There's a game I saw at a friend's yesterday, that I often see at people's homes, but never for enough time to think on it too hard. It's called peg solitaire (thanks @R.M) So I came home and I wanted to find a solution in Mathematica, so I did the following

There's a game I saw at a friend's yesterday, that I often see at people's homes, but never for enough time to think on it too hard. It's called peg solitaire (thanks @R.M). So I came home and I wanted to find a solution in Mathematica, so I did the following

(* solve, given a board tab, returns a list of subsequent moves to win, or $Failed *)
(* markTab is recursive. If a board is a success, marks it with $Success and makes all subsequent markTab calls return $NotNecessary *)
(* If a board is not a success and doesn't have any more moves, returns $Failed. If it has moves, it just calls itself on every board,
saving the move made in the head of the new boards. I know, weird *)
Module[{$Success,$NotNecessary, parseSol, $guard, markTab},

markTab[tab_/;Count[tab, 1, {2}]===1]:=$Success/;!($guard=False)/;$guard;
i:markTab[tab_]:=With[{moves=findMoves[tab]},(i=If[moves==={}, $Failed,(#[markTab@makeMove[tab, #]]&/@moves)])/;$guard];
markTab[tab_]/;!$guard:=$NotNecessary;

(* parseSol converts the tree returned by markTab into the list of moves until $Success, or in $Failed *)
parseSol[sol_]/;FreeQ[{sol}, $Success]:=$Failed;
parseSol[sol_]:=sol[[Apply[Sequence,#;;#&/@First@Position[sol, $Success]]]]//#/.r_Rule:>Null/;(Sow[r];False)&//Reap//#[[2, 1]]&;

solve[tab_]:=Block[{$guard=True},parseSol@markTab@tab];
]

(* solve, given a board tab, returns a list of subsequent moves to win, or $Failed *)
(* markTab is recursive. If a board is a success, marks it with $Success and makes all subsequent markTab calls return $NotNecessary *)
(* If a board is not a success and doesn't have any more moves, returns $Failed. If it has moves, it just calls itself on every board,
saving the move made in the head of the new boards. I know, weird *)
Module[{$Success,$NotNecessary, parseSol, $guard, markTab},

markTab[tab_/;Count[tab, 1, {2}]===1]:=$Success/;!($guard=False)/;$guard;
i:markTab[tab_]:=With[{moves=findMoves[tab]},(i=If[moves==={}, $Failed,(#[markTab@makeMove[tab, #]]&/@moves)])]/;$guard;
markTab[tab_]/;!$guard:=$NotNecessary;

(* parseSol converts the tree returned by markTab into the list of moves until $Success, or in $Failed *)
parseSol[sol_]/;FreeQ[{sol}, $Success]:=$Failed;
parseSol[sol_]:=sol[[Apply[Sequence,#;;#&/@First@Position[sol, $Success]]]]//#/.r_Rule:>Null/;(Sow[r];False)&//Reap//#[[2, 1]]&;

solve[tab_]:=Block[{$guard=True},parseSol@markTab@tab];
]