## Problem of the Day #78: A Mic and a Meal
*June 5, 2011*

*Posted by Seungln in : potd , trackback*

After coming back from an AMAZING ARML trip (with the successful performance of ARML Glee, of course), SeungIn decides to make more covers of songs. (He figures that it would be good to start soon, because he already has about 10 on his list.) However, he first has to go to a Best Buy for a mic and a restaurant to get dinner.

Let SeungIn’s house be the origin on a coordinate plane. There are three Best Buys around his house, one at (250, 0), one at (70, -240), and one at (-150, 200). There are four places that SeungIn considers for a restaurant: Cheesecake Factory at (75, 180), T.G.I.Friday’s at (0, 195), Papa John’s at (-168, 99), and Olive Garden at (-117, -156). Assuming that cost does not interfere with SeungIn’s decision of his path, and assuming that SeungIn will visit only one Best Buy and only one restaurant, the difference in length between the longest possible path and the shortest possible path is $x$. Find $[x]$ when $[n]$ is the greatest integer less than or equal to $n$.

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