Gamemaster General Game Playing minorities Description Minorities is played on a made of hexagonal cells. The board is initially empty, except for six unusable cells. The first player places a stone on any unoccupied cell, then players take turns placing pieces on empty cells. A majority of stones in a line wins that line. A majority of parallel lines in a direction wins that direction. A majority of directions wins the game. The value for any state is the number of lines in which it has a majority until it achieves majorities in two directions, at which point the value is 100. Rulesheet %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% minorities %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% metadata %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% role(red) role(blue) base(cell(M,N,R)) :- oob(M,N) & role(R) base(line_count(Id,R,Count)) :- line_id(Id) & role(R) & num(Count) base(num_letter_lines(R,Count)) :- role(R) & num(Count) base(num_number_lines(R,Count)) :- role(R) & num(Count) base(num_vertical_lines(R,Count)) :- role(R) & num(Count) base(control(R)) :- role(R) action(place(M,N)) :- oob(M,N) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% init %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% init(line_count(Id,R,0)) :- line_id(Id) & role(R) init(num_letter_lines(R,0)) :- role(R) init(num_number_lines(R,0)) :- role(R) init(num_vertical_lines(R,0)) :- role(R) init(control(red)) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% legal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% legal(place(M,N)) :- oob(M,N) & ~cell(M,N,red) & ~cell(M,N,blue) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% operations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% place(M,N) :: control(R) ==> cell(M,N,R) place(M,N) :: control(R) & in_line(Id,M,N) & line_count(Id,R,Prev) & succ(Prev,Count) ==> ~line_count(Id,R,Prev) & line_count(Id,R,Count) place(M,N) :: control(R) & inrow(Id,M,N) & one_short_of_line_majority(Id,R) & num_letter_lines(R,Prev) & succ(Prev,Count) ==> ~num_letter_lines(R,Prev) & num_letter_lines(R,Count) place(M,N) :: control(R) & incol(Id,M,N) & one_short_of_line_majority(Id,R) & num_number_lines(R,Prev) & succ(Prev,Count) ==> ~num_number_lines(R,Prev) & num_number_lines(R,Count) place(M,N) :: control(R) & inver(Id,M,N) & one_short_of_line_majority(Id,R) & num_vertical_lines(R,Prev) & succ(Prev,Count) ==> ~num_vertical_lines(R,Prev) & num_vertical_lines(R,Count) place(M,N) :: control(red) ==> ~control(red) & control(blue) place(M,N) :: control(blue) ==> ~control(blue) & control(red) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% goal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% goal(R,100) :- majority_numbers(R) & majority_letters(R) goal(R,100) :- majority_numbers(R) & majority_verticals(R) goal(R,100) :- majority_letters(R) & majority_verticals(R) goal(R,N) :- ~majority_numbers(R) & ~majority_letters(R) & num_lines(R,N) goal(R,N) :- ~majority_numbers(R) & ~majority_verticals(R) & num_lines(R,N) goal(R,N) :- ~majority_letters(R) & ~majority_verticals(R) & num_lines(R,N) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% terminal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% terminal :- goal(R,100) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Views %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% num_lines(R,N) :- num_letter_lines(R,X) & num_number_lines(R,Y) & num_vertical_lines(R,Z) & plus(X,Y,Z,N) majority_letters(R) :- num_letter_lines(R,5) majority_letters(R) :- num_letter_lines(R,6) majority_letters(R) :- num_letter_lines(R,7) majority_numbers(R) :- num_number_lines(R,5) majority_numbers(R) :- num_number_lines(R,6) majority_numbers(R) :- num_number_lines(R,7) majority_verticals(R) :- num_vertical_lines(R,5) majority_verticals(R) :- num_vertical_lines(R,6) majority_verticals(R) :- num_vertical_lines(R,7) line_id(Id) :- row(Id) line_id(Id) :- col(Id) line_id(Id) :- ver(Id) in_line(Id,M,N) :- inrow(Id,M,N) in_line(Id,M,N) :- incol(Id,M,N) in_line(Id,M,N) :- inver(Id,M,N) inrow(M,M,N) :- row(M) & col(N) incol(N,M,N) :- row(M) & col(N) one_short_of_line_majority(Id,R) :- maj(Id,Maj_req) & succ(One_short,Maj_req) & line_count(Id,R,One_short) & ~line_count(Id,R,Maj_req) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Data %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% row(a) row(b) row(c) row(d) row(e) row(f) row(g) row(h) row(i) col(1) col(2) col(3) col(4) col(5) col(6) col(7) col(8) col(9) ver(a5) ver(a6) ver(a7) ver(a8) ver(a9) ver(b9) ver(c9) ver(d9) ver(e9) inver(a5,a,5) inver(a5,b,4) inver(a5,c,3) inver(a5,d,2) inver(a5,e,1) inver(a6,a,6) inver(a6,b,5) inver(a6,c,4) inver(a6,d,3) inver(a6,e,2) inver(a6,f,1) inver(a7,a,7) inver(a7,b,6) inver(a7,c,5) inver(a7,d,4) inver(a7,e,3) inver(a7,f,2) inver(a7,g,1) inver(a8,a,8) inver(a8,b,7) inver(a8,c,6) inver(a8,d,5) inver(a8,e,4) inver(a8,f,3) inver(a8,g,2) inver(a8,h,1) inver(a9,a,9) inver(a9,b,8) inver(a9,c,7) inver(a9,d,6) inver(a9,e,5) inver(a9,f,4) inver(a9,g,3) inver(a9,h,2) inver(a9,i,1) inver(b9,b,9) inver(b9,c,8) inver(b9,d,7) inver(b9,e,6) inver(b9,f,5) inver(b9,g,4) inver(b9,h,3) inver(b9,i,2) inver(c9,c,9) inver(c9,d,8) inver(c9,e,7) inver(c9,f,6) inver(c9,g,5) inver(c9,h,4) inver(c9,i,3) inver(d9,d,9) inver(d9,e,8) inver(d9,f,7) inver(d9,g,6) inver(d9,h,5) inver(d9,i,4) inver(e9,e,9) inver(e9,f,8) inver(e9,g,7) inver(e9,h,6) inver(e9,i,5) oob(a,5) oob(a,6) oob(a,7) oob(a,8) oob(a,9) oob(b,4) oob(b,5) oob(b,6) oob(b,7) oob(b,9) oob(c,3) oob(c,4) oob(c,5) oob(c,6) oob(c,7) oob(c,8) oob(c,9) oob(d,2) oob(d,3) oob(d,4) oob(d,5) oob(d,7) oob(d,8) oob(d,9) oob(e,1) oob(e,3) oob(e,5) oob(e,6) oob(e,7) oob(e,8) oob(e,9) oob(f,1) oob(f,2) oob(f,3) oob(f,4) oob(f,6) oob(f,7) oob(f,8) oob(g,1) oob(g,2) oob(g,3) oob(g,4) oob(g,5) oob(g,6) oob(g,7) oob(h,1) oob(h,2) oob(h,3) oob(h,4) oob(h,6) oob(i,1) oob(i,2) oob(i,3) oob(i,4) oob(i,5) maj(a,3) maj(b,3) maj(c,4) maj(d,4) maj(e,4) maj(f,4) maj(g,4) maj(h,3) maj(i,3) maj(1,3) maj(2,3) maj(3,4) maj(4,4) maj(5,4) maj(6,4) maj(7,4) maj(8,3) maj(9,3) maj(a5,3) maj(a6,3) maj(a7,4) maj(a8,4) maj(a9,4) maj(b9,4) maj(c9,4) maj(d9,3) maj(e9,3) num(0) num(1) num(2) num(3) num(4) num(5) num(6) num(7) succ(0,1) succ(1,2) succ(2,3) succ(3,4) succ(4,5) succ(5,6) succ(6,7) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Stylesheet //------------------------------------------------------------------------------ // Majorities //------------------------------------------------------------------------------ function renderstate (state) {var role = compfindx('R',seq('control','R'),state,library); var redrows = compfindx('N',seq('num_letter_lines','red','N'),state,library); var redcols = compfindx('N',seq('num_number_lines','red','N'),state,library); var redvert = compfindx('N',seq('num_vertical_lines','red','N'),state,library); var bluerows = compfindx('N',seq('num_letter_lines','blue','N'),state,library); var bluecols = compfindx('N',seq('num_number_lines','blue','N'),state,library); var bluevert = compfindx('N',seq('num_vertical_lines','blue','N'),state,library); var table = document.createElement('table'); table.setAttribute('border','0'); row = table.insertRow(0); var cell = row.insertCell(0); cell.innerHTML = "Rows: " + redrows + "<br/>Columns: " + redcols + "<br/>Verticals: " + redvert; cell = row.insertCell(1); var board = renderboard(state); cell.appendChild(board); cell = row.insertCell(2); cell.innerHTML = "Rows: " + bluerows + "<br/>Columns: " + bluecols + "<br/>Verticals: " + bluevert; row = table.insertRow(1); var cell = row.insertCell(0); cell.setAttribute('colspan',3); cell.setAttribute('align','center'); cell.setAttribute('style','font-size:20px'); if (compfindp('terminal',state,library)) {cell.innerHTML = 'Game over'} else {cell.innerHTML = 'Control: ' + role}; return table} function renderboard (state) {var canvas = document.createElement('canvas'); canvas.setAttribute('width','340px'); canvas.setAttribute('height','441px'); drawhex(140, 40,canvas); drawhex(110, 60,canvas); drawhex(170, 60,canvas); drawhex(80, 80,canvas); drawblack(140, 80,canvas); drawhex(200, 80,canvas); drawhex(50,100,canvas); drawhex(110,100,canvas); drawhex(170,100,canvas); drawhex(230,100,canvas); drawhex(20,120,canvas); drawhex(80,120,canvas); drawhex(140,120,canvas); drawhex(200,120,canvas); drawhex(260,120,canvas); drawhex(50,140,canvas); drawhex(110,140,canvas); drawhex(170,140,canvas); drawhex(230,140,canvas); drawhex(20,160,canvas); drawhex(80,160,canvas); drawblack(140,160,canvas); drawhex(200,160,canvas); drawhex(260,160,canvas); drawhex(50,180,canvas); drawhex(110,180,canvas); drawhex(170,180,canvas); drawhex(230,180,canvas); drawhex(20,200,canvas); drawhex(80,200,canvas); drawhex(140,200,canvas); drawhex(200,200,canvas); drawhex(260,200,canvas); drawhex(50,220,canvas); drawblack(110,220,canvas); drawblack(170,220,canvas); drawhex(230,220,canvas); drawhex(20,240,canvas); drawhex(80,240,canvas); drawhex(140,240,canvas); drawhex(200,240,canvas); drawhex(260,240,canvas); drawblack(50,260,canvas); drawhex(110,260,canvas); drawhex(170,260,canvas); drawblack(230,260,canvas); drawhex(20,280,canvas); drawhex(80,280,canvas); drawhex(140,280,canvas); drawhex(200,280,canvas); drawhex(260,280,canvas); drawhex(50,300,canvas); drawhex(110,300,canvas); drawhex(170,300,canvas); drawhex(230,300,canvas); drawhex(80,320,canvas); drawhex(140,320,canvas); drawhex(200,320,canvas); drawhex(110,340,canvas); drawhex(170,340,canvas); drawhex(140,360,canvas); for (var i=0; i<state.length; i++) {if (state[i][0]=='cell') {var x = xpos(state[i][1],state[i][2]); var y = ypos(state[i][1],state[i][2]); if (state[i][3]=='red') {drawred(x,y,canvas)}; if (state[i][3]=='blue') {drawblue(x,y,canvas)}}}; return canvas} function xpos (m,n) {return xm(m)+xn(n)-100} function ypos (m,n) {return 200+ym(m)-yn(n)} function xm (m) {if (m=='a') {return 0}; if (m=='b') {return 30}; if (m=='c') {return 60}; if (m=='d') {return 90}; if (m=='e') {return 120}; if (m=='f') {return 150}; if (m=='g') {return 180}; if (m=='h') {return 210}; if (m=='i') {return 240}; return 330} function ym (m) {if (m=='a') {return 0}; if (m=='b') {return 20}; if (m=='c') {return 40}; if (m=='d') {return 60}; if (m=='e') {return 80}; if (m=='f') {return 100}; if (m=='g') {return 120}; if (m=='h') {return 140}; if (m=='i') {return 160}; return 330} function yn (n) {if (n=='1') {return 0}; if (n=='2') {return 20}; if (n=='3') {return 40}; if (n=='4') {return 60}; if (n=='5') {return 80}; if (n=='6') {return 100}; if (n=='7') {return 120}; if (n=='8') {return 140}; if (n=='9') {return 160}; return 330} function xn (n) {if (n=='1') {return 0}; if (n=='2') {return 30}; if (n=='3') {return 60}; if (n=='4') {return 90}; if (n=='5') {return 120}; if (n=='6') {return 150}; if (n=='7') {return 180}; if (n=='8') {return 210}; if (n=='9') {return 240}; return 330} //------------------------------------------------------------------------------ // Drawing subroutines //------------------------------------------------------------------------------ // function drawhex (x,y,w) // {var ctx = w.getContext('2d'); // ctx.beginPath(); // ctx.lineWidth=1; // ctx.moveTo(x+10,y+ 0); // ctx.lineTo(x+30,y+ 0); // ctx.lineTo(x+40,y+20); // ctx.lineTo(x+30,y+40); // ctx.lineTo(x+10,y+40); // ctx.lineTo( x+0,y+20); // ctx.closePath(); // ctx.fillStyle = "#fff0f0"; // ctx.fill(); // ctx.stroke()} // // function drawhex (x,y,w) // {var ctx = w.getContext('2d'); // ctx.beginPath(); // ctx.lineWidth=1; // ctx.moveTo(x+10,y+ 0); // ctx.lineTo(x+30,y+ 0); // ctx.lineTo(x+40,y+20); // ctx.lineTo(x+30,y+40); // ctx.lineTo(x+10,y+40); // ctx.lineTo( x+0,y+20); // ctx.closePath(); // ctx.fillStyle = "#dddddd"; // ctx.fill(); // ctx.stroke()} function drawhex (x,y,canvas) {drawline(x+ 0,y+20,x+10,y+ 0,canvas); drawline(x+10,y+ 0,x+30,y+ 0,canvas); drawline(x+30,y+ 0,x+40,y+20,canvas); drawline(x+40,y+20,x+30,y+40,canvas); drawline(x+30,y+40,x+10,y+40,canvas); drawline(x+10,y+40, x+0,y+20,canvas)} function drawred (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=2; ctx.arc(x+20,y+20,12,0,2*Math.PI,false); ctx.stroke(); ctx.fillStyle = "#ff8888"; ctx.fill();} function drawblue (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=2; ctx.arc(x+20,y+20,12,0,2*Math.PI,false); ctx.stroke(); ctx.fillStyle = "#8888ff"; ctx.fill();} function drawblack (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=2; ctx.arc(x+20,y+20,12,0,2*Math.PI,false); ctx.stroke(); ctx.fillStyle = "#000000"; ctx.fill();} function drawblank (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=2; ctx.arc(x+20,y+20,12,0,2*Math.PI,false); ctx.stroke(); ctx.fillStyle = "#ffffff"; ctx.fill();} function drawline(u,v,x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=1; ctx.moveTo(u,v); ctx.lineTo(x,y); ctx.stroke()} function drawnode (node,x,y,canvas) {var mark = compfindx('X',seq('cell',node,'X'),state,library); if (mark=='red') {drawred(x,y,canvas); return true}; if (mark=='black') {drawblack(x,y,canvas); return true}; drawblank(x,y,canvas); return true} function drawtext (text,x,y,w) {var ctx = w.getContext('2d'); ctx.fillStyle = "#000000"; ctx.font="italic 14px Times" ctx.fillText(text,x+12,y+18); return true} function drawscore (text,x,y,w) {var ctx = w.getContext('2d'); ctx.fillStyle = "#000000"; ctx.font="28px Times" ctx.fillText(text,x+12,y+18); return true} //------------------------------------------------------------------------------ //------------------------------------------------------------------------------ //------------------------------------------------------------------------------ Ownership