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Finding Sets - Difficult one !

  1. #1
    sandip.dhamapurkar@gmail.com
    Guest

    Finding Sets - Difficult one !

    Combination of TWO
    ===============

    I have four basic numbers 1 2 3 4. If I have to make all possible
    combinations of TWO out of these four basic numbers, then the answer
    would be SIX =COMBIN(4,2).

    I am planning to make unique sets out of these combinations. Since
    there are four basic numbers, I will have to make a grid of 2 X 2
    consisting all unique numbers which comes out to be THREE

    1. 1-2 & 3-4 (All individual numbers in each set is unique)
    2. 1-3 & 2-4
    3. 1-4 & 2-3

    If I have six basic numbers 1 2 3 4 5 6 and if I have to make all
    possible combinations of TWO, then the answer would be FIFTEEN
    =COMBIN(6,2)

    If I make unique sets out of these combinations, I will have to make a
    grid of 3 X 2 which comes out to be FIFTEEN

    1. 1-2 & 3-4 & 5-6 (All individual numbers in each set is unique)
    2. 1-2 & 3-5 & 4-6
    3. 1-2 & 3-6 & 4-5
    4. 1-3 & 2-4 & 5-6
    5. 1-3 & 2-5 & 4-6
    6. 1-3 & 2-6 & 4-5
    7. 1-4 & 2-3 & 5-6
    8. 1-4 & 2-5 & 3-6
    9. 1-4 & 2-6 & 3-5
    10. 1-5 & 2-3 & 4-6
    11. 1-5 & 2-4 & 3-6
    12. 1-5 & 2-6 & 3-4
    13. 1-6 & 2-3 & 4-5
    14. 1-6 & 2-4 & 3-5
    15. 1-6 & 2-5 & 3-4

    Combination of THREE
    =================

    I have six basic numbers 1 2 3 4 5 6. If I have to make all possible
    combinations of THREE out of these six basic numbers, then the answer
    would be TWENTY =COMBIN(3,3).

    If I have to make unique sets out of these combinations. Since there
    are six basic numbers, I will have to make a grid of 3 X 2 consisting
    all unique numbers which comes out to be TEN

    1. 1-2-3 & 4-5-6 (All individual numbers in each set is unique)
    2. 1-2-4 & 3-5-6
    3. 1-2-5 & 3-4-6
    4. 1-2-6 & 3-4-5
    5. 1-3-4 & 2-5-6
    6. 1-3-5 & 2-4-6
    7. 1-3-6 & 2-4-5
    8. 1-4-5 & 2-3-6
    9. 1-4-6 & 2-3-5
    10. 1-5-6 & 2-3-4

    If I have Nine basic numbers 1 2 3 4 5 6 7 8 9 and if I have to make
    all possible combinations of THREE, then the answer would be EIGHTY
    FOUR =COMBIN(9,3)

    If I make unique sets out of these combinations, I will have to make a
    grid of 3 X 3 which comes out to be 280

    1. 1-2-3 & 4-5-6 & 7-8-9 (All individual numbers in each set is unique)
    2. 1-2-3 & 4-5-7 & 6-8-9
    ..
    ..
    ..
    ..
    ..
    ..
    280. 1-8-9 & 2-6-7 & 3-4-5

    X------------X------ End of the problem ------X------------X

    Answer for first scenario was 3
    Answer for second scenario was 15
    Answer for third scenario was 10
    Answer for last scenario was 280

    What I want to know is whether there is any mathematical/statistical
    formula to calculate the result. I want to know is there any way to
    derive the answer from any formula?

    Sandy


  2. #2
    sandip.dhamapurkar@gmail.com
    Guest

    Re: Finding Sets - Difficult one !

    Had a hard time listing these 280 sets manually. Anyways, here are
    they:

    01. 1-2-3 & 4-5-6 & 7-8-9 | 141. 1-4-6 & 2-3-5 & 7-8-9
    02. 1-2-3 & 4-5-7 & 6-8-9 | 142. 1-4-6 & 2-3-7 & 5-8-9
    03. 1-2-3 & 4-5-8 & 6-7-9 | 143. 1-4-6 & 2-3-8 & 5-7-9
    04. 1-2-3 & 4-5-9 & 6-7-8 | 144. 1-4-6 & 2-3-9 & 5-7-8
    05. 1-2-3 & 4-6-7 & 5-8-9 | 145. 1-4-6 & 2-5-7 & 3-8-9
    06. 1-2-3 & 4-6-8 & 5-7-9 | 146. 1-4-6 & 2-5-8 & 3-7-9
    07. 1-2-3 & 4-6-9 & 5-7-8 | 147. 1-4-6 & 2-5-9 & 3-7-8
    08. 1-2-3 & 4-7-8 & 5-6-9 | 148. 1-4-6 & 2-7-8 & 3-5-9
    09. 1-2-3 & 4-7-9 & 5-6-8 | 149. 1-4-6 & 2-7-9 & 3-5-8
    10. 1-2-3 & 4-8-9 & 5-6-7 | 150. 1-4-6 & 2-8-9 & 3-5-7
    11. 1-2-4 & 3-5-6 & 7-8-9 | 151. 1-4-7 & 2-3-5 & 6-8-9
    12. 1-2-4 & 3-5-7 & 6-8-9 | 152. 1-4-7 & 2-3-6 & 5-8-9
    13. 1-2-4 & 3-5-8 & 6-7-9 | 153. 1-4-7 & 2-3-8 & 5-6-9
    14. 1-2-4 & 3-5-9 & 6-7-8 | 154. 1-4-7 & 2-3-9 & 5-6-8
    15. 1-2-4 & 3-6-7 & 5-8-9 | 155. 1-4-7 & 2-5-6 & 3-8-9
    16. 1-2-4 & 3-6-8 & 5-7-9 | 156. 1-4-7 & 2-5-8 & 3-6-9
    17. 1-2-4 & 3-6-9 & 5-7-8 | 157. 1-4-7 & 2-5-9 & 3-6-8
    18. 1-2-4 & 3-7-8 & 5-6-9 | 158. 1-4-7 & 2-6-8 & 3-5-9
    19. 1-2-4 & 3-7-9 & 5-6-8 | 159. 1-4-7 & 2-6-9 & 3-5-8
    20. 1-2-4 & 3-8-9 & 5-6-7 | 160. 1-4-7 & 2-8-9 & 3-5-6
    21. 1-2-5 & 3-4-6 & 7-8-9 | 161. 1-4-8 & 2-3-5 & 6-7-9
    22. 1-2-5 & 3-4-7 & 6-8-9 | 162. 1-4-8 & 2-3-6 & 5-7-9
    23. 1-2-5 & 3-4-8 & 6-7-9 | 163. 1-4-8 & 2-3-7 & 5-6-9
    24. 1-2-5 & 3-4-9 & 6-7-8 | 164. 1-4-8 & 2-3-9 & 5-6-7
    25. 1-2-5 & 3-6-7 & 4-8-9 | 165. 1-4-8 & 2-5-6 & 3-7-9
    26. 1-2-5 & 3-6-8 & 4-7-9 | 166. 1-4-8 & 2-5-7 & 3-6-9
    27. 1-2-5 & 3-6-9 & 4-7-8 | 167. 1-4-8 & 2-5-9 & 3-6-7
    28. 1-2-5 & 3-7-8 & 4-6-9 | 168. 1-4-8 & 2-6-7 & 3-5-9
    29. 1-2-5 & 3-7-9 & 4-6-8 | 169. 1-4-8 & 2-6-9 & 3-5-7
    30. 1-2-5 & 3-8-9 & 4-6-7 | 170. 1-4-8 & 2-7-9 & 3-5-6
    31. 1-2-6 & 3-4-5 & 7-8-9 | 171. 1-4-9 & 2-3-5 & 6-7-8
    32. 1-2-6 & 3-4-7 & 5-8-9 | 172. 1-4-9 & 2-3-6 & 5-7-8
    33. 1-2-6 & 3-4-8 & 5-7-9 | 173. 1-4-9 & 2-3-7 & 5-6-8
    34. 1-2-6 & 3-4-9 & 5-7-8 | 174. 1-4-9 & 2-3-8 & 5-6-7
    35. 1-2-6 & 3-5-7 & 4-8-9 | 175. 1-4-9 & 2-5-6 & 3-7-8
    36. 1-2-6 & 3-5-8 & 4-7-9 | 176. 1-4-9 & 2-5-7 & 3-6-8
    37. 1-2-6 & 3-5-9 & 4-7-8 | 177. 1-4-9 & 2-5-8 & 3-6-7
    38. 1-2-6 & 3-7-8 & 4-5-9 | 178. 1-4-9 & 2-6-7 & 3-5-8
    39. 1-2-6 & 3-7-9 & 4-5-8 | 179. 1-4-9 & 2-6-8 & 3-5-7
    40. 1-2-6 & 3-8-9 & 4-5-7 | 180. 1-4-9 & 2-7-8 & 3-5-6
    41. 1-2-7 & 3-4-5 & 6-8-9 | 181. 1-5-6 & 2-3-4 & 7-8-9
    42. 1-2-7 & 3-4-6 & 5-8-9 | 182. 1-5-6 & 2-3-7 & 4-8-9
    43. 1-2-7 & 3-4-8 & 5-6-9 | 183. 1-5-6 & 2-3-8 & 4-7-9
    44. 1-2-7 & 3-4-9 & 5-6-8 | 184. 1-5-6 & 2-3-9 & 4-7-8
    45. 1-2-7 & 3-5-6 & 4-8-9 | 185. 1-5-6 & 2-4-7 & 3-8-9
    46. 1-2-7 & 3-5-8 & 4-6-9 | 186. 1-5-6 & 2-4-8 & 3-7-9
    47. 1-2-7 & 3-5-9 & 4-6-8 | 187. 1-5-6 & 2-4-9 & 3-7-8
    48. 1-2-7 & 3-6-8 & 4-5-9 | 188. 1-5-6 & 2-7-8 & 3-4-9
    49. 1-2-7 & 3-6-9 & 4-5-8 | 189. 1-5-6 & 2-7-9 & 3-4-8
    50. 1-2-7 & 3-8-9 & 4-5-6 | 190. 1-5-6 & 2-8-9 & 3-4-7
    51. 1-2-8 & 3-4-5 & 6-7-9 | 191. 1-5-7 & 2-3-4 & 6-8-9
    52. 1-2-8 & 3-4-6 & 5-7-9 | 192. 1-5-7 & 2-3-6 & 4-8-9
    53. 1-2-8 & 3-4-7 & 5-6-9 | 193. 1-5-7 & 2-3-8 & 4-6-9
    54. 1-2-8 & 3-4-9 & 5-6-7 | 194. 1-5-7 & 2-3-9 & 4-6-8
    55. 1-2-8 & 3-5-6 & 4-7-9 | 195. 1-5-7 & 2-4-6 & 3-8-9
    56. 1-2-8 & 3-5-7 & 4-6-9 | 196. 1-5-7 & 2-4-8 & 3-6-9
    57. 1-2-8 & 3-5-9 & 4-6-7 | 197. 1-5-7 & 2-4-9 & 3-6-8
    58. 1-2-8 & 3-6-7 & 4-5-9 | 198. 1-5-7 & 2-6-8 & 3-4-9
    59. 1-2-8 & 3-6-9 & 4-5-7 | 199. 1-5-7 & 2-6-9 & 3-4-8
    60. 1-2-8 & 3-7-9 & 4-5-6 | 200. 1-5-7 & 2-8-9 & 3-4-6
    61. 1-2-9 & 3-4-5 & 6-7-8 | 201. 1-5-8 & 2-3-4 & 6-7-9
    62. 1-2-9 & 3-4-6 & 5-7-8 | 202. 1-5-8 & 2-3-6 & 4-7-9
    63. 1-2-9 & 3-4-7 & 5-6-8 | 203. 1-5-8 & 2-3-7 & 4-6-9
    64. 1-2-9 & 3-4-8 & 5-6-7 | 204. 1-5-8 & 2-3-9 & 4-6-7
    65. 1-2-9 & 3-5-6 & 4-7-8 | 205. 1-5-8 & 2-4-6 & 3-7-9
    66. 1-2-9 & 3-5-7 & 4-6-8 | 206. 1-5-8 & 2-4-7 & 3-6-9
    67. 1-2-9 & 3-5-8 & 4-6-7 | 207. 1-5-8 & 2-4-9 & 3-6-7
    68. 1-2-9 & 3-6-7 & 4-5-8 | 208. 1-5-8 & 2-6-7 & 3-4-9
    69. 1-2-9 & 3-6-8 & 4-5-7 | 209. 1-5-8 & 2-6-9 & 3-4-7
    70. 1-2-9 & 3-7-8 & 4-5-6 | 210. 1-5-8 & 2-7-9 & 3-4-6
    71. 1-3-4 & 2-5-6 & 7-8-9 | 211. 1-5-9 & 2-3-4 & 6-7-8
    72. 1-3-4 & 2-5-7 & 6-8-9 | 212. 1-5-9 & 2-3-6 & 4-7-8
    73. 1-3-4 & 2-5-8 & 6-7-9 | 213. 1-5-9 & 2-3-7 & 4-6-8
    74. 1-3-4 & 2-5-9 & 6-7-8 | 214. 1-5-9 & 2-3-8 & 4-6-7
    75. 1-3-4 & 2-6-7 & 5-8-9 | 215. 1-5-9 & 2-4-6 & 3-7-8
    76. 1-3-4 & 2-6-8 & 5-7-9 | 216. 1-5-9 & 2-4-7 & 3-6-8
    77. 1-3-4 & 2-6-9 & 5-7-8 | 217. 1-5-9 & 2-4-8 & 3-6-7
    78. 1-3-4 & 2-7-8 & 5-6-9 | 218. 1-5-9 & 2-6-7 & 3-4-8
    79. 1-3-4 & 2-7-9 & 5-6-8 | 219. 1-5-9 & 2-6-8 & 3-4-7
    80. 1-3-4 & 2-8-9 & 5-6-7 | 220. 1-5-9 & 2-7-8 & 3-4-6
    81. 1-3-5 & 2-4-6 & 7-8-9 | 221. 1-6-7 & 2-3-4 & 5-8-9
    82. 1-3-5 & 2-4-7 & 6-8-9 | 222. 1-6-7 & 2-3-5 & 4-8-9
    83. 1-3-5 & 2-4-8 & 6-7-9 | 223. 1-6-7 & 2-3-8 & 4-5-9
    84. 1-3-5 & 2-4-9 & 6-7-8 | 224. 1-6-7 & 2-3-9 & 4-5-8
    85. 1-3-5 & 2-6-7 & 4-8-9 | 225. 1-6-7 & 2-4-5 & 3-8-9
    86. 1-3-5 & 2-6-8 & 4-7-9 | 226. 1-6-7 & 2-4-8 & 3-5-9
    87. 1-3-5 & 2-6-9 & 4-7-8 | 227. 1-6-7 & 2-4-9 & 3-5-8
    88. 1-3-5 & 2-7-8 & 4-6-9 | 228. 1-6-7 & 2-5-8 & 3-4-9
    89. 1-3-5 & 2-7-9 & 4-6-8 | 229. 1-6-7 & 2-5-9 & 3-4-8
    90. 1-3-5 & 2-8-9 & 4-6-7 | 230. 1-6-7 & 2-8-9 & 3-4-5
    91. 1-3-6 & 2-4-5 & 7-8-9 | 231. 1-6-8 & 2-3-4 & 5-7-9
    92. 1-3-6 & 2-4-7 & 5-8-9 | 232. 1-6-8 & 2-3-5 & 4-7-9
    93. 1-3-6 & 2-4-8 & 5-7-9 | 233. 1-6-8 & 2-3-7 & 4-5-9
    94. 1-3-6 & 2-4-9 & 5-7-8 | 234. 1-6-8 & 2-3-9 & 4-5-7
    95. 1-3-6 & 2-5-7 & 4-8-9 | 235. 1-6-8 & 2-4-5 & 3-7-9
    96. 1-3-6 & 2-5-8 & 4-7-9 | 236. 1-6-8 & 2-4-7 & 3-5-9
    97. 1-3-6 & 2-5-9 & 4-7-8 | 237. 1-6-8 & 2-4-9 & 3-5-7
    98. 1-3-6 & 2-7-8 & 4-5-9 | 238. 1-6-8 & 2-5-7 & 3-4-9
    99. 1-3-6 & 2-7-9 & 4-5-8 | 239. 1-6-8 & 2-5-9 & 3-4-7
    100. 1-3-6 & 2-8-9 & 4-5-7 | 240. 1-6-8 & 2-7-9 & 3-4-5
    101. 1-3-7 & 2-4-5 & 6-8-9 | 241. 1-6-9 & 2-3-4 & 5-7-8
    102. 1-3-7 & 2-4-6 & 5-8-9 | 242. 1-6-9 & 2-3-5 & 4-7-8
    103. 1-3-7 & 2-4-8 & 5-6-9 | 243. 1-6-9 & 2-3-7 & 4-5-8
    104. 1-3-7 & 2-4-9 & 5-6-8 | 244. 1-6-9 & 2-3-8 & 4-5-7
    105. 1-3-7 & 2-5-6 & 4-8-9 | 245. 1-6-9 & 2-4-5 & 3-7-8
    106. 1-3-7 & 2-5-8 & 4-6-9 | 246. 1-6-9 & 2-4-7 & 3-5-8
    107. 1-3-7 & 2-5-9 & 4-6-8 | 247. 1-6-9 & 2-4-8 & 3-5-7
    108. 1-3-7 & 2-6-8 & 4-5-9 | 248. 1-6-9 & 2-5-7 & 3-4-8
    109. 1-3-7 & 2-6-9 & 4-5-8 | 249. 1-6-9 & 2-5-8 & 3-4-7
    110. 1-3-7 & 2-8-9 & 4-5-6 | 250. 1-6-9 & 2-7-8 & 3-4-5
    111. 1-3-8 & 2-4-5 & 6-7-9 | 251. 1-7-8 & 2-3-4 & 5-6-9
    112. 1-3-8 & 2-4-6 & 5-7-9 | 252. 1-7-8 & 2-3-5 & 4-6-9
    113. 1-3-8 & 2-4-7 & 5-6-9 | 253. 1-7-8 & 2-3-6 & 4-5-9
    114. 1-3-8 & 2-4-9 & 5-6-7 | 254. 1-7-8 & 2-3-9 & 4-5-6
    115. 1-3-8 & 2-5-6 & 4-7-9 | 255. 1-7-8 & 2-4-5 & 3-6-9
    116. 1-3-8 & 2-5-7 & 4-6-9 | 256. 1-7-8 & 2-4-6 & 3-5-9
    117. 1-3-8 & 2-5-9 & 4-6-7 | 257. 1-7-8 & 2-4-9 & 3-5-6
    118. 1-3-8 & 2-6-7 & 4-5-9 | 258. 1-7-8 & 2-5-6 & 3-4-9
    119. 1-3-8 & 2-6-9 & 4-5-7 | 259. 1-7-8 & 2-5-9 & 3-4-6
    120. 1-3-8 & 2-7-9 & 4-5-6 | 260. 1-7-8 & 2-6-9 & 3-4-5
    121. 1-3-9 & 2-4-5 & 6-7-8 | 261. 1-7-9 & 2-3-4 & 5-6-8
    122. 1-3-9 & 2-4-6 & 5-7-8 | 262. 1-7-9 & 2-3-5 & 4-6-8
    123. 1-3-9 & 2-4-7 & 5-6-8 | 263. 1-7-9 & 2-3-6 & 4-5-8
    124. 1-3-9 & 2-4-8 & 5-6-7 | 264. 1-7-9 & 2-3-8 & 4-5-6
    125. 1-3-9 & 2-5-6 & 4-7-8 | 265. 1-7-9 & 2-4-5 & 3-6-8
    126. 1-3-9 & 2-5-7 & 4-6-8 | 266. 1-7-9 & 2-4-6 & 3-5-8
    127. 1-3-9 & 2-5-8 & 4-6-7 | 267. 1-7-9 & 2-4-8 & 3-5-6
    128. 1-3-9 & 2-6-7 & 4-5-8 | 268. 1-7-9 & 2-5-6 & 3-4-8
    129. 1-3-9 & 2-6-8 & 4-5-7 | 269. 1-7-9 & 2-5-8 & 3-4-6
    130. 1-3-9 & 2-7-8 & 4-5-6 | 270. 1-7-9 & 2-6-8 & 3-4-5
    131. 1-4-5 & 2-3-6 & 7-8-9 | 271. 1-8-9 & 2-3-4 & 5-6-7
    132. 1-4-5 & 2-3-7 & 6-8-9 | 272. 1-8-9 & 2-3-5 & 4-6-7
    133. 1-4-5 & 2-3-8 & 6-7-9 | 273. 1-8-9 & 2-3-6 & 4-5-7
    134. 1-4-5 & 2-3-9 & 6-7-8 | 274. 1-8-9 & 2-3-7 & 4-5-6
    135. 1-4-5 & 2-6-7 & 3-8-9 | 275. 1-8-9 & 2-4-5 & 3-6-7
    136. 1-4-5 & 2-6-8 & 3-7-9 | 276. 1-8-9 & 2-4-6 & 3-5-7
    137. 1-4-5 & 2-6-9 & 3-7-8 | 277. 1-8-9 & 2-4-7 & 3-5-6
    138. 1-4-5 & 2-7-8 & 3-6-9 | 278. 1-8-9 & 2-5-6 & 3-4-7
    139. 1-4-5 & 2-7-9 & 3-6-8 | 279. 1-8-9 & 2-5-7 & 3-4-6
    140. 1-4-5 & 2-8-9 & 3-6-7 | 280. 1-8-9 & 2-6-7 & 3-4-5


  3. #3
    sandip.dhamapurkar@gmail.com
    Guest

    Re: Finding Sets - Difficult one !

    One more thing to clarify things out:

    Take the first example (01. 1-2-3 & 4-5-6 & 7-8-9)

    There are three combinations of three numbers and it covers all basic
    nine numbers
    1 2 3
    4 5 6
    7 8 9

    Second example (02. 1-2-3 & 4-5-7 & 6-8-9)

    Again there are three combinations of three numbers and it also covers
    all the basic nine numbers but BOTH AS A SET are different from each
    other.
    1 2 3
    4 5 7 (the number 7 was in third combination in first example)
    6 8 9 (the number 6 was in second combination in first example)

    I hope this will be helpful to understand the whole scenario.

    sandip.dhamapurkar@gmail.com wrote:
    > Had a hard time listing these 280 sets manually. Anyways, here are
    > they:
    >
    > 01. 1-2-3 & 4-5-6 & 7-8-9 | 141. 1-4-6 & 2-3-5 & 7-8-9
    > 02. 1-2-3 & 4-5-7 & 6-8-9 | 142. 1-4-6 & 2-3-7 & 5-8-9



  4. #4
    Tom Ogilvy
    Guest

    Re: Finding Sets - Difficult one !

    Why isn't
    1-6-8 & 3-5-7 & 2-4-9

    a legal combination.

    --
    Regards,
    Tom Ogilvy

    <sandip.dhamapurkar@gmail.com> wrote in message
    news:1150824071.761128.133200@h76g2000cwa.googlegroups.com...
    > One more thing to clarify things out:
    >
    > Take the first example (01. 1-2-3 & 4-5-6 & 7-8-9)
    >
    > There are three combinations of three numbers and it covers all basic
    > nine numbers
    > 1 2 3
    > 4 5 6
    > 7 8 9
    >
    > Second example (02. 1-2-3 & 4-5-7 & 6-8-9)
    >
    > Again there are three combinations of three numbers and it also covers
    > all the basic nine numbers but BOTH AS A SET are different from each
    > other.
    > 1 2 3
    > 4 5 7 (the number 7 was in third combination in first example)
    > 6 8 9 (the number 6 was in second combination in first example)
    >
    > I hope this will be helpful to understand the whole scenario.
    >
    > sandip.dhamapurkar@gmail.com wrote:
    > > Had a hard time listing these 280 sets manually. Anyways, here are
    > > they:
    > >
    > > 01. 1-2-3 & 4-5-6 & 7-8-9 | 141. 1-4-6 & 2-3-5 & 7-8-9
    > > 02. 1-2-3 & 4-5-7 & 6-8-9 | 142. 1-4-6 & 2-3-7 & 5-8-9

    >




  5. #5
    Tom Ogilvy
    Guest

    Re: Finding Sets - Difficult one !

    Why isn't
    1-6-8 & 3-5-7 & 2-4-9

    a legal combination.

    --
    Regards,
    Tom Ogilvy

    <sandip.dhamapurkar@gmail.com> wrote in message
    news:1150824071.761128.133200@h76g2000cwa.googlegroups.com...
    > One more thing to clarify things out:
    >
    > Take the first example (01. 1-2-3 & 4-5-6 & 7-8-9)
    >
    > There are three combinations of three numbers and it covers all basic
    > nine numbers
    > 1 2 3
    > 4 5 6
    > 7 8 9
    >
    > Second example (02. 1-2-3 & 4-5-7 & 6-8-9)
    >
    > Again there are three combinations of three numbers and it also covers
    > all the basic nine numbers but BOTH AS A SET are different from each
    > other.
    > 1 2 3
    > 4 5 7 (the number 7 was in third combination in first example)
    > 6 8 9 (the number 6 was in second combination in first example)
    >
    > I hope this will be helpful to understand the whole scenario.
    >
    > sandip.dhamapurkar@gmail.com wrote:
    > > Had a hard time listing these 280 sets manually. Anyways, here are
    > > they:
    > >
    > > 01. 1-2-3 & 4-5-6 & 7-8-9 | 141. 1-4-6 & 2-3-5 & 7-8-9
    > > 02. 1-2-3 & 4-5-7 & 6-8-9 | 142. 1-4-6 & 2-3-7 & 5-8-9

    >




  6. #6
    sandip.dhamapurkar@gmail.com
    Guest

    Re: Finding Sets - Difficult one !

    Because it is already there in the list of 280. Have a look at 237th
    record 1-6-8 & 2-4-9 & 3-5-7

    The basic idea is that there should be 3 combinations of 3 numbers each
    and all the 9 basic numbers should be covered.

    The formula that I discoved is as follows but I am not sure if this is
    mathematically correct.

    Basic numbers : 9
    Combinations: 3

    9/3=3 (there should be three steps to arrive to the final answer)

    step1:

    =combin(basic numbers,combination)/3
    =combin(9,3)/3
    =84/3=28

    step2:
    =combin(basic numbers - 3,combinations)/2
    =combin(6,3)/2
    =20/2=10

    step3:
    =combin(basic numbers - 6,combinations)/1
    =combin(3,3)/1
    =1/1=1

    step1 answer x step2 answer x step3 answer

    28*10*1=280


    Tom Ogilvy wrote:
    > Why isn't
    > 1-6-8 & 3-5-7 & 2-4-9 a legal combination.



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