September's Challenge

Using common mathematical symbols and exactly four fours, it is possible to create arithmetic expressions for every integer from 0 to 100. For example, we can express 68 as or . Your job is to create similar arithmetic expressions using exactly four fours for the following numbers: 13, 30, and 33.

If you create expressions for only two of the three numbers, we’d still like you to submit your solutions.

We received a nice variety of expressions for all three numbers. Some of the more interesting and clever ones were submitted by the following students

	The Ladywood High School Calculus class
	Hyunje Grace Cho, Grosse Pointe South H. S.
	Steve Hannon, Jackson High School
	Milena Soc, Ann Arbor Huron High School
	Ezra Bakker, Charlevoix High School
	Tom Weaver, Jenison High School

Also solving all three: Alex Bordyukov, Eva Dou, Spencer MacGriff (Grosse Pointe South H.S.); Erin Stec, Bill Briggs (Grand Rapids Catholic Central H.S.); Young-Key Chung, Anirudha Rathman, David Kye, Dan Le, Harsha Hebbale (Troy Athens H.S.); Matheus Falasa, Samantha Falasa, Alex Piskin, Mike Roth (Forest Hills Eastern H.S.); Adam Carlson, Mike Meindertsma, Elise Miller, Vishakh Ponnuru, Rob Reyers, Chase Schuler, Travis Worst (Forest Hills Northern H.S.); Candice Penn (Ladywood High School); Peter Denton (East Grand Rapids H.S.); Justin Shaler (Holland H.S.); Ben Montgomery (Marquette H.S.); Marci Hart, April Kusowski, Kyle Mack, Nathan McDonald, Brian Miller, Nathan Moreau, Christine Rovoll, Tom Savage, Brandon Turnbull (Birch Run H.S.); Zita Anderson, Brad Cyr, Chris Golski, Emily Haffling, Ian Hughes, Mia Matchett, Dan Myers, Jennifer Rich, Scott Sladek, Chris Wyniawskyj (Charlevoix H.S.); Mary Hogan (Marshall H.S.); Gregory Haberl (Lansing Cath. Central H.S.); Yu Han, Lisa Tian, Teresa Wang, Kevin Wenxin Zhu (Plymouth-Canton H.S.); Edward Kennedy, Erik Kynast (Saginaw Heritage H.S.); Austina Davis, Kyle Travis (Shepherd H.S.); Myron Chang (Salem H.S.); Mitchell Brown (Birmingham Seaholm H.S.);
Chaitanya Malla (Farmington H.S.); Terina Li (CMU Math Prog); Marc Nichols (Charlotte H.S.).

Solving 2 of the 3: Matt Ankrapp (Plymouth H.S.); Michael Vo (Midland H.S.); Michael Sayward (Charlevoix H.S.); Cassie Schumacher (G. R. Catholic Central H.S.); Jim Dunneback, Juliana O’Neill, Grant Schertzing (Lansing Catholic Central H.S.); Kelsey Bos (Holland H.S.); Rachel Brown, Joel Coldwell, Scott Shoemaker, Nick Wilson (Shepherd H.S.); Shelly Jiang (Plymouth H.S.); Tabbetha Klaft, Elizabeth Prentice (Traverse City Central H.S.).