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Brute Force Solution for Minimum Spanning Network with Varying Number of Cities

Explore the brute force solution for finding a minimum spanning network in a city set with an increasing number of cities. Each additional city exponentially increases the number of attempts required. Discover the complexity of the process as you progress from 5 to 12 cities.

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Brute Force Solution for Minimum Spanning Network with Varying Number of Cities

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  1. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43

  2. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 75+43+59+53 = 230

  3. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 75+43+59+53 = 230 75+71+34+83 = 263

  4. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 75+43+59+53 = 230 75+71+34+83 = 263 75+43+34+53 = 205

  5. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 75+43+59+53 = 230 75+49+34+53 = ... 75+71+34+83 = 263 75+49+53+59 = 75+43+34+53 = 205 75+49+34+59 = 67+43+34+53 = 197 75+43+59+34 = 75+83+43+53 = 75+77+53+34 = 75+83+71+43 = 75+77+59+34 = 75+83+67+71 = 75+77+53+59 =

  6. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 75+43+59+53 = 230 75+49+34+53 = ... 75+71+34+83 = 263 75+49+53+59 = 75+43+34+53 = 205 75+49+34+59 = 67+43+34+53 = 197 75+43+59+34 = 75+83+43+53 = Number tries = 210 75+77+53+34 = 75+83+71+43 = 75+77+59+34 = 75+83+67+71 = 75+77+53+59 =

  7. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 Number tries for 5 cities = 210

  8. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 Number tries for 5 cities = 210 Number tries for 6 cities = 3003

  9. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 Number tries for 5 cities = 210 Number tries for 6 cities = 3003 Number tries for 7 cities = 54264

  10. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 Number tries for 5 cities = 210 Number tries for 6 cities = 3003 Number tries for 7 cities = 54264 Number tries for 8 cities = 1184040

  11. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 Number tries for 5 cities = 210 Number tries for 6 cities = 3003 Number tries for 7 cities = 54264 Number tries for 8 cities = 1184040 Number tries for 10 cities = 886163000

  12. Minimum Spanning Network: Brute Force Solution 71 67 34 83 53 59 75 49 77 43 Number tries for 5 cities = 210 Number tries for 6 cities = 3003 Number tries for 7 cities = 54264 Number tries for 8 cities = 1184040 Number tries for 10 cities = 886163000 Number tries for 12 cities = 1037670000000 (12 days @ 10 per sec) 6

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