The 21 Game: A Variant of Nim
2020-12-28 15:12
This GeoGebra applet demonstrates the classic '21 Game,' a variant of the mathematical game of Nim. Two players (Red and Blue) take turns removing 1, 2, or 3 objects from a pile, and the player who takes the 21st object wins. Featuring interactive buttons, state-tracking lists, and win-condition logic, this model visually illustrates winning strategies in game theory and the principles of addition
In collections
Math Games with GeoGebra
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<show object="true" label="false" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<listType val="point"/>
<pointSize val="9"/>
<pointStyle val="2"/>
<angleStyle val="0"/>
</element>
<command name="Polygon">
<input a0="{(x(Corner[1]), -3), (x(Corner[2]), -3), Corner[3], Corner[4]}"/>
<output a0="maskRule"/>
</command>
<element type="polygon" label="maskRule">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showRule"/>
<objColor r="64" g="64" b="64" alpha="0.949999988079071"/>
<layer val="7"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<ggbscript val="SetValue[showRule,false]"/>
</element>
<element type="button" label="buttonRule">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="250" b="205" alpha="255"/>
<layer val="7"/>
<labelOffset x="414" y="721"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[showRule,!showRule]"/>
<font serif="false" sizeM="4" size="72" style="1"/>
<startPoint x="2.4" y="-3.3" z="1"/>
<caption val="Game Rule"/>
</element>
<command name="Polygon">
<input a0="{Corner[1], Corner[2], (x(Corner[3]), -1), (x(Corner[4]), -1)}"/>
<output a0="maskNewGame"/>
</command>
<element type="polygon" label="maskNewGame">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showNewGame"/>
<objColor r="128" g="0" b="128" alpha="1"/>
<layer val="8"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
</element>
<expression label="textRule" exp=""遊戲規則
 檯面上有若干顆彈珠，兩位玩家輪流取珠，
每人每次可取1~3顆，最後將檯面上的彈珠
取完的玩家獲勝。

Game Rule
 There are pinballs on the table. Two players
take turns getting pinballs. You can take 1~3 
pinball(s) each turn. The one who taking the
last pinball wins the game.""/>
<element type="text" label="textRule">
<show object="true" label="false" ev="40"/>
<condition showObject="showRule"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="10" style="1"/>
<startPoint x="-2.5837768439666284" y="5.502045310344636" z="1"/>
</element>
<element type="boolean" label="showNewGame">
<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>
<element type="numeric" label="nSetup">
<value val="21"/>
<show object="true" label="true"/>
<condition showObject="showNewGame"/>
<objColor r="255" g="255" b="0" alpha="0.10000000149011612"/>
<bgColor r="255" g="250" b="205" alpha="255"/>
<layer val="8"/>
<labelOffset x="-80" y="-2"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<slider min="10" max="30" absoluteScreenLocation="true" width="440" x="275" y="717" fixed="true" horizontal="true" showAlgebra="false"/>
<pointSize val="20"/>
<lineStyle thickness="50" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<caption val="彈珠數 PinBalls：%v"/>
</element>
<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"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="button" label="buttonNewStart">
<show object="false" label="true"/>
<condition showObject="showNewGame"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="8"/>
<labelOffset x="49" y="564"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="If[SelectedIndex(mode)==1,SetVisibleInView( textP1, 1, true ),SetVisibleInView( textP1, 1, false )]
If[SelectedIndex(mode)==1,SetVisibleInView( textP2, 1, true ),SetVisibleInView( textP2, 1, false )]
If[SelectedIndex(mode)!=1,SetVisibleInView( textPlayer, 1, true ),SetVisibleInView( textPlayer, 1, false )]
If[SelectedIndex(mode)!=1,SetVisibleInView( textCom, 1, true ),SetVisibleInView( textCom, 1, false )]

SetValue[n,nSetup]
SetValue[showNewGame,false]
SetValue[showRule,false]

listLeft=CopyFreeObject(Sequence(n))
listBlue={}
listRed={}
listTmp={}
showOkB=false
showOkR=false
SetBackgroundColor[buttonB1,"white"]
SetBackgroundColor[buttonB2,"white"]
SetBackgroundColor[buttonB3,"white"]
SetBackgroundColor[buttonR1,"white"]
SetBackgroundColor[buttonR2,"white"]
SetBackgroundColor[buttonR3,"white"]

If[SelectedIndex(mode)==3,SetValue(showMaskB,true),SetValue(showMaskB,false)]
If[SelectedIndex(mode)==3,SetValue(showMaskR,false),SetValue(showMaskR,true)]
If[SelectedIndex(mode)==3,SetValue(α,0°)]
If[SelectedIndex(mode)==3,SetValue(showThinking,true)]
If[SelectedIndex(mode)==3,StartAnimation(α)]"/>
<font serif="false" sizeM="4" size="72" style="1"/>
<dimensions width="180" height="80" />
<startPoint x="-2.8" y="-1.4" z="1"/>
<caption val="Start"/>
</element>
<element type="button" label="buttonNewCancel">
<show object="true" label="true"/>
<condition showObject="showNewGame"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="250" b="205" alpha="255"/>
<layer val="8"/>
<labelOffset x="50" y="654"/>
<labelMode val="3"/>
<tooltipMode val="2"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[showNewGame,false]
SetValue[showRule,false]
SetValue[nSetup,n]"/>
<font serif="false" sizeM="4" size="72" style="1"/>
<dimensions width="180" height="80" />
<startPoint x="-2.8" y="-2.8" z="1"/>
<caption val="Cancel"/>
</element>
<expression label="mode" exp="{"Palyer1 vs Player2", "Player first vs Com", "Com first vs Player"}"/>
<element type="list" label="mode">
<show object="true" label="false" ev="4"/>
<condition showObject="showNewGame"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="250" b="205" alpha="255"/>
<layer val="8"/>
<labelOffset x="252" y="572"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<selectedIndex val="1"/>
<comboBox val="true"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<font serif="false" sizeM="2" size="24" style="1"/>
<angleStyle val="0"/>
<symbolic val="true" />
</element>
<expression label="textCom" exp=""Com""/>
<element type="text" label="textCom">
<show object="true" label="false" ev="40"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="10" style="1"/>
<startPoint x="5.7" y="5.5" z="1"/>
</element>
<expression label="textPlayer" exp=""Player""/>
<element type="text" label="textPlayer">
<show object="true" label="false" ev="40"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="10" style="1"/>
<startPoint x="-2.8" y="5.5" z="1"/>
</element>
<element type="numeric" label="rnd">
<value val="3"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="8"/>
<labelMode val="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<element type="boolean" label="showThinking">
<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>
<command name="Circle">
<input a0="A" a1="0.2"/>
<output a0="thinkingC"/>
</command>
<element type="conic" label="thinkingC">
<show object="true" label="false" ev="4"/>
<condition showObject="showThinking"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="61.042500000000004" A3="0" A4="-5.4" A5="-5.65"/>
<eqnStyle style="specific"/>
</element>
<command name="CircleSector">
<input a0="A" a1="A + ((0.2 * cos(90° - α)), (0.2 * sin(90° - α)))" a2="A + (0, 0.5)"/>
<output a0="thinkingS"/>
</command>
<element type="conicpart" label="thinkingS">
<show object="true" label="false" ev="4"/>
<condition showObject="showThinking"/>
<objColor r="153" g="51" b="0" alpha="1"/>
<layer val="8"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="61.042500000000004" A3="0" A4="-5.4" A5="-5.65"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="textLeft" exp=""剩餘 Left：" + (nleft - Length[listTmp]) + """ />
<element type="text" label="textLeft">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="10" style="1"/>
<startPoint x="0.5380659296781034" y="-2.461417756899343" z="1"/>
</element>
<element type="image" label="picDia">
<file name="00738fee1b951a9c625ae689973d2aa2/鑽石.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="(Mod[n - 1, 5] - 0.3, 4.65 - floor((n - 1) / 5))"/>
<startPoint number="1" exp="(Mod[n - 1, 5] + 0.3, 4.65 - floor((n - 1) / 5))"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="4"/>
<labelMode val="0"/>
<tooltipMode val="2"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
</construction>
</geogebra>