[r-t] doubles principle

Alexander Holroyd holroyd at math.ubc.ca
Tue Jul 11 17:01:53 UTC 2006


Here is this week's challenge, folks: find a decent (or even passable) 
extent of the doubles principle 5.1.3.5.1 (5 changes/lead).  How difficult 
can it be - it's only _doubles_?  Nevertheless I haven't been able to do 
it.

To demonstrate that it "ought" to be possible: it's easy to get 4 courses 
giving 100.  The remaining 20 changes are 2 courses of plain hunt, which 
can indeed be split into 4 leads of the method (if you do your splitting 
at the pn 3).  Thus e.g. one has the following (which certainly doesn't 
count as a passable extent of the method):

               : 12345
part1[p[5     : 21435 1
         1     : 24153 2
         3     : 42135 3
         5     : 24315 4
         1]    : 23451 5
       p       : 34512 10
       p       : 45123 15
       p       : 51234 20
       b[5     : 15324 21
         1     : 13542 22
         3     : 31524 23
         5     : 13254 24
         125]] : 13524 25
part1         : 15432 50
part2[p       : 54321 55
       p       : 43215 60
       p       : 32154 65
       p       : 21543 70
       x[5     : 12453 71
         1     : 14235 72
         345   : 41235 73
         5     : 14325 74
         1]    : 13452 75
       y[5     : 31542 76
         1     : 35124 77
         5     : 53214 78
         1     : 52341 79
         5]    : 25431 80
       z[1     : 24513 81
         5     : 42153 82
         145   : 41253 83
         5     : 14523 84
         125]] : 14253 85
part2         : 12345 120 Rounds

Ander




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