独立钻石棋（孔明棋）英式标准33孔盘面
2021-01-05 15:38
本范例使用GeoGebra构建了经典的英式标准33孔独立钻石棋（孔明棋）盘面。通过圆、多边形和序列等几何命令，精确绘制了十字形棋盘及33个棋孔的位置。该模型不仅展示了几何作图在棋盘游戏设计中的应用，还可作为逻辑推理与路径规划等离散数学问题的交互式演示平台，帮助学习者直观理解棋盘状态与游戏规则。
所属专题
用GeoGebra制作数学游戏
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<show object="true" label="false" ev="4"/>
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<layer val="5"/>
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<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(-3,-1)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
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<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="(3, 0)" a1="r"/>
<output a0="c20"/>
</command>
<element type="conic" label="c20">
<show object="true" label="false" ev="4"/>
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<layer val="5"/>
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<labelMode val="3"/>
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<fixed val="true"/>
<ggbscript val="SetValue[F,(3,0)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
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<eqnStyle style="specific"/>
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<command name="Circle">
<input a0="(-2, -1)" a1="r"/>
<output a0="c22"/>
</command>
<element type="conic" label="c22">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
<labelOffset x="-10" y="21"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(-2,-1)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
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<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="(-1, -1)" a1="r"/>
<output a0="c23"/>
</command>
<element type="conic" label="c23">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
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<labelMode val="3"/>
<tooltipMode val="2"/>
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
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<eqnStyle style="specific"/>
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<command name="Circle">
<input a0="(0, -1)" a1="r"/>
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</command>
<element type="conic" label="c24">
<show object="true" label="false" ev="4"/>
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<layer val="5"/>
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<ggbscript val="SetValue[F,(0,-1)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
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<eqnStyle style="specific"/>
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<command name="Circle">
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<element type="conic" label="c25">
<show object="true" label="false" ev="4"/>
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
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<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="(3, -1)" a1="r"/>
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</command>
<element type="conic" label="c27">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
<labelOffset x="-7" y="21"/>
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<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(3,-1)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="9.75" A3="0" A4="-3" A5="1"/>
<eqnStyle style="specific"/>
<caption val="(3, -1)"/>
</element>
<command name="Circle">
<input a0="(-1, -2)" a1="r"/>
<output a0="c28"/>
</command>
<element type="conic" label="c28">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
<labelOffset x="-10" y="21"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(-1,-2)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="4.75" A3="0" A4="1" A5="2"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="(0, -2)" a1="r"/>
<output a0="c29"/>
</command>
<element type="conic" label="c29">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
<labelOffset x="-6" y="21"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(0,-2)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="3.75" A3="0" A4="0" A5="2"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="(1, -2)" a1="r"/>
<output a0="c30"/>
</command>
<element type="conic" label="c30">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
<labelOffset x="-5" y="21"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(1,-2)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
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<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="(-1, -3)" a1="r"/>
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</command>
<element type="conic" label="c31">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
<labelOffset x="-10" y="22"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(-1,-3)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
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<eqnStyle style="specific"/>
<caption val="(-1, -3)"/>
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<command name="Circle">
<input a0="(0, -3)" a1="r"/>
<output a0="c32"/>
</command>
<element type="conic" label="c32">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
<labelOffset x="-7" y="21"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(0,-3)]
"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="8.75" A3="0" A4="0" A5="3"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="(1, -3)" a1="r"/>
<output a0="c33"/>
</command>
<element type="conic" label="c33">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.05000000074505806"/>
<layer val="5"/>
<labelOffset x="-6" y="23"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<ggbscript val="SetValue[F,(1,-3)]
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<lineStyle thickness="1" type="0" typeHidden="1" opacity="0"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="9.75" A3="0" A4="-1" A5="3"/>
<eqnStyle style="specific"/>
</element>
<expression label="focusongo" exp="{If[focuson(1) + (1, 0) ∈ checkers, focuson(1) + (2, 0)], If[focuson(1) + (-1, 0) ∈ checkers, focuson(1) + (-2, 0)], If[focuson(1) + (0, 1) ∈ checkers, focuson(1) + (0, 2)], If[focuson(1) + (0, -1) ∈ checkers, focuson(1) + (0, -2)]}" />
<element type="list" label="focusongo">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Intersection">
<input a0="focusongo" a1="spaces"/>
<output a0="spacesgo1"/>
</command>
<element type="list" label="spacesgo1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<listType val="point"/>
<pointSize val="9"/>
<pointStyle val="3"/>
<angleStyle val="0"/>
</element>
<expression label="F" exp="(2, 2)" type="point"/>
<element type="point" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="RunClickScript(buttonMove)"/>
<coords x="2" y="2" z="1"/>
<pointSize val="9"/>
<pointStyle val="4"/>
</element>
<expression label="S" exp="(2, 2)" type="point"/>
<element type="point" label="S">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2" y="2" z="1"/>
<pointSize val="9"/>
<pointStyle val="4"/>
</element>
<expression label="T" exp="(2, 2)" type="point"/>
<element type="point" label="T">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2" y="2" z="1"/>
<pointSize val="9"/>
<pointStyle val="4"/>
</element>
<element type="button" label="buttonRestart">
<show object="true" label="true" ev="2"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="7"/>
<labelOffset x="294" y="647"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="spaces={(0,0)}

F=(2,2)
S=(2,2)
T=(2,2)

focuson={}
Gamelog={}

showLog=false
showCoordinate=false
showRule=false
showResult=false"/>
<font serif="false" sizeM="3" size="40" style="1"/>
<dimensions width="170" height="70" />
<startPoint x="-1" y="-4" z="1"/>
<caption val="Restart"/>
</element>
<command name="RemoveUndefined">
<input a0="Sequence[If[(focuson(1) + spacesgo1(k)) / 2 ∈ checkers, spacesgo1(k)], k, 1, Length[spacesgo1]]"/>
<output a0="spacesgo"/>
</command>
<element type="list" label="spacesgo">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<listType val="point"/>
<pointSize val="9"/>
<pointStyle val="3"/>
<angleStyle val="0"/>
</element>
<command name="Polygon">
<input a0="{(-1.5, -3.5), (1.5, -3.5), (1.5, -1.5), (3.5, -1.5), (3.5, 1.5), (1.5, 1.5), (1.5, 3.5), (-1.5, 3.5), (-1.5, 1.5), (-3.5, 1.5), (-3.5, -1.5), (-1.5, -1.5)}"/>
<output a0="polyBoard"/>
</command>
<element type="polygon" label="polyBoard">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="255" b="0" alpha="1" inverseFill="true"/>
<layer val="1"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<ggbscript val="F=(2,2)
S=(2,2)
T=(2,2)
focuson={}
SelectObjects()"/>
</element>
<element type="point" label="A">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2" y="-3" z="1"/>
<pointSize val="9"/>
<pointStyle val="1"/>
</element>
<element type="image" label="picMarble">
<file name="6d3dd647aa379cf884da63bdb8774136/transferImage.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="A"/>
<startPoint number="1" exp="A + (0.75, 0)"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="8"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Polygon">
<input a0="{(-1.5, -3.5), (1.5, -3.5), (1.5, -1.5), (3.5, -1.5), (3.5, 1.5), (1.5, 1.5), (1.5, 3.5), (-1.5, 3.5), (-1.5, 1.5), (-3.5, 1.5), (-3.5, -1.5), (-1.5, -1.5)}"/>
<output a0="polyBoardEdge"/>
</command>
<element type="polygon" label="polyBoardEdge">
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<ggbscript val="F=(2,2)
S=(2,2)
T=(2,2)
focuson={}
SelectObjects()"/>
</element>
<command name="Polygon">
<input a0="{Corner[1], Corner[2], Corner[3], Corner[4]}"/>
<output a0="polyBackground"/>
</command>
<element type="polygon" label="polyBackground">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="255" b="255" alpha="0.18000000715255737"/>
<layer val="0"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="S=(2,2)
T=(2,2)
focuson={}
SelectObjects()"/>
</element>
<command name="Length">
<input a0="checkers"/>
<output a0="numR"/>
</command>
<element type="numeric" label="numR">
<value val="32"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<element type="button" label="buttonMove">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="8"/>
<labelOffset x="101" y="187"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[T,(2,2)]
If[F∈checkers,Execute({"SetValue[focuson,{F}]","SetValue[S,F]"})]
If[F∈spacesgo,SetValue[T,F]]

If[T∈spacesgo,SetValue(Gamelog,CopyFreeObject(If(Last(Gamelog(nGL))=={S},Join(First(Gamelog,nGL-1),{Join(Gamelog(nGL),{T})}),Append(Gamelog,{S,T}))))]

If[T∈spacesgo,Execute({"SetValue[spaces,Append(spaces,S)]","SetValue[spaces,Remove(spaces,{T})]","SetValue[spaces,Append(spaces,(S+T)/2)]","SetValue[focuson,{F}]"})]
If[spacesgo=={},SetValue[focuson,{}],SetValue[S,F]]

SelectObjects()
If[allgo=={},SetValue(showResult,true)]
"/>
<font serif="false" sizeM="2" size="20" style="0"/>
<caption val="MoveScript"/>
</element>
<command name="Length">
<input a0="Gamelog"/>
<output a0="nGL"/>
</command>
<element type="numeric" label="nGL">
<value val="0"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="showCoordinate" exp="false"/>
<element type="boolean" label="showCoordinate">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="7"/>
<labelOffset x="542" y="733"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Coordinate"/>
</element>
<command name="Sequence">
<input a0="Translate[picMarble, Vector[A, checkers(k) + (-0.375, -0.375)]]" a1="k" a2="1" a3="Length[checkers]"/>
<output a0="checkersM"/>
</command>
<element type="list" label="checkersM">
<show object="true" label="false" ev="4"/>
<objColor r="75" g="0" b="130" alpha="1"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Circle[checkers(k), 0.375]" a1="k" a2="1" a3="Length[checkers]"/>
<output a0="checkersC"/>
</command>
<element type="list" label="checkersC">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" 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>
<command name="Sequence">
<input a0="Circle[spacesgo(k), 0.375]" a1="k" a2="1" a3="Length[spacesgo]"/>
<output a0="spacesgoC"/>
</command>
<element type="list" label="spacesgoC">
<show object="true" label="false" ev="4"/>
<objColor r="127" g="0" b="255" alpha="0.5"/>
<layer val="3"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<listType val="conic"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="focusonC" exp="{Circle[focuson(1), 0.375]}" />
<element type="list" label="focusonC">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0.4000000059604645"/>
<layer val="3"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Circle[spaces(k), 0.375]" a1="k" a2="1" a3="Length[spaces]"/>
<output a0="spacesC"/>
</command>
<element type="list" label="spacesC">
<show object="true" label="false" ev="4"/>
<objColor r="192" g="192" b="192" alpha="0.75"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="showRule" exp="false"/>
<element type="boolean" label="showRule">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="5" y="65"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="showLog" exp="false"/>
<element type="boolean" label="showLog">
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跳。棋子只能跳過相鄰的棋子到空位上，並且把被跳
過的棋子吃掉。棋子可以沿格線橫、縱方向跳，但是
不能斜跳，剩下越少棋子越好。
最佳結果是在最後只留下一個棋子在盤面的正中央，
最少所需的移動步數為18步(連續跳躍視為同一步)。

Peg solitaire (or Solo Noble) is a board game for one 
player involving movement of pegs on a board with 
holes.You have to remove the pegs one after the other 
by jumping horizontally or vertically over one. In the 
end one peg should be left in the centre hole. 
The “world record” is a solution with 18 moves by 
E. Bergholt from 1912.
Consecutive multi-jump counts as one move.""/>
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You have spent " + nGL + " moves, 
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Rank: " + (If[numR > 6, rankEng(1), ""]) + "" + (If[numR ≟ 6, rankEng(2), ""]) + "" + (If[numR ≟ 5, rankEng(3), ""]) + "" + (If[numR ≟ 4, rankEng(4), ""]) + "" + (If[numR ≟ 3, rankEng(5), ""]) + "" + (If[numR ≟ 2, rankEng(6), ""]) + "" + (If[numR ≟ 1 ∧ checkers ≠ {(0, 0)} ∧ nGL ≠ 18, rankEng(7), ""]) + "" + (If[numR ≟ 1 ∧ checkers ≟ {(0, 0)} ∧ nGL ≠ 18, rankEng(8), ""]) + "" + (If[numR ≟ 1 ∧ checkers ≟ {(0, 0)} ∧ nGL ≟ 18, rankEng(9), ""]) + """ />
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您走了 " + nGL + " 步，剩餘 " + numR + " 個棋子
評級: " + (LaTeX[If[numR > 6, rankCht(1)]]) + "" + (LaTeX[If[numR ≟ 6, rankCht(2)]]) + "" + (LaTeX[If[numR ≟ 5, rankCht(3)]]) + "" + (LaTeX[If[numR ≟ 4, rankCht(4)]]) + "" + (LaTeX[If[numR ≟ 3, rankCht(5)]]) + "" + (LaTeX[If[numR ≟ 2, rankCht(6)]]) + "" + (LaTeX[If[numR ≟ 1 ∧ checkers ≠ {(0, 0)} ∧ nGL ≠ 18, rankCht(7)]]) + "" + (LaTeX[If[numR ≟ 1 ∧ checkers ≟ {(0, 0)} ∧ nGL ≠ 18, rankCht(8)]]) + "" + (LaTeX[If[numR ≟ 1 ∧ checkers ≟ {(0, 0)} ∧ nGL ≟ 18, rankCht(9)]]) + """ />
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