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Traveling Salesman Problem 6 Cities Calculator
Find the shortest distance route starting from City A and visiting all the remaining 5 cities just once and then return back to original starting point City A. There are 15 input distances and 120 possible combination to get the shortest route distance.
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The reverse direction is also correct: Solution 109, AFEDCBA
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Change distance b to e from 33 to 3. What is the shortest route? Answer = 42, solution 13, ABECDFA or the reverse direction solution 105, AFDCEBA
Change distance b to d from 44 to 4. What is the shortest route? Answer = 41, solution 12, ABDCEFA or the reverse direction solution 112, AFECDBA
Change distance a to b from 5 to 59. What is the shortest route? Answer = 86, solution 59, ADCBEFA or the reverse direction solution 113, AFEBCDA
Instructions
- Click the Clear button before entering new data to compute the shortest distance.
-
If no distance is provided between two nodes, enter
1e9in the input box.
This large value simulates an unreachable path by making the total calculated distance extremely high, effectively excluding it from the shortest route.
Tip: Use 1e9 to represent missing connections—this ensures the algorithm treats them as non-viable paths.
This is interactive so try it. if the edge or line has no distance enter 1e9 (meaning 1,000,000,000) there is no available road to connect the two nodes. For example go to Drawing #1 example node A to node D no line so you enter 1e9 as input. (line is also called as edge, path, circuit in graph of traveling salesman analysis).
Graph Terminology Clarification
In the source material, the term "line" is used informally and is said to be interchangeable with edge, path, and circuit in graph of traveling salesman analysis. However, in formal graph theory, these terms have distinct meanings:
- Edge: A direct connection between two nodes (also called a vertex).
- Path: A sequence of edges that connects a series of nodes without repeating any node.
- Circuit: A path that starts and ends at the same node, forming a closed loop.
While the source uses "line" as a general term, it's important to use precise terminology when teaching or analyzing graphs to avoid confusion.
ENTER YOUR NEW DATA HERE
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a to b |
a to e |
a to d |
a to c |
|
b to e |
b to c |
c to d |
c to e |
|
d to e |
b to d |
e to f |
a to f |
|
b to f |
d to f |
c to f |
shortest distance |
120 Possible combinations of car tour visiting all six (6) cities starting from city A as the default starting point and returning to the same starting point A. The travelling salesman problem is to find the shortest route distance. Another contraint of the problem that must be satisfied is you must visit each city once.
| solution 1 A B C D E F A |
solution 2 A B C D F E A |
solution 3 A B C E D F A |
solution 4 A B C E F D A |
| solution 5 A B C F D E A |
solution 6 A B C F E D A |
solution 7 A B D F E C A |
solution 8 A B D F C E A |
| solution 9 A B D E C F A |
solution 10 A B D E C F A |
solution 11 A B D C F E A |
solution 12 A B D C E F A |
| solution 13 A B E C D F A |
solution 14 A B E C F D A |
solution 15 A B E D C F A |
solution 16 A B E D F C A |
| solution 17 A B E F D C A |
solution 18 A B E F C D A |
solution 19 A B F D E C A |
solution 20 A B F D C E A |
| solution 21 A B F C D E A |
solution 22 A B F C E D A |
solution 23 A B F E C D A |
solution 24 A B F E D C A |
| solution 25 A C B D E F A |
solution 26 A C B D F E A |
solution 27 A C B E F D A |
solution 28 A C B E D F A |
| solution 29 A C B F E D A |
solution 30 A C B F D E A |
solution 31 A C D E F B A |
solution 32 A C D E B F A |
| solution 33 A C D F E B A |
solution 34 A C D F B E A |
solution 35 A C D B E F A |
solution 36 A C D B F E A |
| solution 37 A C E B D F A |
solution 38 A C E B F D A |
solution 39 A C E D B F A |
solution 40 A C E D F B A |
| solution 41 A C E F B D A |
solution 42 A C E F D B A |
solution 43 A C F D E B A |
solution 44 A C F D B E A |
| solution 45 A C F E B D A |
solution 46 A C F E D B A |
solution 47 A C F B E D A |
solution 48 A C F B D E A |
| solution 49 A D B C E F A |
solution 50 A D B C F E A |
solution 51 A D B E C F A |
solution 52 A D B E F C A |
| solution 53 A D B F E C A |
solution 54 A D B F C E A |
solution 55 A D C E B F A |
solution 56 A D C E F B A |
| solution 57 A D C F B E A |
solution 58 A D C F E B A |
solution 59 A D C B E F A |
solution 60 A D C B F E A |
| solution 61 A D E C B F A |
solution 62 A D E C F B A |
solution 63 A D E B C F A |
solution 64 A D E B F C A |
| solution 65 A D E F B C A |
solution 66 A D E F C B A |
solution 67 A D F E B C A |
solution 68 A D F E C B A |
| solution 69 A D F B E C A |
solution 70 A D F B C E A |
solution 71 A D F C B E A |
solution 72 A D F C E B A |
| solution 73 A E C D B F A |
solution 74 A E C D F B A |
solution 75 A E C F D B A |
solution 76 A E C F B D A |
| solution 77 A E C B D F A |
solution 78 A E C B F D A |
solution 79 A E D C B F A |
solution 80 A E D C F B A |
| solution 81 A E D C B F A |
solution 82 A E D C F B A |
solution 83 A E D F C B A |
solution 84 A E D F B C A |
| solution 85 A E F D B C A |
solution 86 A E F D C B A |
solution 87 A E F B D C A |
solution 88 A E F B C D A |
| solution 89 A E F C B D A |
solution 90 A E F C D B A |
solution 91 A E B C D F A |
solution 92 A E B C F D A |
| solution 93 A E B D C F A |
solution 94 A E B D F C A |
solution 95 A E B F C D A |
solution 96 A E B F D C A |
| solution 97 A F C D E B A |
solution 98 A F C D B E A |
solution 99 A F C E B D A |
solution 100 A F C E D B A |
| solution 101 A F C B E D A |
solution 102 A F C B D E A |
solution 103 A F D E B C A |
solution 104 A F D E C B A |
| solution 105 A F D C E B A |
solution 106 A F D C B E A |
solution 107 A F D B E C A |
solution 108 A F D B C E A |
| solution 109 A F E D C B A |
solution 110 A F E D B C A |
solution 111 A F E C B D A |
solution 112 A F E C D B A |
| solution 113 A F E B C D A |
solution 114 A F E B D C A |
solution 115 A F B C E D A |
solution 116 A F B C D E A |
| solution 117 A F B D E C A |
solution 118 A F B D C E A |
solution 119 A F B E D C A |
solution 120 A F B E C D A |
Drawing # 1
| Input A | Input B | Input C | Input D |
|---|---|---|---|
| AB =4 | AE =1e9 | AD =1e9 | AC =7 |
| BE =1e9 | BC =4 | CD =5 | CE =9 |
| DE =3 | BD =1e9 | EF =5 | AF =5 |
| BF =1e9 | DF =1e9 | CF =1e9 |
Drawing # 1 Answer 26 Solution 1
Drawing # 2
| Input A | Input B | Input C | Input D |
|---|---|---|---|
| AB =4 | AE =1e9 | AD =6 | AC =7 |
| BE =1e9 | BC =4 | CD =5 | CE =9 |
| DE =3 | BD =6 | EF =5 | AF =5 |
| BF =1e9 | DF =5 | CF =1e9 |
Drawing # 2 Answer 26 Solution 1, Zoo to Library and Library to Home was added
Drawing # 3
| Input A | Input B | Input C | Input D |
|---|---|---|---|
| AB =5 | AE =30 | AD =1e9 | AC =1e9 |
| BE =1e9 | BC =20 | CD =2 | CE =1e9 |
| DE =2 | BD =1e9 | EF =15 | AF =7 |
| BF =10 | DF =9 | CF =15 |
Drawing # 3 Answer 51 Solution 1
Travelling Salesman 7 Cities
Travelling Salesman 5 Cities
Travelling Salesman 4 Cities
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| Year | Top 10 countries | Pages visited |
| 2023 | 1. USA 2. Great Britain 3. Germany 4. Canada 5. Iran 6. Netherlands 7. India 8. China 9. Australia 10. Philippines | 127,256 Pages / 27,541 Visitors |
| 2024 | 1. USA 2. China 3. Canada 4. Poland 5. India 6. Philippines 7. Great Britain 8. Australia 9. Indonesia 10. Russia | 164,130 Pages / 40,724 Visitors |
| Daily Site Visitor Ranking 11/29/2025 | 1. USA 2. Israel 3. China 4. Vietnam 5. Japan 6. India 7. Canada 8. Australia 9. Argentina 10. Brazil | Year to Date 214,992 Pages / 76,185 Visitors |
Data source: Advanced Web Statistics 7.8
Approximately between 2.3 and 2.5 million schools globally, according to the latest available data from government and education ministry reports.
🔗 The challenges schools face: 2025/2026 🔗 USA ~ Public 98,500 ~ Private 30,000 ~ Total 128,500 🔗 Canada ~ Public 15,500 ~ Private 2,000 ~ Total 17,500 🔗 Brazil ~ Public 138,000 ~ Private 40,000 ~ Total 178,000 🔗 Vietnam ~ Public 42,000 ~ Private 8,000 ~ Total 50,000 🔗 China ~ Public 217,200 ~ Private 152,800 ~ Total 470,000 🔗 India ~ Public 1,022,386 ~ Private 335,844 ~ Total 1,358,230 🔗 Japan ~ Public 30,240 ~ Private included ~ Total 30,240 🔗 Morocco ~ Public 20,600 ~ Private 6,300 ~ Total 26,900 🔗 Indonesia ~ Public 390,718 ~ Private included ~ Total 390,718 🔗 Philippines ~ Public 47,831 ~ Private 13,000 ~ Total 60,831 🔗 Great Britain ~ Public 29,202 ~ Private included ~ Total 29,202 🔗 Australia ~ Public 9,653 ~ Private included ~ Total 9,653 🔗 Russia ~ Public 39,070 ~ Private included ~ Total 39,070 🔗 Germany ~ Public 31,039 ~ Private included ~ Total 31,039 🔗 Poland ~ Public 36,291 ~ Private included ~ Total 36,291 🔗 Iran ~ Public 80,000 ~ Private included ~ Total 80,000 🔗 France ~ Public 58,100 ~ Private included ~ Total 58,100 🔗 Mexico ~ Public 132,505 ~ Private included ~ Total 132,505