Question 94
There are thirteen broken computers situated at the following set $S$ of thirteen points in the plane:
$$
\begin{array}{lll}
A=(1,10) & B=(976,9) & C=(666,87) \\
D=(377,422) & E=(535,488) & F=(775,488) \\
G=(941,500) & H=(225,583) & I=(388,696) \\
J=(3,713) & K=(504,872) & L=(560,934) \\
& M=(22,997) &
\end{array}
$$
At time $t=0$, a repairman begins moving from one computer to the next, traveling continuously in straight lines at unit speed. Assuming the repairman begins at $A$ and fixes computers instantly, what path does he take to minimize the total downtime of the computers? List the points he visits in order. Your score will be $\left\lfloor\frac{N}{40}\right\rfloor$, where
$$
N=1000+\lfloor\text{ the optimal downtime }\rfloor-\lfloor\text{ your downtime }\rfloor,
$$
or $0$, whichever is greater. By total downtime we mean the sum
$$
\sum_{P \in S} t_{P}
$$
where $t_{P}$ is the time at which the repairman reaches $P$.
$$
\begin{array}{lll}
A=(1,10) & B=(976,9) & C=(666,87) \\
D=(377,422) & E=(535,488) & F=(775,488) \\
G=(941,500) & H=(225,583) & I=(388,696) \\
J=(3,713) & K=(504,872) & L=(560,934) \\
& M=(22,997) &
\end{array}
$$
At time $t=0$, a repairman begins moving from one computer to the next, traveling continuously in straight lines at unit speed. Assuming the repairman begins at $A$ and fixes computers instantly, what path does he take to minimize the total downtime of the computers? List the points he visits in order. Your score will be $\left\lfloor\frac{N}{40}\right\rfloor$, where
$$
N=1000+\lfloor\text{ the optimal downtime }\rfloor-\lfloor\text{ your downtime }\rfloor,
$$
or $0$, whichever is greater. By total downtime we mean the sum
$$
\sum_{P \in S} t_{P}
$$
where $t_{P}$ is the time at which the repairman reaches $P$.