The following list of math problems have been collected by NAMC directors, Math Circle leaders, and presenters at past workshops which may be of use to Math Circle leaders. Like many math puzzles, the original source is sometimes unknown. We believe these resources are available for free use and we have done our best to list the origins of each. However, if you can add information, please contact us at info@mathcircles.org

**Bard Math Circle Problems**

Created by the **Bard Math Circle**

**Bard Math Circle problems (September 2012)****Bard Math Circle problems (October 2012)****Bard Math Circle problems (November 2012)****Bard Math Circle problems (December 2012)****Bard Math Circle problems (February 2013)****Bard Math Circle problems (March 2013)****Bard Math Circle problems (April 2013)****Bard Math Circle problems (May 2013)****Bard Math Circle problems (June 2013)**_{6}C_{3}Problems – Bard Math Circle JMM Poster Session

**GCD, LCM, Division Algorithm & The Euclidean Algorithm**

Created by Gowri Meda & Michael Klucznik for the OMSI Math Circle for Sixth through Ninth Graders (October 2011)

**ABBA Language / Magic Braid Problems**

*Source unknown*

**How to Gamble If You Must **(Probability)

Created by Paul Zeitz for The Teachers’ Circle (March 2012)

**Angles: How High Does It Fly?**

*Source unknown*

**Any Conic Section So Long as It is a Parabola **

*Created by Tatiana Shubin for the Houston Circle on the Road 2011*

**Art Math Questions for the Kansas State Math Circle 2011-2012**

*Source unknown*

**Balloon Numbers**

*Created for Julia Robinson Math Festival, based on “Computation Balloon Twisting: The Theory of Balloon Polyhedra” by Erik D. Demaine, Martin L. Demaine, and Vi Hart*

**Binpacking**

*Created by Tom Davis (2006) *

**Blue Eyed Islanders Problem**

*Created by Blake Thornton (2012)*

**Boomerang Fractions**

*Used at the BIRS Conference on Integer Sequences February 27 – March 1, 2015, it was explored by Gordon Hamilton, Joshua Zucker, and Richard Guy. *

**Circle of Differences**

*Directed by Joshua Zucker at the Julia Robinson Math Festival *

**Circle of Differences 2**

*Directed by Joshua Zucker at the Julia Robinson Math Festival *

**Combinatorial Problems**

*Created by Tom Davis (2000)*

**Classical Geometric Construct**

*Created by Tom Davis (2002)*

**Counting Things**

*Created by Tom Davis (2006)*

**Coupon Collector Problem**

*Source Unknown*

**Coupon Collector Problem 2**

*Source Unknown *

**Crack the Graham**

*Source Unknown*

**Cryptography Mentor’s Guide**

*Source Unknown*

**Cryptography**

*Created by Tom Davis (2000)*

**Cryptography Take 1**

*Created by Blake Thornton and Louis Beaugris *

**Difference Engine**

*Directed by Joshua Zucker at the Julia Robinson Math Festival *

**Division Algorithm and Remainder Arithmetic**

*Math Circle – November 2 and 9*

**Dominoes, Problem Solving, and Graph Theory**

*Fairfield County Math Teachers’ Circle – Lauren Rose, Bard College (2013)*

**Dots and Dashes**

*Created by James Tanton (2010 MSRI) *

**Easy Nim Exercise**

*Source Unknown*

**Elementary Planar Geometry**

*Source Unknown*

**Equations and Unknowns**

*Source Unknown*

**Euclidean Algorithm and Linear Diophantine Equations**

*Newark Area Math Circle, April 13, 2013, Grades 5-8*

**Look at the Extremes**

*Created by Razvan Gelca, Texas Tech University *

**Fermi Estimates Activity Directions**

*Source Unknown *

**Fermi Estimates Lesson Plans **

*Source Unknown *

**Fibonacci Numbers**

*Created by David Patrick (2012) *

**Folding and Pouring**

*Created by James Tanton (July 2010 MSRI)*

**Four Points on a Circle**

*Created by Tom Davis (2002) *

**Fractions Lesson Plan**

*Santa Ana Math Club (2010)*

**Fractions Revisted **

*Created by Joshua Zucker (2010)*

**Favorite Problems from the UWM Math Circle**

*Created by Gabriella Pinter *

**Friezi Patterns for Circle on the Road **

*Created by David W. Brown, San Diego Math Circle (2011) *

**Frieze Patterns (1)****Frieze Patterns (2)****Frieze Patterns (3-1)****Frieze Patterns (3-2)****Frieze Patterns (3-3)****Frieze Patterns (3-4)**

**GEM Seminar. Polynomials and Pyramids**

*Sergei Tabachnikov (2011)*

**Geodesic Dome**

*Created by Tom Davis (2010) *

**Geometry and Geography**

*Created by Tom Davis (2009)*

**Getting started, KenKen Strategies**

*Source Unknown*

**Zome Patterns**

*Created by Tom Davis *

**Graph Theory Problems and Solutions**

*Created by Tom Davis (2005)*

**Out of the Shadows**

*Created by Dave Auckly*

**Induction Problems**

*Created by Tom Davis (2005)*

**Mathematical Induction**

*Created by Tom Davis (2000) *

**Instant Insanity (Tantalizer)**

*Unknown Source *

**Intersection Math**

*Created by James Tanton*

**Modular Arithmetic, ISBN Numbers, and Check Digits**

*Created by Semra Kilic-Bahi (2014)*

**Laura Givental Drawings**

*Created by Laura Givental*

**Circle on the Road 2013. Julia Robinson Festival Lesson on Word Arithmetic**

*Created by Anna Burago (2013)*

**Circle on the Road 2013. Julia Robinson Festival Problems on Word Arithmetic**

*Created by Anna Burago (2013)*

**Operation Cookie Jar**

*Source Unknown*

**Cryptography Thornton Beaugris**

*Created by Blake Thornton and Louis Beaugris (2013)*

**Kalah**

*Source Unknown*

**Kayles**

*Created by Shahed Sharif*

**Kenken for Teachers**

*Tom Davis*

**Using KenKen to Build Mathematical Thinking Skills**

*Created by Harold B. Reiter*

**Knot Symmetry**

*Source Unknown*

**Laughter and Insight**

*Source Unkown*

**Laughter Guide**

*Source Unknown*

**Lesson Plan the Fourth Dimension**

*Source Unknown*

**Numerical Puzzles: Runaway Digits**

*Created by Anna Burago*

**Switching Light Bulbs**

*Created by Joshua Zucker*

**Logic 2 Solutions**

*Source Unknown*

**Logic Games Story**

*Rodi Steinig (2012)*

**Logic Lesson Notes**

*Unkown Source*

**Polyomino Exploration**

*Created by Canisius College Math Circle (2013)*

**Math Circle Games**

*Created by Dimitar Grantcharov*

**Math Circle Inequalities**

*Created by Dimitar Grantcharov*

**Polynomials and Complex Numbers**

*Created by Dimitar Grantcharov (2012)*

**Power of Point Plan**

*Created by Dimitar Grantcharov*

**Quadratic Functions and Recursion**

*Created by Dimitar Grantcharov*

**Symmetric Polynomials**

*Created by Dimitar Grantcharov*

**The Game of Life**

*Source Unknown*

**Math Club Tetris Tiles**

*Source Unknown*

**Mathematical Introduction**

*Source Unknown*

**Introduction to Matrices**

*Created by Tom Davis (2000)*

**Santa Ana Math Club**

*Source Unknown (2010)*

**Mathematics in Your Head: the Secrets of Mental Math**

*Source Unknown*

**Terrific Tiles**

*Source Unknown*

**Probability, Polynomials, and Weird Dice**

*Created by Lauren Rose (2014)*

**Möbius Strip Worksheet**

*Source Unknown*

**Modular Arithmetic**

*Source Unknown (2013)*

**Introduction to Modular Arithmetic**

*Created by Semra Kilic-Bahi (2014)*

**Geometry From Ancient Iraq**

*Created by Judith Montgomery (2012)*

**Multiplication Graphs**

*Created by Sam Vandervelde (2011)*

**Musical Symmetry**

*Source Unknown*

**Music Dance Mix Match**

*Source Unknown*

**Math Wrangle Practice 2**

*Source Unknown (2012)*

**MW 2012 Practice 2 Slns opt small Part2**

*Source Unknown*

**Wrangle 2012 Practice 3 Problems and Solutions**

*Source Unknown*

**MW 2012 Practice Round 1 St**

*Created by SJMC*

**MW Golden Section 2012 Solns**

*Source Unknown*

**MW Golden Section 2012**

*Source Unknown*

**Curvature and the Gauss Bonnet Theorem**

*Source Unknown (2012)*

**Chomp the Graph A Mathematical Game of Strategy**

*Created by Kathy Niedbalski (2013)*

**NATM Student Handout**

*Created by Kathy Niedbalski*

**The Rabbit Scenario**

*Created by Brandy Wiegers (2011)*

**Nim and Jim**

*Created by Japheth Wood (2011)*

**Pennies, Piles, and Games**

*Created by Joshua Zucker*

**The Game of Nim**

*Created by Japheth Wood (2011)*

**The Magic Birthday Trick**

*Created by Japheth Wood (2011)*

**NLMTC Polydron Activity**

*Created by Judith Covington*

**Number Bracelets NAMC**

*Source Unknown*

**Number Theory and the ABC Conjecture**

*Created by David Patrick (2012)*

**The Geometry of Math Circles**

*Created by Olga Radko*

**The Geometry of Math Circles part 2**

*Created by Olga Radko*

**On Reflection**

*Created by James Tanton (2010)*

**Couting Cube Colorings**

*Source Unknown*

**Owls and Voles**

*Created by Amanda Serenevey*

**Parity Lesson Plan**

*Source Unknown*

**Playing with Parity**

*Created by Ashley Ahlin, Julia Brodsky, Marie Brodsky, Maria Droujkova and Emily McCullough *

**Math Teachers Circle Topic**

*Source Unknown*

**Parking Sequences Handout**

*Source Unknown (2012)*

**A Penny for Your Thoughts**

*Source Unknown*

**Mathematical Origami:PHiZZ Dodecahedron**

*Source Unknown*

**Pile Splitting Script**

*Created by James Tanton (2011)*

**Subdividing a Pile**

*Created by Joshua Zucker and Tom Davis (2007)*

**Planar Graph Basics**

*Source Unknown*

**Points and Lines in the Plane**

*Created by Benjamin Braun*

**Polya’s Counting Theory**

*Created by Tom Davis (2006)*

**Polygons**

*Created by Tom Davis (2006)*

**Polynomials as Base x**

*Source Unknown*

**The Monty Hall Problem**

*Source Unknown*

**Problems Kids Love to Solve**

*Created by Julia Brodsky*

**The HL Protein Folding Model**

*Source Unknown*

**Public Key Cryptography**

*Source Unknown (2013)*

**Puppy Walk**

*Source Unknown*

**Puzzles**

*Created by David Patrick (2012)*

**Pythagorean Fractal Auctions Houston handout**

*Source Unknown*

**Rational Tangles**

*Source Unknown*

**Regions of a Circle, Difference Equations, and the Field of Sequences**

*Created by Lee Windsperger*

**The Regions of a Circle**

*Created by Lee Windsperger*

**Regular Polygons**

*Created by Rasvan Gelca*

**River Crossing**

*Source Unknown*

**RSA Encryption**

*Created by Tom Davis (2003)*

**Untuition**

*Created by Brian Conrey (2013)*

**The Game of Set**

*Source Unknown*

**Shapes Lesson Plan**

*Created by Santa Ana Math Club (2011)*

**Show What You Know**

*Source Unknown*

**SJSU Math Circle Content **

*Created by Tom Davis *

**Ski Jumps**

*Source Unknown*

**Counting Things Solutions**

*Tom Davis (2006)*

**Solving BAMO Problems**

*Tom Davis (2000)*

**Soma Cube**

*Created by Stan Isaacs (2010)*

**Investigating the Mathematics of Sona: Sand Drawings from Angola Instructor Notes**

*Created by Jane Long*

**A Note About Music**

*Source Unknown*

**Stern Brocot Tree**

*James Tanton (2010)*

**Logic Games Stories About the Kingdom**

*Created by Rodi Steinig (2012)*

**Taking Graphs Deeper**

*Source Unknown*

**Tangle Dance Guide**

*Source Unknown*

**Taxicab Geometry**

*Created by Olga Radko (2012)*

**Constructing Voting Paradoxes With Logic and Symmetry Teacher’s Notes**

*Created by Elena Galaktionova*

**Tessellations**

*Created by James Tanton (2010)*

**The Game of Criss Cross**

*Source Unknown*

**The Time Fillers**

*Source Unknown*

**Theons Ladder and Squangular Numbers**

*Created by James Tanton (2010)*

**Remodeling the Floor**

*Created by Dave Auckly*

**Tile Guide**

*Created by Dave Auckly*

**Tiling with Dominos, Straight, Bent, and Triangular Triominos**

*Source Unknown*

**Tiling Handout**

*Source Unknown*

**Tiling**

*Source Unknown*

**Tiling grid**

*Source Unknown*

**Tiling Torment**

*Created by Brandy Wiegers (2013)*

**The Topology of Surfaces and 3-Dimensional Spaces Lesson Plan**

*Created by Linda (Marin Math Circle 2011)*

**Towers of Hanoi **

*Source Unknown (2011)*

**Traffic Jam
**

*Source Unknown*

**Tiling n x n Boards with Bent Triominos**

*Source Unknown*

**Grid Power**

*Created by Tatiana Shubin (2012)*

**Lesson Plan: Peering Through Tubes**

*Source Unknown*

**Un-Holey Cubes**

*Source Unknown*

**Counting Principles**

*Source Unknown (2010)*

**A Grid of Numbers**

*Source Unknown*

**Visualizing Algebra**

*Created by the Santa Ana Math Club (2010)*

**Voting Paradoxes**

*Created by Elena Galaktionova*

**Constructing Voting Paradoxes With Logic and Symmetry**

*Created by Elena Galaktionova*

**Warm-up Problems**

*Created by Dave Auckly*

**The Watermelon Problem**

*Created by Linda at Marin Math Circle (2011)*

**What is a Matrix**

*Source Unknown*

**Exploring Kleinian Groups**

*Source Unknown*

**Wright**

*Source Unknown*

**Linear Geometric Transformations**

*Tom Davis (2000)*

**Introduction to the Mathematics of Zome**

*Tom Davis (2008)*