Suppose you’re standing at the base of a stairway in a house. Nearby there are three electrical switches on the wall, all in the “off” position. The three switches control three different 100-watt light bulbs, all of which are upstairs and turned off. One light is in the blue bedroom, one light is in the green bedroom, and one light is in the bath-room. You’d like to discover which switch controls the light in the green bedroom. How can you do this if you’re only allowed to go upstairs once? [You cannot see the rooms from the base of the stairs, and you may not use any apparatus to assist you.]
Solution by Dan Le, Troy Athens High School
Turn on the first two switches. 15 minutes later turn off the second one. Then check the green bedroom. If the light is on, then it’s the first switch. If the light is off and the bulb is warm, then it’s the second switch.If the light is off and the bulb is cold, then it’s the third switch.
Also solved by: Jacob Arnett, Jason Yates (Alma H.S.); John Gibbs, Chris Holmes, Adam Keyes, Alex Howison, Joe Jacquemin, Andrew Speer (Alpena H.S.); Milena Soc (Ann Arbor Huron H.S.); Tiffany Fritzler, Nathan McDonald, Brian Miller, Nathan Moreau, Brandon Turnbull (Birch Run H.S.); Zita Anderson, Emily Heffling (Charlevoix H.S.); Rebe Henry, Mengyuan Hou, Terina Li (CMU. Math Program); John Paddock (De La Salle Collegiate H.S.); Scott Fitzgerald, Kevin Soulby (Det. Cath. Central H.S.); Dua Al-Dasouqi (Flushing H.S.); Ridwaan Albeiruti (Forest Hills Central H.S.); Kyle DeBoer, Vicky Tittle (Forest Hills Eastern H.S.); Colin Alexander, Jordan Amodeo,Emily Aupperlee, Adam Carlson, Nick Cianfarani, Ben Curtis, Katelyn Evans, Rebecca Fauble, Michelle Feenstra, Steve Gordon, Kyle Josephson, Stephi Malburg, Alex Mead, Mike Meindertsma, Erik Mika, Elise Miller, Drew Monks, Annie Ostrander, Wesley Pohl,Vishakh Ponnuru, Matt Post, Rob Reyers, Josh Samp, Tari VanGeest, Emily Venezia, Paige Williams (Forest Hills Northern H.S.); Trey Springer (G. R. Catholic Central H.S.); Alex Bordyukov, Hyunje Grace Cho, Timothy Cragg, Eva Dou, Edward Geha, Ian Talbot (Grosse Pointe South H.S.); Daniel Bos, Kelsey Bos (Holland H.S.); Jon Dent (Jenison H.S.); Chris Rovin (Marquette H.S.); Mary Hogan (Marshall H.S.); Jonathan Joseph, Hillary Fox (Lansing Cath. Central H.S.); Mark Bourne (Midland Dow H.S.); Nathan McDonald (Okemos H.S.); Matt Ankrapp, Namita Patel, Lisa Tian, Teresa Wang (Plymouth-Canton H.S.); Anoop Gopal, Alex Mihelick, Nick Taggie (Plymouth H.S.); Alyssa Messing (Plymouth Christian Academy); Jeremy Barth (Port Huron Northern H.S.); Brittany Allen, Sean Chiplock, Jeff Graves, Erik Kynast, Braxton Meyer, Daniel Xu (Saginaw Heritage H.S.); Brittany Gnida, Yiyang Lu, Rosanna Zhang (Salem H.S.); Jeremy Aldrich, Rachel Brown, Kate Cyster, Cody Showalter, Jacob Stanke, Kyle Travis, Nick Wilson (Shepherd H.S.); Anthony Guarnaccia (St. Johns H.S.); Davi Comstock, Jessica Fowler, Mallory Snyder, Emily Ward (St. Louis H.S.); Brittany Gulch (Temperance Bedford H.S.); Steve Colvin (West Bloomfield H.S.); Jared Baragar, Jordan Notenbaum (Wyoming Park H.S.).