(define "IncressPath"
    (is Path Edge Mover length:(exact (count Moves))) 
)

(define "HamiltonianCycle"
    (is Path Edge Mover length:(exact (count Sites "Board")) closed:True)
)

//---------------------------------------------------

(game "Icosian" 
    (players 1)
    (equipment { 
        (board 
            (graph
                vertices:{ 
                {4 0} {12 0} {5 3} {8 4} {11 3} {4 6} {6 7} {8 6} {10 7} {12 6} 
                {0 10} {3 9} {7 9} {9 9} {13 9} {16 10} {5 11} {11 11} {8 13} {8 16}}
                edges:{
                {0 1} {0 2} {0 10} {1 4} {1 15} {2 3} {2 5} {3 4} {3 7} {4 9} {5 6} 
                {5 11} {10 11} {11 16} {6 12} {6 7} {7 8} {8 9} {9 14} {14 15} {8 13} 
                {13 12} {12 16} {13 17} {14 17} {16 18} {18 17} {18 19} {10 19} {15 19}}
            )
            use:Vertex
        )   
    }) 
    
    (rules 
        phases:{
        (phase "Init" P1 
            (play 
                (move Add
                    (to
                        Edge 
                        (sites Empty Edge)	 
                    )
                )
            )
            (nextPhase "PathMaking") 
        )
        
        (phase "PathMaking" P1 
            (play 
                (or
                    (do 
                        (move Add
                            (to
                                Edge 
                                (sites Empty Edge)   
                            )
                        )
                        ifAfterwards:"IncressPath"
                    )
                    (do 
                        (move Add
                            (to
                                Edge 
                                (sites Empty Edge)
                            )
                        )
                        ifAfterwards:"HamiltonianCycle"
                    )
                )
            )	   
        )
        }  
        (end 	 	
            (if 
                (>= (count Moves) (count Sites "Board")) 
                (result Mover Win)
            )
        )
    )
)

//------------------------------------------------------------------------------

(metadata
    
    (info
        {
        (description "The Icosian Game was invented in 1857 by William Rowan Hamilton. It is also called the Hamiltonian game (Ball and Coxeter 1987, p. 262), is the problem of finding a Hamiltonian cycle along the edges of a dodecahedron. Hamilton sold this game to a London game dealer in 1859 for 25 pounds, and the game was subsequently marketed in Europe in a number of forms (Gardner 1957). The game marketed two versions of it, under the name Around the World. One version, for the parlor, was played on a flat board; another, for the traveler, consisted of an actual dodecahedron. In both cases, nails at each vertex stood for a major city of the world and the player wrapped a piece of string around these nails as they went. In the event, the game was a complete sales flop, mainly because it was too easy, even for children – but not for Hamilton himself who always used the icosian calculus to figure out his moves, instead of just trying different paths like everyone else!")
        (aliases {"Hamiltonian game"})
        (rules "The player aims to make a Hamiltonian cycle, which is a path in which each vertex is visited once, no edge is visited twice, and the ending point is the same as the starting point.")
        (id "615")
        (source "<a href=\"https://mathworld.wolfram.com/IcosianGame.html\" target=\"_blank\" class=\"style1\" style=\"color: #0000EE\" />mathworld</a> and <a href=\"https://www.daviddarling.info/encyclopedia/I/Icosian_Game.html\" target=\"_blank\" class=\"style1\" style=\"color: #0000EE\" />daviddarling</a>")
        (version "1.3.13")
        (classification "math/graph")
        (author "Sir William Rowan Hamilton")
        (credit "Tahmina Begum")
        (date "1857")
        }
    )
    
    (graphics {
        (player Colour P1 (colour Red))
        (board Style PenAndPaper replaceComponentsWithFilledCells:True)
        (show Edges Orthogonal ThinDotted)
    })
    
    (ai
        "Icosian_ai"
    )
)