25_avoidance.tex
Paper X: Universal Residual Seeds and Conditional Occupied-System Completion
25_avoidance.tex
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5 \path[draw=black!25,fill=black!17] (1.78,3.44) rectangle (2.5,4.02);
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7 \path[draw=black!25,fill=white] (2.56,3.44) rectangle (3.28,4.02);
8 \node[font=\small,align=center,font=\scriptsize] at (2.92,3.75) {$2$};
9 \path[draw=black!25,fill=white] (3.34,3.44) rectangle (4.06,4.02);
10 \node[font=\small,align=center,font=\scriptsize] at (3.7,3.75) {$3$};
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12 \node[font=\small,align=center,font=\scriptsize] at (4.48,3.75) {$4$};
13 \path[draw=black!25,fill=white] (4.9,3.44) rectangle (5.62,4.02);
14 \node[font=\small,align=center,font=\scriptsize] at (5.26,3.75) {$5$};
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20 \node[font=\small,align=center,font=\scriptsize] at (2.92,3.06) {$8$};
21 \path[draw=black!25,fill=white] (3.34,2.75) rectangle (4.06,3.33);
22 \node[font=\small,align=center,font=\scriptsize] at (3.7,3.06) {$9$};
23 \path[draw=black!25,fill=white] (4.12,2.75) rectangle (4.84,3.33);
24 \node[font=\small,align=center,font=\scriptsize] at (4.48,3.06) {$10$};
25 \path[draw=black!25,fill=black!17] (4.9,2.75) rectangle (5.62,3.33);
26 \node[font=\small,align=center,font=\scriptsize] at (5.26,3.06) {$11$};
27 \path[draw=black!25,fill=white] (1,2.06) rectangle (1.72,2.64);
28 \node[font=\small,align=center,font=\scriptsize] at (1.36,2.37) {$12$};
29 \path[draw=black!25,fill=black!17] (1.78,2.06) rectangle (2.5,2.64);
30 \node[font=\small,align=center,font=\scriptsize] at (2.14,2.37) {$13$};
31 \path[draw=black!25,fill=white] (2.56,2.06) rectangle (3.28,2.64);
32 \node[font=\small,align=center,font=\scriptsize] at (2.92,2.37) {$14$};
33 \path[draw=black!25,fill=white] (3.34,2.06) rectangle (4.06,2.64);
34 \node[font=\small,align=center,font=\scriptsize] at (3.7,2.37) {$15$};
35 \path[draw=black!25,fill=white] (4.12,2.06) rectangle (4.84,2.64);
36 \node[font=\small,align=center,font=\scriptsize] at (4.48,2.37) {$16$};
37 \path[draw=black!25,fill=black!17] (4.9,2.06) rectangle (5.62,2.64);
38 \node[font=\small,align=center,font=\scriptsize] at (5.26,2.37) {$17$};
39 \path[draw=black!25,fill=white] (1,1.37) rectangle (1.72,1.95);
40 \node[font=\small,align=center,font=\scriptsize] at (1.36,1.68) {$18$};
41 \path[draw=black!25,fill=black!17] (1.78,1.37) rectangle (2.5,1.95);
42 \node[font=\small,align=center,font=\scriptsize] at (2.14,1.68) {$19$};
43 \path[draw=black!25,fill=white] (2.56,1.37) rectangle (3.28,1.95);
44 \node[font=\small,align=center,font=\scriptsize] at (2.92,1.68) {$20$};
45 \path[draw=black!25,fill=white] (3.34,1.37) rectangle (4.06,1.95);
46 \node[font=\small,align=center,font=\scriptsize] at (3.7,1.68) {$21$};
47 \path[draw=black!25,fill=white] (4.12,1.37) rectangle (4.84,1.95);
48 \node[font=\small,align=center,font=\scriptsize] at (4.48,1.68) {$22$};
49 \path[draw=black!25,fill=black!17] (4.9,1.37) rectangle (5.62,1.95);
50 \node[font=\small,align=center,font=\scriptsize] at (5.26,1.68) {$23$};
51 \path[draw=black!25,fill=white] (1,0.68) rectangle (1.72,1.26);
52 \node[font=\small,align=center,font=\scriptsize] at (1.36,0.99) {$24$};
53 \path[draw=black!25,fill=white] (1.78,0.68) rectangle (2.5,1.26);
54 \node[font=\small,align=center,font=\scriptsize] at (2.14,0.99) {$25$};
55 \path[draw=black!25,fill=white] (2.56,0.68) rectangle (3.28,1.26);
56 \node[font=\small,align=center,font=\scriptsize] at (2.92,0.99) {$26$};
57 \path[draw=black!25,fill=white] (3.34,0.68) rectangle (4.06,1.26);
58 \node[font=\small,align=center,font=\scriptsize] at (3.7,0.99) {$27$};
59 \path[draw=black!25,fill=white] (4.12,0.68) rectangle (4.84,1.26);
60 \node[font=\small,align=center,font=\scriptsize] at (4.48,0.99) {$28$};
61 \path[draw=black!25,fill=black!17] (4.9,0.68) rectangle (5.62,1.26);
62 \node[font=\small,align=center,font=\scriptsize] at (5.26,0.99) {$29$};
63 \path[draw,line width=1pt] (4.87,0.65) rectangle (5.65,1.29);
64 \node[font=\small,align=center] at (9.8,4.2) {Choose one residue in each quotient};
65 \node[font=\small,align=center] at (9.8,3.2) {$a\equiv1\pmod2$};
66 \node[font=\small,align=center] at (9.8,2.45) {$a\equiv2\pmod3$};
67 \node[font=\small,align=center] at (9.8,1.7) {$a\equiv4\pmod5$};
68 \node[font=\small,align=center] at (9.8,0.75) {$a=29,\quad\gcd(29,30)=1$};
69 \node[font=\small,align=center,font=\footnotesize] at (7,-0.1) {Shaded values avoid $2$, $3$, and $5$ simultaneously.};
70 \end{tikzpicture}
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