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Art of Problem Solving
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AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
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and language arts learners in grades 2-12.
![[asy] /* THE BEST CHESS SET EVER LOGO (Yes, it's really called that) The code may be very convoluted, just warning you... VERSION 1.7 */ unitsize(1inch); //COLORS+LINE TYPES //Guide Lines pen g=(linetype("2 3")+gray+linewidth(.5)); //Knight Outline pen b=(white+linewidth(.5)); //Knight Fill pen[][] c={{red, red+yellow},{red+yellow, yellow}}; //*GUIDE POINTS* //C C pair A=(0,0); //C U4 pair B=(0,3.125); //C D4 pair C=(0,-3.125); //L4 C pair D=(-3.75,0); //R4 C pair E=(3.75,0); //L1 C pair F=(-1.25,0); //L1 U1 pair G=(-1.25,0.75); //L1 U2 pair H=(-1.25, 1.5); //L1 D1 pair I=(-1.25, -0.75); //L1 U3 pair K=(-1.25,2.75); //L1 D3 pair L=(-1.25,-2.75); //R1 C pair M=(1.25,0); //R1 U1 pair N=(1.25,0.75); //R1 U2 pair O=(1.25, 1.5); //R1 D1 pair P=(1.25, -0.75); //R1 D2 pair Q=(1.25, -1.5); //R1 U3 pair R=(1.25,2.75); //R1 D3 pair S=(1.25,-2.75); //L2 U1 pair T=(-1.875, .75); //L2 U2 pair U=(-1.875, 1.5); //L2 D1 pair V=(-1.875, -.75); //L2 D2 pair W=(-1.875, -1.5); //R2 U1 pair X=(1.875, .75); //R2 U2 pair Y=(1.875, 1.5); //R2 D1 pair Z=(1.875, -.75); //R2 D2 pair AA=(1.875, -1.5); //L3 U1 pair BB=(-2.75, .78125); //L3 D1 pair CC=(-2.75, -.78125); //R3 U1 pair DD=(2.75, .78125); //R3 D1 pair EE=(2.75, -.78125); //Diagonal line ends pair ELD=(-2.875, -.125); pair ELU=(-2.875, .125); pair ERD=(2.875, -.125); pair ERU=(2.875, .125); //Diagonal line starts pair SLD=(-1.5625, -2.5); pair SLU=(-1.5625, 2.5); pair SRD=(1.5625, -2.5); pair SRU=(1.5625, 2.5); //Circle Intersections pair CLD=(-1.25, -.78125); pair CLU=(-1.25, .78125); pair CRD=(1.25, -.78125); pair CRU=(1.25, .78125); //Polar Lines pair PUL=(-2, 1.5); pair PUR=(2, 1.5); pair PDL=(-2, -1.5); pair PDR=(2, -1.5); //Central Points pair CPU=(0,1.5); pair CPD=(0,-1.5); //KNIGHT POINTS pair KCC=(0,0); pair KRC=(0.375,0); pair KCU=(0,0.1875); pair KRU=(0.125,0.1875); pair KLU=(-.25,.1875); pair KCUUU=(0,.6875); pair KLC=(-0.8125, 0); pair KLUU=(-.3125,.5625); pair KLLUUU=(-.4375,1.0625); pair KLLUUUU=(-.8125, .6875); pair KLLUU=(-.8125, .4375); pair KCUUUU=(0, .9375); pair KCUUUUU=(0, 1.1875); pair KLUUUUU=(-.25, 1.1875); pair KRUU=(.25,.3125); pair KRRUU=(.5625,.25); pair KRRUUU=(.5625,.375); pair KRUUU=(.4375,.875); pair KRRU=(.6875,.125); pair KRRRU=(.9375,.125); pair KRRRUUUU=(.4375,.875); pair KRRRRRUUU=(.875,.6875); pair KRRRRRUU=(1,.25); pair KRUUUU=(.25,1); pair KCUUUUUU=(0,1.625); pair KLUUUUUU=(-.0625,.6875); pair KRDDD=(.375,-.5625); pair KRRRDDD=(.921875,-.5625); pair KCD=(0,-.75); pair KRRDDD=(.5,-1); pair KCDD=(0,-1.125); pair KRDDDD=(.5,-1.21875); pair KCDDD=(0,-1.5); pair KLD=(-.3125,-.1875); pair KLLD=(-.5,-.375); pair KLLLLD=(-.75,-.625); pair KLLLDDDDD=(-.4375,-1.1875); pair ICANTHELPMYSELF=(-.46875,-1.1875); //KNIGHT BASE pair KBRT=(.8125,-1.03125); pair KBRU=(.9375,-1.25); pair KBRD=(1.0625,-1.25); pair KBRB=(1.0625,-1.5); pair KBLT=(-.8125,-1.03125); pair KBLU=(-.9375,-1.25); pair KBLD=(-1.0625,-1.25); pair KBLB=(-1.0625,-1.5); //DRAWING SYSTEMS fill((3.1875,3.125)--(-3.1875,3.125)--(-3.1875,-3.125)--(3.1875,-3.125)--cycle, black); //GUIDE draw(circle((0,0),.375), g); draw(circle((.625,.375),.375),g); draw(circle((-.625,.375),.375),g); draw(circle((-.625,-.375),.375),g); draw(circle((.625,-.375),.375),g); draw(circle((0,-1.4375),.375),g); draw(circle((0,1.4375),.375),g); draw(circle((CRU),.375),g); draw(circle((CLU),.375),g); draw(circle((CLD),.375),g); draw(circle((CRD),.375),g); draw(B--A--C, g); draw((-3.1875,0)--(0,0)--(3.1875,0), g); draw(ELD--CPU--SRU, g); draw(ERD--CPU--SLU, g); draw(ELU--CPD--SRD, g); draw(ERU--CPD--SLD, g); draw(K--L, g); draw(R--S, g); draw(CLU--BB, g); draw(CLD--CC, g); draw(CRU--DD, g); draw(CRD--EE, g); draw(PDR--PDL, g); draw(PUL--PUR, g); //Knight //Fill latticeshade(KLC--KLLD--KLLLLD--(-.3125,-.90625)--(-.46875,-1.234375)--(-.8125,-1.03125)--KBLU--KBLD--KBLB--KBRB--KBRD--KBRU--KBRT--KRDDDD--KRRDDD--KRRRDDD--KRC--KRU--KRUU--KRRUU--KRRU--KRRRU--KRRUUU--KRRRRRUU--KRRRRRUUU--KRUUU--KRUUUU--KCUUUUU--CPU--(-.1875,1.375)--KLUUUUU--KLLUUU--KLLUUUU--cycle, c); //Outline //Quadrant LU draw(KCC--KCU--KLU--cycle, b); draw(KCC--KLU--KLC--cycle, b); draw(KCUUU--KCU--KLU--cycle, b); draw(KCUUU--KLU--KLC--KLUU--cycle, b); draw(KLC--KLLUUUU--KLUU--cycle, b); draw(KCUUUU--KCUUU--KLLUUU--cycle, b); draw(KLLUUU--KCUUU--KLUU--cycle, b); draw(KLLUUU--KLLUUUU--KLUU--cycle, b); draw(KCUUUU--KLLUUU--KLUUUUU--KCUUUUU--cycle, b); draw(CPU--KCUUUUU--KLUUUUU--(-.1875,1.375)--cycle, b); //Quadrant RU draw(KCC--KRC--KRU--KCU--cycle, b); draw(KRUU--KCUUU--KCU--KRU--cycle, b); draw(KCUUU--KRRUUU--KRRUU--KRUU--cycle, b); draw(KRRU--KRRRU--KRRUUU--KRRUU--cycle, b); draw(KCUUU--KCUUUU--KRRRUUUU--cycle, b); draw(KCUUU--KRRUUU--KRRRUUUU--cycle, b); draw(KRRRRRUUU--KRRUUU--KRRRUUUU--cycle, b); draw(KRRRRRUUU--KRRRRRUU--KRRUUU--cycle, b); draw(KCUUUUU--KRUUUU--KRUUU--KCUUUU--cycle, b); //Quadrant RD draw(KCC--KRDDD--KCD--cycle, b); draw(KRC--KRDDD--KCC--cycle, b); draw(KRC--KRRRDDD--KRDDD--cycle, b); draw(KRRRDDD--KRDDD--KCD--cycle, b); draw(KCDD--KRRDDD--KCD--cycle, b); draw(KRRRDDD--KRRDDD--KCD--cycle, b); draw(KCDD--KRRDDD--KRDDDD--cycle, b); draw(KCDD--KCDDD--KRDDDD--cycle, b); draw(KCDDD--KBRT--KBRU--cycle, b); draw(KCDDD--KBRU--KBRD--KBRB--cycle, b); //Quadrant LD draw(KCC--KLC--KLLD--KLD--cycle, b); draw(KCC--KCD--KLD--cycle, b); draw(KCD--KLLD--KLD--cycle, b); draw(KCD--KLLD--KLLLLD--cycle, b); draw(KCD--KLLLLD--KCDD--cycle, b); draw(KCDDD--(-.40625,-1.28125)--KCDD--cycle, b); draw((-.46875,-1.234375)--(-.40625,-1.28125)--KCDD--(-.3125,-.90625)--cycle, b); draw(KCDDD--KBLT--KBLU--cycle, b); draw(KCDDD--KBLU--KBLD--KBLB--cycle, b); [/asy]](http://latex.artofproblemsolving.com/a/d/6/ad61abe5ec1f70e3d280a5066be4570c754869d8.png)
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