Math Problems

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

 

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) 

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)