Help:=proc(): print(` PSB(m,n), IP(m,n), RHM(S,B), Moves(S,B) , RG(S,B) , Cont(L,B) , AllGramesK(S,B)  `):end:

PSB:=proc(m,n) local i,j:
{
seq(seq([i,j],i=m+1..m+2*n-1),j=1..m),
seq(seq([i,j],i=1..2*m+2*n-1),j=m+1..m+2*n-1),
seq(seq([i,j],i=m+1..m+2*n-1),j=m+n+1..2*m+2*n-1)}
end:

IP:=proc(m,n): PSB(m,n) minus {[m+n,m+n]}: end:

#RHM(S,B): Given a position S in a peg-solitaire with board B, all the right horizontal moves in Peg Solitaire
RHM:=proc(S,B) local mo,s:

mo:={}:

for s in S do
 if member(s+[1,0],S) and  (not member(s+[2,0],S)) and member(s+[2,0],B) then
  mo:=mo union {S minus {s,s+[1,0]} union {s+[2,0]}}:
 fi:
od:

mo:

end:



#LHM(S,B): Given a position S in a peg-solitaire with board B, all the left  horizontal moves in Peg Solitaire
LHM:=proc(S,B) local mo,s:

mo:={}:

for s in S do
 if member(s-[1,0],S) and  (not member(s-[2,0],S)) and member(s-[2,0],B) then
  mo:=mo union {S minus {s,s-[1,0]} union {s-[2,0]}}:
 fi:
od:

mo:

end:



#UVM(S,B): Given a position S in a peg-solitaire with board B, all the up vertical  moves in Peg Solitaire
UVM:=proc(S,B) local mo,s:

mo:={}:

for s in S do
 if member(s+[0,1],S) and  (not member(s+[0,2],S)) and member(s+[0,2],B) then
  mo:=mo union {S minus {s,s+[0,1]} union {s+[0,2]}}:
 fi:
od:

mo:

end:


#DVM(S,B): Given a position S in a peg-solitaire with board B, all the down vertical  moves in Peg Solitaire
DVM:=proc(S,B) local mo,s:

mo:={}:

for s in S do
 if member(s-[0,1],S) and  (not member(s-[0,2],S)) and member(s-[0,2],B) then
  mo:=mo union {S minus {s,s-[0,1]} union {s-[0,2]}}:
 fi:
od:

mo:

end:

Moves:=proc(S,B):RHM(S,B) union LHM(S,B) union UVM(S,B) union DVM(S,B): end:


#RG(S,B): a random game
RG:=proc(S,B) local L,S1,mo:
L:=[S];

S1:=S:

while Moves(S1,B)<>{} do
 mo:=Moves(S1,B):
 S1:=mo[rand(1..nops(mo))()]:
 L:=[op(L),S1]:
od:

L:

end:

Cont:=proc(L,B) local la,gu,gu1:
 la:=L[-1]:
 gu:=Moves(la,B):
 {seq([op(L),gu1],gu1 in gu)}
end:


#AllGamesK(S,B,K) of length K
AllGamesK:=proc(S,B,K) local gu,gu1:
option remember:
if K=0 then
 RETURN({[S]}):
fi:

gu:=AllGamesK(S,B,K-1):

{seq(op(Cont(gu1,B)), gu1 in gu)}:

end: