Tower of Hanoi – Inverted Solution:
If the tower consisted of only 1 disk, the puzzle could be completed in only 1 move. If the tower consisted of 2 disks, the puzzle could be completed in 3 moves. if the tower consisted of 3 disks, the puzzle could be completed in 7 moves. For each of these cases, the number of moves is . Thus for the 5 disk model, the puzzle could be completed in moves.
The Travelling Salesman Solution:
The distances between the various cities, as measured in centimeters on the model, are shown on the table below.
|Olympia||Salem||Boise||Helena||Sacramento||Carson City||Salt Lake City||Cheyenne||Denver||Santa Fe||Phoenix|
|Salt Lake City||60.2||56.8||30.5||39.6||46.9||37.7||35.3||36.2||44.7||46.2|
Selecting Salt Lake City as the starting city, a Mathematica computer program ran for 2 days to arrive at the path that generated the shortest distance of 276.7 cm. That path is
Salt Lake City – Carson City – Sacramento – Salem – Olympia – Boise – Helena – Cheyenne – Denver – Santa Fe – Phoenix
The path from Salt Lake City with the second shortest length of 281.2 cm is
Salt Lake City – Cheyenne – Denver – Santa Fe – Phoenix – Carson City – Sacramento – Salem – Olympia – Boise – Helena
If the starting city is Boise, the shortest path of 276.6 cm is
Boise – Helena – Olympia – Salem – Sacramento – Carson City – Salt Lake City – Cheyenne – Denver – Santa Fe – Phoenix
The path from Boise with the second shortest length of 284.6 cm is
Boise – Helena – Olympia – Salem – Carson City – Sacramento – Salt Lake City – Cheyenne – Denver – Santa Fe – Phoenix