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− | {{AoPSWiki:Sandbox/header}} <!-- Please do not delete this line -->
| + | =A= |
− | In the computer world, a '''sandbox''' is a place to test and experiment -- essentially, it's a place to play.
| + | ==B== |
− | | + | ===C=== |
− | This is the AoPSWiki Sandbox. Feel free to experiment here.
| + | ====E==== |
− | | + | Apple |
− | Warning: anything you place here is subject to deletion without notice.
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− | | |
− | [''This was deleted due to its inappropriateness.'']
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− | | |
− | ==Test 1==
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− | | |
− | <asy>
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− | | |
− | dot((0,0));
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− | dot((1,0));
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− | dot((0,1));
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− | dot((1,1));
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− | dot((2,0));
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− | dot((0,2));
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− | dot((1,2));
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− | dot((2,1));
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− | dot((2,2));
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− | dot((3,0));
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− | dot((3,1));
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− | dot((3,2));
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− | dot((3,3));
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− | dot((2,3));
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− | dot((1,3));
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− | dot((0,3));
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− | dot((0,4));
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− | dot((1,4));
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− | dot((2,4));
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− | dot((3,4));
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− | dot((4,4));
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− | dot((4,3));
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− | dot((4,2));
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− | dot((4,1));
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− | dot((4,0));
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− | dot((5,0));
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− | dot((5,1));
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− | dot((5,2));
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− | dot((5,3));
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− | dot((5,4));
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− | dot((5,5));
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− | dot((4,5));
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− | dot((3,5));
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− | dot((2,5));
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− | dot((1,5));
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− | dot((0,5));
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− | dot((0,6));
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− | dot((1,6));
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− | dot((2,6));
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− | dot((3,6));
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− | dot((4,6));
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− | dot((5,6));
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− | dot((6,6));
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− | dot((6,5));
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− | dot((6,4));
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− | dot((6,3));
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− | dot((6,2));
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− | dot((6,1));
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− | dot((6,0));
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− | dot((7,0));
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− | dot((7,1));
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− | dot((7,2));
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− | dot((7,3));
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− | dot((7,4));
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− | dot((7,5));
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− | dot((7,6));
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− | dot((7,7));
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− | dot((6,7));
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− | dot((5,7));
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− | dot((4,7));
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− | dot((3,7));
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− | dot((2,7));
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− | dot((1,7));
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− | dot((0,7));
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− | draw((0,1)--(1,7),pink);
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− | draw((1,7)--(7,6),red);
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− | draw((7,6)--(6,0),red);
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− | draw((6,0)--(0,1),pink);
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− | draw((2,7)--(7,5),blue);
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− | draw((0,2)--(2,7),blue);
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− | draw((5,0)--(0,2),blue);
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− | draw((5,0)--(7,5),red);
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− | draw((3,7)--(7,4),green);
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− | draw((7,4)--(4,0),black);
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− | draw((4,0)--(0,3),green);
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− | draw((0,3)--(3,7),pink);
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− | draw((4,7)--(7,3),green);
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− | draw((7,3)--(3,0),green);
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− | draw((3,0)--(0,4),red);
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− | draw((0,4)--(4,7),green);
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− | draw((5,7)--(7,2),black);
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− | draw((7,2)--(2,0),black);
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− | draw((2,0)--(0,5),orange);
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− | draw((0,5)--(5,7),black);
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− | draw((0,6)--(1,0),green);
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− | draw((1,0)--(7,1),brown);
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− | draw((7,1)--(6,7),brown);
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− | draw((0,6)--(6,7),brown);
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− | | |
− | </asy>
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− | Hi there ''yall
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− | | |
− | ==Test 2== | |
− | <b>Test</b>
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− | | |
− | <asy>
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− | | |
− | dot((50,1));
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− | dot((2,1));
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− | dot((3,1));
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− | dot((4,1));
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− | dot((5,1));
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− | dot((6,1));
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− | dot((7,1));
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− | dot((1,2));
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− | dot((2,2));
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− | dot((3,2));
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− | dot((4,2));
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− | dot((5,2));
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− | dot((6,2));
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− | dot((7,2));
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− | dot((1,3));
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− | dot((2,3));
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− | dot((3,3));
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− | dot((4,3));
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− | dot((5,3));
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− | dot((6,3));
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− | dot((7,3));
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− | dot((1,4));
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− | dot((2,4));
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− | dot((3,4));
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− | dot((4,4));
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− | dot((5,4));
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− | dot((6,4));
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− | dot((7,4));
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− | dot((1,5));
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− | dot((2,5));
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− | dot((3,5));
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− | dot((4,5));
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− | dot((5,5));
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− | dot((6,5));
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− | dot((7,5));
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− | dot((1,6));
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− | dot((2,6));
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− | dot((3,6));
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− | dot((4,6));
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− | dot((5,6));
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− | dot((6,6));
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− | dot((7,6));
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− | dot((1,7));
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− | dot((2,7));
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− | dot((3,7));
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− | dot((4,7));
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− | dot((5,7));
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− | dot((6,7));
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− | dot((7,7));
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− | draw((1,1)--(1,3)--(3,3),red);
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− | draw((1,4)--(3,4)--(3,2),yellow);
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− | draw((4,4)--(4,2)--(2,2),green);
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− | draw((4,1)--(2,1)--(2,3),blue);
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− | draw((7,1)--(7,3)--(5,3),red);
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− | draw((7,4)--(5,4)--(5,2),yellow);
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− | draw((4,2)--(6,2),green);
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− | draw((4,1)--(6,1)--(6,3),blue);
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− | draw((1,7)--(1,5)--(3,5),red);
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− | draw((3,4)--(3,6),yellow);
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− | draw((4,4)--(4,6)--(2,6),green);
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− | draw((4,7)--(2,7)--(2,5),blue);
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− | draw((7,7)--(7,5)--(5,5),red);
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− | draw((5,4)--(5,6),yellow);
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− | draw((4,6)--(6,6),green);
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− | draw((4,7)--(6,7)--(6,5),blue);
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− | </asy>
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− | | |
− | This is what epicness looks like.
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− | | |
− | BUT JEFFCHEN WOULDN'T KNOW
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− | | |
− | | |
− | <asy2>unitsize(33);pair A,B,C,D,I;A=origin; B=1.6*right; C=1.6*dir(60); D=0.8*right;
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− | I=incenter(A,B,C); draw(A--B--C--cycle);draw(incircle(A,B,C)); draw(C--D);
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− | </asy2>
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− | | |
− | ==Test 3== | |
− | <asy>
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− | dot((0,0));
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− | dot((0,4));
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− | dot((3,4444));
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− | dot((3,0));
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− | dot((1.5,2));
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− | draw((0,0)--(3,4444),pink);
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− | draw((0,4)--(3,0),purple);
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− | draw((0,0)--(0,4),green);
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− | draw((0,4)--(3,4),blue);
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− | draw((3,0)--(3,4),yellow);
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− | draw((3,0)--(0,0),red);
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− | </asy>
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− | | |
− | Test 4.0000000000000000000000000000000000000000000000000000000000000000000
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− | <math>\binom{\binom{3}{2}}{/binom{6}{2}}</math>
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− | <math>\sqrt{5}=50</math>
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− | | |
− | ==Test 5==
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− | | |
− | n1000 is editing this.
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− | yay! (Made better by AoPS)
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− | | |
− | <asy>
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− | pair A,B,C,D,E,F,G,H;
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− | | |
− | A=(1,0);
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− | B=(2,0);
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− | C=(3,1);
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− | D=(3,2);
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− | E=(2,3);
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− | F=(1,3);
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− | G=(0,2);
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− | H=(0,1);
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− | | |
− | path octagon,square1,square2,star,bow1,bow2;
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− | octagon=(A--B--C--D--E--F--G--H--cycle);
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− | square1=(A--C--E--G--cycle);
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− | square2=(B--D--F--H--cycle);
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− | star=(A--D--G--B--E--H--C--F--cycle);
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− | bow1=(A--B--F--E--cycle);
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− | bow2=(C--D--H--G--cycle);
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− | | |
− | path[] all;
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− | all=(octagon^^square1^^square2^^star^^bow1^^bow2);
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− | | |
− | draw(all);
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− | | |
− | fill(octagon,pink);
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− | fill((bow1)^^(bow2),purple);
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− | fill(all,evenodd+blue);
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− | | |
− | </asy>
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− | | |
− | | |
− | Who loves me?
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− | only <math>x^2</math>
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− | | |
− | ==Test 6==
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− | | |
− | NeoMathematicalKid was here. And he broke the line of asy diagrams.
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− | | |
− | <math>\begin{align*}\sum^4_{k=1}\left(\sum^k_{j=1}kj\right)&=\sum^4_{k=1}\left(k\sum^k_{j=1}j\right)\\
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− | &=\sum^4_{k=1}\left(k(1+2+\cdots +k)\right)\\
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− | &=\sum^4_{k=1}(k+2k+\cdots +k^2)\\
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− | &=(1)+(2+4)+(3+6+9)+(4+8+12+16)\\
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− | &=1+6+18+40\\
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− | &=\boxed{65}
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− | \end{align*}</math>
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− | notice how the square root signs are becoming progressively less slanted...
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− | What is <math>\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{e^{1\pi\pi\sqrtpi}}}}}}+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{20}}}}}}</math>?!?! I got carried away.
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− | | |
− | ==Test 7==
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− | <math>\text{Use a calculator:}</math>
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− | | |
− | <math>\int_{-\frac{877\pi}{7e^{e^{e^e}}}}^{1492.558} \sum^{9000!}_{k=0} \left(\cfrac{k^{kx+e}-\cfrac{1}{x^e-\cfrac{k-x}{k^{1337^e}+\cfrac{1}{k-x+\pi-42}}}}{x^{122.8}+\cfrac{71^k}{k+x+\cfrac{\sqrt{\sqrt{\pi^{12000.4x}}}}{94.5^{89x}}}-k^{100}100^xx^k}+2\right)\frac{d}{dx}+10^{10^{76}}</math>!
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− | | |
− | silentazn's trillion dollar question
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− | bobthesmartypants's answer: There is not enough space in the observable universe to write this number down, so there s no valid answer.
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− | my answer: There's not enough matter in the observable universe to store this number in memory, so you don't know the valid answer.
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