| A bug is sitting at the midpoint A of the top edge of a cube and wants to walk to lower left corner point B of the front face. If each edge of the cube is 4 inches long, what’s the length of the shortest path the bug can take? |  |
Solution by Roxanne Walker, Forest Hills Northern High School
If we flatten out the cube, we see that the shortest distance between A
and B is a straight line. The points A, B and C
form a right triangle with BC = 4 and AC = 6.
Therefore we know that: 
Also solved by: Patrick Julius, Peter Kim, Milena Soc,
Alexander Tang* (Ann Arbor Huron H.S.); Josh Underhill (Detroit
Catholic Central H.S.); Mark Bourne (Midland Dow H.S.); Pascal
Carole, Remy Carole, Adam Kidder, Ethan Sams (Saginaw Arts and Sciences
Academy); Alex Bordyukov, Mikhail Bordyukov, Hyunje Grace Cho, Eva Dou,
Brian Sullivan (Grosse Pointe South H.S.); Joe Burrett, Marci
Hart, Brian Miller, Nadia Minnekhanova, Nathan Moreau (Birch Run H.S.);
Jaehyun Jung (Jenison H.S.); Young-Key Chung, Adam
DeSantis, Abid Rahman (Troy Athens H.S.); Colin Alexander,
Lesley Berquist, Adam Carlson, Anna Carlson, Katie Ciosek, Stephanie Garbacik,
Zeth Hearld, Emily Krieger, Mike Meindertsma, Elise Miller, Drew Monks, Lauren
Pucci, Rob Reyers, Josh Samp, Jeff Vredenburg (Forest Hills Northern
H.S.); Charles Bunce, Louis Denniston, Kristin Hoyt, Kelsey Leonard,
Stacie Lippert, Brent Nixon, Craig Rogers, Kyle Sinko (St. Louis H.S.);
Steve Colvin, Jonah Stiennon (West Bloomfield H.S.); Andrew
Adkins, Brandon Rosinski (Plymouth-Canton Ed. Park); Rebecca
Masten-Davies, Tim Parker (Lansing Catholic Central H.S.); Joe
Tsao (Rochester H.S.); Sunil Abraham (Adrian H.S.);
So Young Park (Traverse City Central H.S.); Keith Boruta
(Plymouth Christian Academy); Woo Jung Kim (Alpena H.S.); Hillary
Rawlings (East Grand Rapids H.S.); Aimee Cairati (Marquette
H.S.);
* Alexander Tang recognized that there were two possible shortest paths.