Ultimate Tic-Tac-Toe
2021-01-08 12:42
This applet demonstrates the board construction for Ultimate Tic-Tac-Toe. Using polygon commands, it renders a large 3x3 grid composed of 9 smaller tic-tac-toe boards, illustrating the visual layout of combinatorial games on geometric grids, suitable for logical strategy analysis and discrete math board modeling.
In collections
Math Games with GeoGebra
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<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m1(2) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(1,2)]"/>
</element>
<command name="Polygon">
<input a0="{(2, 8), (2 + 1, 8), (2 + 1, 8 + 1), (2, 8 + 1)}"/>
<output a0="p13"/>
</command>
<element type="polygon" label="p13">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m1(3) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(1,3)]"/>
</element>
<command name="Polygon">
<input a0="{(3, 8), (3 + 1, 8), (3 + 1, 8 + 1), (3, 8 + 1)}"/>
<output a0="p21"/>
</command>
<element type="polygon" label="p21">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m2(1) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(2,1)]"/>
</element>
<command name="Polygon">
<input a0="{(4, 8), (4 + 1, 8), (4 + 1, 8 + 1), (4, 8 + 1)}"/>
<output a0="p22"/>
</command>
<element type="polygon" label="p22">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m2(2) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(2,2)]"/>
</element>
<command name="Polygon">
<input a0="{(5, 8), (5 + 1, 8), (5 + 1, 8 + 1), (5, 8 + 1)}"/>
<output a0="p23"/>
</command>
<element type="polygon" label="p23">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m2(3) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(2,3)]"/>
</element>
<command name="Polygon">
<input a0="{(6, 8), (6 + 1, 8), (6 + 1, 8 + 1), (6, 8 + 1)}"/>
<output a0="p31"/>
</command>
<element type="polygon" label="p31">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m3(1) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(3,1)]"/>
</element>
<command name="Polygon">
<input a0="{(7, 8), (7 + 1, 8), (7 + 1, 8 + 1), (7, 8 + 1)}"/>
<output a0="p32"/>
</command>
<element type="polygon" label="p32">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m3(2) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(3,2)]"/>
</element>
<command name="Polygon">
<input a0="{(8, 8), (8 + 1, 8), (8 + 1, 8 + 1), (8, 8 + 1)}"/>
<output a0="p33"/>
</command>
<element type="polygon" label="p33">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m3(3) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(3,3)]"/>
</element>
<command name="Polygon">
<input a0="{(0, 8), (0 + 1, 8), (0 + 1, 8 + 1), (0, 8 + 1)}"/>
<output a0="p11"/>
</command>
<element type="polygon" label="p11">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="m1(1) ≟ 0"/>
<objColor r="255" g="255" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[F,(1,1)]"/>
</element>
<expression label="F" exp="(6, 9)" type="point"/>
<element type="point" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="RunClickScript(buttonScript)"/>
<coords x="6" y="9" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="m1" exp="{1, -1, -1, 0, 1, -1, 0, 1, -1}"/>
<element type="list" label="m1">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<ggbscript val="If[((m1(1)+m1(2)+m1(3)==3)||(m1(4)+m1(5)+m1(6)==3)||(m1(7)+m1(8)+m1(9)==3)||(m1(1)+m1(4)+m1(7)==3)||(m1(2)+m1(5)+m1(8)==3)||(m1(3)+m1(6)+m1(9)==3)||(m1(1)+m1(5)+m1(9)==3)||(m1(3)+m1(5)+m1(7)==3))&&mL(1)==0,SetValue(mL,1,1)]

If[((m1(1)+m1(2)+m1(3)==-3)||(m1(4)+m1(5)+m1(6)==-3)||(m1(7)+m1(8)+m1(9)==-3)||(m1(1)+m1(4)+m1(7)==-3)||(m1(2)+m1(5)+m1(8)==-3)||(m1(3)+m1(6)+m1(9)==-3)||(m1(1)+m1(5)+m1(9)==-3)||(m1(3)+m1(5)+m1(7)==-3))&&mL(1)==0,SetValue(mL,1,-1)]"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="m2" exp="{0, 1, 1, -1, 0, 0, -1, -1, 0}"/>
<element type="list" label="m2">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="m3" exp="{-1, 0, 0, -1, 1, 0, -1, 1, 1}"/>
<element type="list" label="m3">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="m4" exp="{1, 0, 0, 0, 1, 0, 0, 0, 1}"/>
<element type="list" label="m4">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="m5" exp="{0, 0, -1, 0, -1, 0, -1, 0, 1}"/>
<element type="list" label="m5">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="m6" exp="{0, 0, 0, 0, 1, 0, 0, 0, 1}"/>
<element type="list" label="m6">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="m7" exp="{1, 1, 1, 0, 0, 0, 0, 0, 0}"/>
<element type="list" label="m7">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="m8" exp="{-1, -1, 0, 0, 1, 0, 0, 0, 1}"/>
<element type="list" label="m8">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="m9" exp="{-1, 1, -1, -1, 0, -1, 0, -1, 0}"/>
<element type="list" label="m9">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
<symbolic val="true" />
</element>
<element type="numeric" label="act">
<value val="9"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<element type="button" label="buttonScript">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelOffset x="577" y="788"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[FtoSC,(Mod(x(F) - 1, 3) * 3 + Mod(y(F) - 1, 3) + 0.5, -floor((x(F) - 1) / 3) * 3 - floor((y(F) - 1) / 3) + 8.5)]

If[turn==true,Execute({"SetValue[m"+x(F)+","+y(F)+",1]"}),Execute({"SetValue[m"+x(F)+","+y(F)+",-1]"})]
If[turn==true,SetValue[sCircles,Append(sCircles,FtoSC)],SetValue[sCrosses,Append(sCrosses,FtoSC)]]

Execute[{"If[((m"+x(F)+"(1)+m"+x(F)+"(2)+m"+x(F)+"(3)==3)||(m"+x(F)+"(4)+m"+x(F)+"(5)+m"+x(F)+"(6)==3)||(m"+x(F)+"(7)+m"+x(F)+"(8)+m"+x(F)+"(9)==3)||(m"+x(F)+"(1)+m"+x(F)+"(4)+m"+x(F)+"(7)==3)||(m"+x(F)+"(2)+m"+x(F)+"(5)+m"+x(F)+"(8)==3)||(m"+x(F)+"(3)+m"+x(F)+"(6)+m"+x(F)+"(9)==3)||(m"+x(F)+"(1)+m"+x(F)+"(5)+m"+x(F)+"(9)==3)||(m"+x(F)+"(3)+m"+x(F)+"(5)+m"+x(F)+"(7)==3))&&mL("+x(F)+")==0,SetValue(mL,"+x(F)+",1)]"}]

Execute[{"If[((m"+x(F)+"(1)+m"+x(F)+"(2)+m"+x(F)+"(3)==-3)||(m"+x(F)+"(4)+m"+x(F)+"(5)+m"+x(F)+"(6)==-3)||(m"+x(F)+"(7)+m"+x(F)+"(8)+m"+x(F)+"(9)==-3)||(m"+x(F)+"(1)+m"+x(F)+"(4)+m"+x(F)+"(7)==-3)||(m"+x(F)+"(2)+m"+x(F)+"(5)+m"+x(F)+"(8)==-3)||(m"+x(F)+"(3)+m"+x(F)+"(6)+m"+x(F)+"(9)==-3)||(m"+x(F)+"(1)+m"+x(F)+"(5)+m"+x(F)+"(9)==-3)||(m"+x(F)+"(3)+m"+x(F)+"(5)+m"+x(F)+"(7)==-3))&&mL("+x(F)+")==0,SetValue(mL,"+x(F)+",-1)]"}]

Execute[{"If[mL(y(F))==0&&0∈m"+y(F)+",SetValue[act,y(F)],SetValue[act,0]]"}]
If[bCircleWin==true||bCrossWin==true,SetValue(act,-1)]
If[bCircleWin==true||bCrossWin==true,SetValue(showResult,true)]

SetValue[turn,!turn]"/>
<font serif="false" sizeM="2" size="20" style="0"/>
</element>
<element type="boolean" label="turn">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="sCircles" exp="{(5.5, 3.5), (7.5, 6.5), (4.5, 8.5), (2.5, 2.5), (0.5, 2.5), (7.5, 2.5), (4.5, 1.5), (1.5, 2.5), (1.5, 4.5), (8.5, 6.5), (5.5, 0.5), (2.5, 3.5), (0.5, 8.5), (7.5, 7.5), (1.5, 6.5), (1.5, 7.5), (5.5, 8.5), (0.5, 5.5), (7.5, 4.5), (8.5, 3.5)}"/>
<element type="list" label="sCircles">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="25"/>
<pointStyle val="2"/>
<angleStyle val="0"/>
</element>
<expression label="sCrosses" exp="{(4.5, 4.5), (8.5, 2.5), (4.5, 2.5), (3.5, 6.5), (6.5, 6.5), (2.5, 6.5), (4.5, 6.5), (3.5, 3.5), (3.5, 7.5), (5.5, 5.5), (7.5, 0.5), (6.5, 1.5), (6.5, 2.5), (2.5, 8.5), (6.5, 8.5), (3.5, 2.5), (1.5, 8.5), (6.5, 7.5), (2.5, 7.5), (8.5, 1.5)}"/>
<element type="list" label="sCrosses">
<show object="true" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="24"/>
<pointStyle val="1"/>
<angleStyle val="0"/>
</element>
<element type="button" label="buttonReset">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="9"/>
<labelOffset x="290" y="766"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="m1={0,0,0,0,0,0,0,0,0}
m2={0,0,0,0,0,0,0,0,0}
m3={0,0,0,0,0,0,0,0,0}
m4={0,0,0,0,0,0,0,0,0}
m5={0,0,0,0,0,0,0,0,0}
m6={0,0,0,0,0,0,0,0,0}
m7={0,0,0,0,0,0,0,0,0}
m8={0,0,0,0,0,0,0,0,0}
m9={0,0,0,0,0,0,0,0,0}
mL={0,0,0,0,0,0,0,0,0}

act=0
sCircles={}
sCrosses={}
turn=false
showResult=false
"/>
<font serif="false" sizeM="3" size="40" style="1"/>
<dimensions width="220" height="90" />
<startPoint x="3.2" y="-0.2" z="1"/>
<caption val="New Game"/>
</element>
<expression label="borderS" exp="{Sequence[Segment[(k, 0), (k, 9)], k, 1, 8], Sequence[Segment[(0, k), (9, k)], k, 1, 8]}" />
<element type="list" label="borderS">
<show object="true" label="false" ev="4"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="borderL" exp="{Sequence[Segment[((3 * k), 0), ((3 * k), 9)], k, 1, 2], Sequence[Segment[(0, (3 * k)), (9, (3 * k))], k, 1, 2]}" />
<element type="list" label="borderL">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<element type="point" label="FtoSC">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="8.5" y="3.5" z="1"/>
<pointSize val="9"/>
<pointStyle val="1"/>
</element>
<command name="Polygon">
<input a0="{(0, 6), (3, 6), (3, 9), (0, 9)}"/>
<output a0="polyMask1"/>
</command>
<element type="polygon" label="polyMask1">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM1"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(3, 6), (6, 6), (6, 9), (3, 9)}"/>
<output a0="polyMask2"/>
</command>
<element type="polygon" label="polyMask2">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM2"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(6, 6), (9, 6), (9, 9), (6, 9)}"/>
<output a0="polyMask3"/>
</command>
<element type="polygon" label="polyMask3">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM3"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(0, 3), (3, 3), (3, 6), (0, 6)}"/>
<output a0="polyMask4"/>
</command>
<element type="polygon" label="polyMask4">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM4"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(3, 3), (6, 3), (6, 6), (3, 6)}"/>
<output a0="polyMask5"/>
</command>
<element type="polygon" label="polyMask5">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM5"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(6, 3), (9, 3), (9, 6), (6, 6)}"/>
<output a0="polyMask6"/>
</command>
<element type="polygon" label="polyMask6">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM6"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(0, 0), (3, 0), (3, 3), (0, 3)}"/>
<output a0="polyMask7"/>
</command>
<element type="polygon" label="polyMask7">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM7"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(3, 0), (6, 0), (6, 3), (3, 3)}"/>
<output a0="polyMask8"/>
</command>
<element type="polygon" label="polyMask8">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM8"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(6, 0), (9, 0), (9, 3), (6, 3)}"/>
<output a0="polyMask9"/>
</command>
<element type="polygon" label="polyMask9">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬showM9"/>
<objColor r="255" g="255" b="255" alpha="0.01" dynamicr="¬turn" dynamicg="0" dynamicb="turn" dynamica="0.01" colorSpace="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<command name="Polygon">
<input a0="{(0, 6), (3, 6), (3, 9), (0, 9)}"/>
<output a0="polyFocus1"/>
</command>
<element type="polygon" label="polyFocus1">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM1"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{(3, 6), (6, 6), (6, 9), (3, 9)}"/>
<output a0="polyFocus2"/>
</command>
<element type="polygon" label="polyFocus2">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM2"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{(6, 6), (9, 6), (9, 9), (6, 9)}"/>
<output a0="polyFocus3"/>
</command>
<element type="polygon" label="polyFocus3">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM3"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{(0, 3), (3, 3), (3, 6), (0, 6)}"/>
<output a0="polyFocus4"/>
</command>
<element type="polygon" label="polyFocus4">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM4"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{(3, 3), (6, 3), (6, 6), (3, 6)}"/>
<output a0="polyFocus5"/>
</command>
<element type="polygon" label="polyFocus5">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM5"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{(6, 3), (9, 3), (9, 6), (6, 6)}"/>
<output a0="polyFocus6"/>
</command>
<element type="polygon" label="polyFocus6">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM6"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{(0, 0), (3, 0), (3, 3), (0, 3)}"/>
<output a0="polyFocus7"/>
</command>
<element type="polygon" label="polyFocus7">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM7"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{(3, 0), (6, 0), (6, 3), (3, 3)}"/>
<output a0="polyFocus8"/>
</command>
<element type="polygon" label="polyFocus8">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM8"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{(6, 0), (9, 0), (9, 3), (6, 3)}"/>
<output a0="polyFocus9"/>
</command>
<element type="polygon" label="polyFocus9">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showM9"/>
<objColor r="153" g="51" b="0" alpha="0.1" dynamicr="turn" dynamicg="0.2" dynamicb="¬turn" dynamica="0.1" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
</element>
<expression label="mL" exp="{-1, 0, -1, 1, -1, 0, 1, 0, 0}"/>
<element type="list" label="mL">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="lCircles" exp="{If[mL(1) ≟ 1, (1.5, 7.5)], If[mL(2) ≟ 1, (4.5, 7.5)], If[mL(3) ≟ 1, (7.5, 7.5)], If[mL(4) ≟ 1, (1.5, 4.5)], If[mL(5) ≟ 1, (4.5, 4.5)], If[mL(6) ≟ 1, (7.5, 4.5)], If[mL(7) ≟ 1, (1.5, 1.5)], If[mL(8) ≟ 1, (4.5, 1.5)], If[mL(9) ≟ 1, (7.5, 1.5)]}" />
<element type="list" label="lCircles">
<show object="true" label="false" ev="4"/>
<objColor r="220" g="20" b="60" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="90"/>
<pointStyle val="2"/>
<angleStyle val="0"/>
</element>
<expression label="lCrosses" exp="{If[mL(1) ≟ -1, (1.5, 7.5)], If[mL(2) ≟ -1, (4.5, 7.5)], If[mL(3) ≟ -1, (7.5, 7.5)], If[mL(4) ≟ -1, (1.5, 4.5)], If[mL(5) ≟ -1, (4.5, 4.5)], If[mL(6) ≟ -1, (7.5, 4.5)], If[mL(7) ≟ -1, (1.5, 1.5)], If[mL(8) ≟ -1, (4.5, 1.5)], If[mL(9) ≟ -1, (7.5, 1.5)]}" />
<element type="list" label="lCrosses">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="85"/>
<pointStyle val="1"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="sCircleSize">
<value val="25"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="8"/>
<labelMode val="1"/>
<slider min="15" max="40" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetPointSize( sCircles, sCircleSize )"/>
</element>
<element type="numeric" label="sCrossSize">
<value val="24"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="8"/>
<labelMode val="1"/>
<slider min="15" max="40" absoluteScreenLocation="true" width="200" x="30" y="90" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetPointSize( sCrosses, sCrossSize )"/>
</element>
<element type="numeric" label="lCircleSize">
<value val="90"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="8"/>
<labelMode val="1"/>
<slider min="50" max="120" absoluteScreenLocation="true" width="200" x="30" y="130" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="5" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetPointSize( lCircles, lCircleSize )"/>
</element>
<element type="numeric" label="lCrossSize">
<value val="85"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="8"/>
<labelMode val="1"/>
<slider min="60" max="120" absoluteScreenLocation="true" width="200" x="30" y="170" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="5" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetPointSize( lCrosses, lCrossSize )"/>
</element>
<expression label="showM1" exp="(act ≟ 1 ∨ act ≟ 0) ∧ mL(1) ≟ 0 ∧ 0 ∈ m1" />
<element type="boolean" label="showM1">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showM2" exp="(act ≟ 2 ∨ act ≟ 0) ∧ mL(2) ≟ 0 ∧ 0 ∈ m2" />
<element type="boolean" label="showM2">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showM3" exp="(act ≟ 3 ∨ act ≟ 0) ∧ mL(3) ≟ 0 ∧ 0 ∈ m3" />
<element type="boolean" label="showM3">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showM4" exp="(act ≟ 4 ∨ act ≟ 0) ∧ mL(4) ≟ 0 ∧ 0 ∈ m4" />
<element type="boolean" label="showM4">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showM5" exp="(act ≟ 5 ∨ act ≟ 0) ∧ mL(5) ≟ 0 ∧ 0 ∈ m5" />
<element type="boolean" label="showM5">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showM6" exp="(act ≟ 6 ∨ act ≟ 0) ∧ mL(6) ≟ 0 ∧ 0 ∈ m6" />
<element type="boolean" label="showM6">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showM7" exp="(act ≟ 7 ∨ act ≟ 0) ∧ mL(7) ≟ 0 ∧ 0 ∈ m7" />
<element type="boolean" label="showM7">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showM8" exp="(act ≟ 8 ∨ act ≟ 0) ∧ mL(8) ≟ 0 ∧ 0 ∈ m8" />
<element type="boolean" label="showM8">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showM9" exp="(act ≟ 9 ∨ act ≟ 0) ∧ mL(9) ≟ 0 ∧ 0 ∈ m9" />
<element type="boolean" label="showM9">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="bCircleWin" exp="mL(1) + mL(2) + mL(3) ≟ 3 ∨ mL(4) + mL(5) + mL(6) ≟ 3 ∨ mL(7) + mL(8) + mL(9) ≟ 3 ∨ mL(1) + mL(4) + mL(7) ≟ 3 ∨ mL(2) + mL(5) + mL(8) ≟ 3 ∨ mL(3) + mL(6) + mL(9) ≟ 3 ∨ mL(1) + mL(5) + mL(9) ≟ 3 ∨ mL(3) + mL(5) + mL(7) ≟ 3" />
<element type="boolean" label="bCircleWin">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If[bCircleWin==true,SetValue(act,-1)]"/>
</element>
<expression label="bCrossWin" exp="mL(1) + mL(2) + mL(3) ≟ -3 ∨ mL(4) + mL(5) + mL(6) ≟ -3 ∨ mL(7) + mL(8) + mL(9) ≟ -3 ∨ mL(1) + mL(4) + mL(7) ≟ -3 ∨ mL(2) + mL(5) + mL(8) ≟ -3 ∨ mL(3) + mL(6) + mL(9) ≟ -3 ∨ mL(1) + mL(5) + mL(9) ≟ -3 ∨ mL(3) + mL(5) + mL(7) ≟ -3" />
<element type="boolean" label="bCrossWin">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If[bCrossWin==true,SetValue(act,-1)]"/>
</element>
<command name="Polygon">
<input a0="{Corner[1], Corner[2], Corner[3], Corner[4]}"/>
<output a0="polyMask"/>
</command>
<element type="polygon" label="polyMask">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showResult"/>
<objColor r="0" g="0" b="0" alpha="0.7900000214576721"/>
<layer val="8"/>
<labelMode val="0"/>
<ggbscript val="SetValue[showResult,false]"/>
</element>
<expression label="showResult" exp="false"/>
<element type="boolean" label="showResult">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="textCircleWin" exp=""遊戲結束
紅方(O) 獲勝！
Game Over
The Red(O) player wins!""/>
<element type="text" label="textCircleWin">
<show object="true" label="false" ev="40"/>
<condition showObject="showResult ∧ bCircleWin"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<bgColor r="0" g="0" b="0" alpha="255"/>
<layer val="8"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="2" size="20" style="1"/>
<startPoint x="2" y="5.5" z="1"/>
</element>
<expression label="textCrossWin" exp=""遊戲結束
藍方(X) 獲勝！
Game Over
The Blue(X) player wins!""/>
<element type="text" label="textCrossWin">
<show object="true" label="false" ev="40"/>
<condition showObject="showResult ∧ bCrossWin"/>
<objColor r="0" g="255" b="255" alpha="0"/>
<bgColor r="0" g="0" b="0" alpha="255"/>
<layer val="8"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="2" size="20" style="1"/>
<startPoint x="2" y="5.5" z="1"/>
</element>
<expression label="textCrossBlueturn" exp="" X Blue ""/>
<element type="text" label="textCrossBlueturn">
<show object="true" label="false" ev="40"/>
<condition showObject="turn ≟ false"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<bgColor r="0" g="0" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="3" size="40" style="1"/>
<startPoint x="0" y="-1" z="1"/>
</element>
<expression label="textCircleRedturn" exp="" O Red ""/>
<element type="text" label="textCircleRedturn">
<show object="true" label="false" ev="40"/>
<condition showObject="turn ≟ true"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<bgColor r="255" g="0" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="3" size="40" style="1"/>
<startPoint x="6.3" y="-1" z="1"/>
</element>
</construction>
</geogebra>