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Technical
How to Derive the Process Given the Draw

Dr Ian Vincent reveals the mechanism for deriving the matches in the Process-half of a Draw and Process competition.

The numbers in the process table can be derived from the draw by the following algorithm:

  1. Deduct 1 from the Draw position (i.e. label the players from 0 to 2(N-1))
  2. Express the result in binary.
  3. Reverse the order of the bits.
  4. Convert back to decimal
  5. Add one, to give the position of that player in the Process.

Thus in the example of the seeding positions quoted for the 16 player draw:

Draw Position

Subtract 1

Convert to Binary

Reverse Digits

Convert to Decimal

Add 1 = Process Position

1

0

0000

0000

0

1

6

5

0101

1010

10

11

11

10

1010

0101

5

6

16

15

1111

1111

15

16

This shows the underlying symmetry between the two draws and illustrates why 6 and 11 are special: they are an inverse pair the maximal distance apart from 1 and 16. Other inverse pairs, such as 0111 (8) and 1110 (15) have one of their members too close to one of the top two seeds.

 

Note: There is an automated Draw routine here.

Author: Dr Ian Vincent
All rights reserved © 2007


Updated 28.i.16
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