 : [12]
  • 1248 : [2]
  • 1249 : [2]
  • 1250 : [2]
  • 1251 : [2]
  • 1252 : [2]
  • 1253 : [2]
  • 1254 : [2, 12]
  • 1255 : [2, 12]
  • 1256 : [2, 12]
  • 1257 : [2, 12]
  • 1258 : [2, 12]
  • 1259 : [12]
  • 1260 : [2]
  • 1261 : [2]
  • 1262 : [2, 11]
  • 1263 : [2, 11, 12]
  • 1264 : [2]
  • 1265 : [2]
  • 1266 : [2]
  • 1267 : [2]
  • 1268 : [2, 12]
  • 1269 : [2, 3, 12]
  • 1270 : [2, 5, 12]
  • 1271 : [12]
  • 1272 : [2]
  • 1273 : [2]
  • 1274 : [2, 5]
  • 1275 : [2, 3, 5, 9, 12, 16]
  • 1276 : [2, 12]
  • 1277 : [9]
  • 1278 : [12]
  • 1279 : [5, 12]
  • 1280 : [2]
  • 1281 : [2]
  • 1282 : [2]
  • 1283 : [2]
  • 1284 : [2]
  • 1285 : [2]
  • 1286 : [2]
  • 1287 : [2]
  • 1288 : [2]
  • 1289 : [2]
  • 1290 : [2]
  • 1291 : [2]
  • 1292 : [2]
  • 1293 : [2]
  • 1294 : [2]
  • 1295 : [12]
  • 1296 : [2]
  • 1297 : [2]
  • 1298 : [2]
  • 1299 : [2]
  • ```
  • > Explanations in answers are optional, but I'm more likely to upvote answers that have one.
#1: Initial revision by user avatar trichoplax‭ · 2022-09-29T22:51:56Z (about 2 years ago)
The holeyest base
Given a positive integer as input, indicate which base from 2 to 16 gives the most holes in the representation of the input in that base.

The digits used are 0123456789ABCDEF. Note that these include upper case letters (the number of holes would be different for lower case letters).

Different fonts have different numbers of holes per character, so the number of holes per digit is as follows for this challenge (in the format `digit : number of holes`):

```text
0 : 1
1 : 0
2 : 0
3 : 0
4 : 1
5 : 0
6 : 1
7 : 0
8 : 2
9 : 1
A : 1
B : 2
C : 0
D : 1
E : 0
F : 0
```

## Input
- A positive integer

## Output
- An integer from 2 to 16
- The output indicates which base gives the representation with the most holes (being the sum of the number of holes in each digit when represented in that base)
- For the purposes of counting holes:
  - Each representation will have no leading zeroes
  - The base indicator characters used by some languages, such as a leading `0b` or `0x` are not included in the counting
- If more than one base has the highest number of holes, any such base is a valid output

## Example
For input `123` the representation in each of the bases from 2 to 16, and the associated number of holes, is as follows (in the format `base : representation : holes`):

```text
2 : 1111011 : 0 + 0 + 0 + 0 + 1 + 0 + 0 = 1
3 : 11120 : 0 + 0 + 0 + 0 + 1 = 1
4 : 1323 : 0 + 0 + 0 + 0 = 0
5 : 443 : 1 + 1 + 0 = 2
6 : 323 : 0 + 0 + 0 = 0
7 : 234 : 0 + 0 + 1 = 1
8 : 173 : 0 + 0 + 0 = 0
9 : 146 : 0 + 1 + 1 = 2
10 : 123 : 0 + 0 + 0 = 0
11 : 102 : 0 + 1 + 0 = 1
12 : A3 : 1 + 0 = 1
13 : 96 : 1 + 1 = 2
14 : 8B : 2 + 2 = 4
15 : 83 : 2 + 0 = 2
16 : 7B : 0 + 2 = 2
```

The highest number of holes is 4, and this only occurs when the base is 14. So the only valid output is 14.

## Test cases
### Test cases with only 1 valid output
These test cases are in the format `input : output`.

```text
2 : 2
3 : 3
4 : 2
7 : 7
8 : 2
10 : 2
12 : 2
16 : 2
17 : 2
18 : 2
20 : 2
24 : 2
27 : 3
32 : 2
33 : 2
34 : 2
35 : 2
36 : 2
37 : 2
38 : 2
40 : 2
41 : 2
42 : 2
48 : 2
49 : 2
50 : 2
51 : 2
54 : 3
59 : 12
60 : 13
61 : 13
62 : 9
63 : 13
64 : 2
65 : 2
66 : 2
67 : 2
68 : 2
69 : 2
70 : 2
72 : 2
73 : 2
74 : 2
76 : 2
77 : 2
80 : 2
82 : 2
84 : 2
85 : 2
87 : 3
94 : 11
95 : 14
96 : 2
97 : 2
98 : 2
123 : 14
```

### Test cases including some with multiple valid outputs
These test cases are in the format `input : [comma separated outputs]` where any of the listed outputs would be valid. These also include all of the single valid output test cases listed above.

```text
0 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
1 : [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
2 : [2]
3 : [3]
4 : [2]
5 : [2, 5]
6 : [2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
7 : [7]
8 : [2]
9 : [2, 3]
10 : [2]
11 : [12, 13, 14, 15, 16]
12 : [2]
13 : [2, 7, 9, 13, 14, 15, 16]
14 : [2, 5, 7, 8, 10, 14]
15 : [3, 5, 9, 11, 15]
16 : [2]
17 : [2]
18 : [2]
19 : [2, 11]
20 : [2]
21 : [2, 13]
22 : [2, 14]
23 : [12, 15]
24 : [2]
25 : [2, 5, 14]
26 : [2, 9, 15]
27 : [3]
28 : [2, 3, 6, 7, 10]
29 : [3, 5]
30 : [3, 11]
31 : [3, 7, 9, 11]
32 : [2]
33 : [2]
34 : [2]
35 : [2]
36 : [2]
37 : [2]
38 : [2]
39 : [2, 14]
40 : [2]
41 : [2]
42 : [2]
43 : [2, 16]
44 : [2, 9]
45 : [2, 3, 5]
46 : [2, 7, 10]
47 : [12, 13]
48 : [2]
49 : [2]
50 : [2]
51 : [2]
52 : [2, 11]
53 : [2, 7, 9, 11, 14, 15]
54 : [3]
55 : [3, 7]
56 : [2, 12]
57 : [2, 3, 12]
58 : [2, 9, 10, 12, 13]
59 : [12]
60 : [13]
61 : [13]
62 : [9]
63 : [13]
64 : [2]
65 : [2]
66 : [2]
67 : [2]
68 : [2]
69 : [2]
70 : [2]
71 : [2, 15]
72 : [2]
73 : [2]
74 : [2]
75 : [2, 16]
76 : [2]
77 : [2]
78 : [2, 9]
79 : [2, 5, 9]
80 : [2]
81 : [2, 3]
82 : [2]
83 : [2, 3, 12]
84 : [2]
85 : [2]
86 : [2, 10, 13]
87 : [3]
88 : [2, 10]
89 : [2, 9, 10, 13]
90 : [2, 3]
91 : [2, 3, 7, 11, 16]
92 : [2, 11, 14]
93 : [2, 3, 11, 14]
94 : [11]
95 : [14]
96 : [2]
97 : [2]
98 : [2]
99 : [2, 3]
123 : [14]
1200 : [2]
1201 : [2]
1202 : [2]
1203 : [2]
1204 : [2]
1205 : [2]
1206 : [2]
1207 : [2, 11]
1208 : [2]
1209 : [2]
1210 : [2]
1211 : [12, 16]
1212 : [2]
1213 : [2, 16]
1214 : [2, 9]
1215 : [3]
1216 : [2]
1217 : [2]
1218 : [2]
1219 : [2]
1220 : [2]
1221 : [2]
1222 : [2]
1223 : [2]
1224 : [2]
1225 : [2]
1226 : [2]
1227 : [2]
1228 : [2]
1229 : [2]
1230 : [2]
1231 : [2]
1232 : [2]
1233 : [2]
1234 : [2]
1235 : [2, 12]
1236 : [2]
1237 : [2]
1238 : [2]
1239 : [2]
1240 : [2]
1241 : [2]
1242 : [2]
1243 : [2, 14, 16]
1244 : [2]
1245 : [2, 5]
1246 : [2]
1247 : [12]
1248 : [2]
1249 : [2]
1250 : [2]
1251 : [2]
1252 : [2]
1253 : [2]
1254 : [2, 12]
1255 : [2, 12]
1256 : [2, 12]
1257 : [2, 12]
1258 : [2, 12]
1259 : [12]
1260 : [2]
1261 : [2]
1262 : [2, 11]
1263 : [2, 11, 12]
1264 : [2]
1265 : [2]
1266 : [2]
1267 : [2]
1268 : [2, 12]
1269 : [2, 3, 12]
1270 : [2, 5, 12]
1271 : [12]
1272 : [2]
1273 : [2]
1274 : [2, 5]
1275 : [2, 3, 5, 9, 12, 16]
1276 : [2, 12]
1277 : [9]
1278 : [12]
1279 : [5, 12]
1280 : [2]
1281 : [2]
1282 : [2]
1283 : [2]
1284 : [2]
1285 : [2]
1286 : [2]
1287 : [2]
1288 : [2]
1289 : [2]
1290 : [2]
1291 : [2]
1292 : [2]
1293 : [2]
1294 : [2]
1295 : [12]
1296 : [2]
1297 : [2]
1298 : [2]
1299 : [2]
```


> Explanations in answers are optional, but I'm more likely to upvote answers that have one.