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| <asy> | | <asy> |
| import three;
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| unitsize(4cm);
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| size(50);
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| currentprojection=orthographic(1/2,-1,1/2);
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| label("(5,38)",(0,0,0));
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| label("(4,29)",(0,1,0));
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| label("(4,35)",(1,0,0));
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| label("(4,39)",(1,1,0));
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| label("(0,30)",(0,0,1));
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| label("(2,38)",(0,1,1));
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| label("(5,39)",(1,0,1));
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| label("(3,46)",(1,1,1));
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| label("(4,46)",(0,0,2));
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| label("(3,46)",(0,1,2));
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| label("(0,36)",(1,0,2));
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| label("(2,46)",(1,1,2));
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| | unitsize(.5cm); |
| | pair bar(pair a) { |
| | return (a.x,-a.y); |
| | }; |
| | pair A[] = { (6.5,0),(1.5,12) }; |
| | pair P[] = { A[0],A[1],-bar(A[1]),-bar(A[0]),(2A[0]-bar(A[0]))/3,(2A[0]+A[1])/3, |
| | (5A[0]-4bar(A[0]))/9,(5A[0]+4A[1])/9 |
| | }; |
| | pair D[] = { (2P[4]+P[5])/3,(P[4]+2P[5])/3 }; |
| | draw( D[0]--P[6] ,blue+1mm); |
| | draw( D[0]--P[4] ,blue+1mm); |
| | draw( P[6]--P[4], black+1mm); |
| | pair E[] = {(D[0]+P[6])/2,D[0] + P[6] - P[4]}; |
| | dot(E[0]);dot(E[1]); |
| | draw(P[6]--E[1],red+1mm); |
| | draw(P[4]--E[1],red+1mm); |
| | draw(P[4]--P[5]); |
| | draw( D[0] -- E[1]); |
| | draw(D[1]--P[7]); |
| | draw( P[3] -- P[0] -- P[1]) ; |
| | for(int i=0;i<10;++i) { |
| | if(i<4) { |
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| label("Sitting 1",(2.5,0,0));
| | } else { |
| label("Sitting 2",(2.5,1,0));
| | dot( (i<8) ? P[i] : D[i-8] ); |
| | } |
| | }; |
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| draw((1,0,0)--(2,0,0));
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| draw((1,1,0)--(2,1,0));
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|
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| label("Area 1",(0,-1.5,0));
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| label("Area 2",(1,-1.5,0));
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|
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| draw((0,0,0)--(0,-1,0));
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| draw((1,0,0)--(1,-1,0));
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| draw((0,0,0)--(1,0,0)--(1,1,0)--(0,1,0)--cycle3,red);
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| draw((0,0,0)--(0,0,1));dot((0,0,.5));
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| draw((0,1,0)--(0,1,1));dot((0,1,.4));
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| draw((1,1,0)--(1,1,1));dot((1,1,.4));
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| draw((1,0,0)--(1,0,1));dot((1,0,.4));
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| draw((0,0,.5)--(0,1,.4)--(1,1,.4)--(1,0,.4)--cycle3,blue);
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| draw((0,0,1)--(1,0,1)--(1,1,1)--(0,1,1)--cycle3,green);
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| draw((0,0,1)--(0,0,2));
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| draw((0,1,1)--(0,1,2));
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| draw((1,1,1)--(1,1,2));
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| draw((1,0,1)--(1,0,2));
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| draw((0,0,2)--(1,0,2)--(1,1,2)--(0,1,2)--cycle3,blue);
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| </asy> | | </asy> |
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| I did everything related to the [[ Mock AIME 3 Pre 2005]]
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| all in one edit - each solution page, the answers, and the entire aime page.
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![[asy] unitsize(.5cm); pair bar(pair a) { return (a.x,-a.y); }; pair A[] = { (6.5,0),(1.5,12) }; pair P[] = { A[0],A[1],-bar(A[1]),-bar(A[0]),(2A[0]-bar(A[0]))/3,(2A[0]+A[1])/3, (5A[0]-4bar(A[0]))/9,(5A[0]+4A[1])/9 }; pair D[] = { (2P[4]+P[5])/3,(P[4]+2P[5])/3 }; draw( D[0]--P[6] ,blue+1mm); draw( D[0]--P[4] ,blue+1mm); draw( P[6]--P[4], black+1mm); pair E[] = {(D[0]+P[6])/2,D[0] + P[6] - P[4]}; dot(E[0]);dot(E[1]); draw(P[6]--E[1],red+1mm); draw(P[4]--E[1],red+1mm); draw(P[4]--P[5]); draw( D[0] -- E[1]); draw(D[1]--P[7]); draw( P[3] -- P[0] -- P[1]) ; for(int i=0;i<10;++i) { if(i<4) { } else { dot( (i<8) ? P[i] : D[i-8] ); } }; [/asy]](http://latex.artofproblemsolving.com/1/a/c/1acf167ef6b59f80eac30a664b77b608ac3cd9ea.png)
