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MathNet 2006 — Part 04 Question 180

Math Olympiad Vault · MathNet 2006 — Part 04

Question 180

$$
\begin{array}{rlrr}
A=(0,428) & B=(9,85) & C=(42,865) & D=(192,875) \\
E=(193,219) & F=(204,108) & G=(292,219) & H=(316,378) \\
I=(375,688) & J=(597,498) & K=(679,766) & L=(739,641) \\
& M=(772,307) & & N=(793,0) \\
&
\end{array}
$$
A fly starts at $A$, visits all the other points, and comes back to $A$ in such a way as to minimize the total distance covered. What path did the fly take? Give the names of the points it visits in order. Your score will be
$$
20+\lfloor\text{ the optimal distance }\rfloor-\lfloor\text{your distance}\rfloor
$$
or $0$, whichever is greater.