RE: Horse Race Puzzle (fwd)

*To*: mathgroup at smc.vnet.net*Subject*: [mg9259] RE: [mg9162] Horse Race Puzzle (fwd)*From*: Robert Pratt <rpratt at math.unc.edu>*Date*: Fri, 24 Oct 1997 01:01:14 -0400*Sender*: owner-wri-mathgroup at wolfram.com

I omitted "{x," in the second replacement rule, which should read "->{x,Flatten[{y,n}],z}}". The corrected version appears below. > The solutions can be computed recursively using pattern matching as > follows: > > HorseRaces[1]={{1}}; > HorseRaces[n_]:=HorseRaces[n]= > Join[ > Flatten[Map[ReplaceList[#,{x___,y___}->{x,n,y}]&,HorseRaces[n-1]],1], > Flatten[ReplaceList[#,{x___,y_,z___}->{x,Flatten[{y,n}],z}]&, > HorseRaces[n-1]],1] > ] > > Unfortunately, Mathematica seems to ignore the Flatten[{y,n}] command, > returning > {y,n} unflattened. However, this only gives some unambiguous extra > nesting in the solutions.