# basic walks
# walks=games[[2]]
basic=rbind(
walks[walks[,1]==1 & walks[,2]==2 ,], # 55
walks[walks[,1]==1 & walks[,2]==5 & walks[,3]==2, ], # 3
walks[walks[,1]==1 & walks[,2]==5 & walks[,3]==6, ], # 2
walks[walks[,1]==1 & walks[,2]==5 & walks[,3]==3, ], # 6
walks[walks[,1]==1 & walks[,2]==5 & walks[,3]==9 & walks[,4]==6, ], # 3
walks[walks[,1]==2 & walks[,2]==3, ], # 21
walks[walks[,1]==2 & walks[,2]==6,], # 3
walks[walks[,1]==2 & walks[,2]==5 & walks[,3]==3,], # 1
walks[walks[,1]==5 & walks[,2]==2 & walks[,3]==1,], # 1
walks[walks[,1]==5 & walks[,2]==3 & walks[,3]==2,]) # 3
games::mirrormatrix(9)
walks=games::bogglewalks[[3]] # around 42K expected solutions
collapse=function(x){paste(x,collapse="")}
table(apply(walks[,1:2],1,collapse)=="12") #
nrow(walks[walks[,1]==1 & walks[,2]==6 & walks[,3]==2,]) # 1623
nrow(walks[walks[,1]==1 & walks[,2]==6 & walks[,3]==3,]) # 1368
nrow(walks[walks[,1]==1 & walks[,2]==6 & walks[,3]==7,]) # 1101
table(apply(walks[,1:4],1,collapse)=="16117") # 118
table(apply(walks[,1:4],1,collapse)=="16118") # 149
table(apply(walks[,1:4],1,collapse)=="161112") # 129
table(apply(walks[,1:5],1,collapse)=="16111612") # 174
table(apply(walks[,1:2],1,collapse)=="21")
table(apply(walks[,1:2],1,collapse)=="23")
table(apply(walks[,1:2],1,collapse)=="27")
table(apply(walks[,1:3],1,collapse)=="263")
table(apply(walks[,1:3],1,collapse)=="267")
table(apply(walks[,1:2],1,collapse)=="62")
table(apply(walks[,1:2],1,collapse)=="63")
table(apply(walks[,1:3],1,collapse)=="673")
table(apply(walks[,1:3],1,collapse)=="674")
table(apply(walks[,1:3],1,collapse)=="678")
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