Thursday, March 21, 2019

Circle Method - Part 3

Examples showing 8 teams and 10 teams

Not doing anything spectacular here, just using the circle method to make matchups for a couple more scenarios.

Here are eight teams. Again, counterclockwise rotation with team 1 locked in place.
1 8    1 7    1 6    1 5    1 4    1 3    1 2
2 7 -> 8 6 -> 7 5 -> 6 4 -> 5 3 -> 4 2 -> 3 8
3 6    2 5    8 4    7 3    6 2    5 8    4 7
4 5    3 4    2 3    8 2    7 8    6 7    5 6
...laying out the matchups into rows (e.g., the leftmost matchup set above is the tiop row below)...
1 v 8   2 v 7   3 v 6   4 v 5
1 v 7   8 v 6   2 v 5   3 v 4
1 v 6   7 v 5   8 v 4   2 v 3
1 v 5   6 v 4   7 v 3   8 v 2
1 v 4   5 v 3   6 v 2   7 v 8
1 v 3   4 v 2   5 v 8   6 v 7
1 v 2   3 v 8   4 v 7   5 v 6
Here are ten teams. Again, counterclockwise rotation with team 1 locked in place.
 1 10     1  9     1  8     1  7     1  6     1  5     1  4     1  3     1  2
 2  9    10  8     9  7     8  6     7  5     6  4     5  3     4  2     3 10
 3  8  >  2  7  > 10  6  >  9  5  >  8  4  >  7  3  >  6  2  >  5 10  >  4  9
 4  7     3  6     2  5    10  4     9  3     8  2     7 10     6  9     5  8
 5  6     4  5     3  4     2  3    10  2     9 10     8  9     7  8     6  7
...laying out the matchups into rows...
1 v10   2 v 9   3 v 8   4 v 7   5 v 6
1 v 9  10 v 8   2 v 7   3 v 6   4 v 5
1 v 8   9 v 7  10 v 6   2 v 5   3 v 4
1 v 7   8 v 6   9 v 5  10 v 4   2 v 3
1 v 6   7 v 5   8 v 4   9 v 3  10 v 2
1 v 5   6 v 4   7 v 3   8 v 2   9 v10
1 v 4   5 v 3   6 v 2   7 v10   8 v 9
1 v 3   4 v 2   5 v10   6 v 9   7 v 8
1 v 2   3 v10   4 v 9   5 v 8   6 v 7
You may notice some patterns in how the numbers fall in the rows if you move your eyes in certain directions around the rows. E.g., look at where team 10 is falling moving diagonally through the grid. The long way I went was recognizing the patterns like that when I had built matchups manually. I struggled to work backwards to an algorithm until I finally went looking online and found this circle method.

In the next part we will tackle an odd case.

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