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

ISBN_Numbers_CAM

ISBN_Numbers_CAM_0

JRMF_B2_Laura_Givental

JRMF_B3_Anna_Burago_ WordArithmLesson

JRMF_B3_Anna_Burago_ WordArithmLesson_Problems

JRMF_B5_OPERATION COOKIE JAR

 

JRMF_B6_Cryptography-Thornton-Beaugris

Kalah

Kayles

Kenken

KenKenKen

Knot-Symmetry2

Knot-Symmetry2-1

Land-of-AH-festival

Laughter-guide

Lesson Plan The Fourth Dimension

LessonPlan_NmPuzzles

LightBulbs

Logic 2 solutions

Logic games story

Logic Lesson Notes

Math Circle Pentominoes

Math_circle_games_NAMC

Math_circle_inequalities

Math_circle_polynomials_plan

Math_circle_power_of_point_plan

 

Math_circle_quadratic_0

Math_circle_sym_polynomials

MathClubLife

MathClubTetrisTiles_0

Math-Intro

Matrices

Mental Math Lesson

Mental Math

MeTiles

Mid-Hudson MathTeachersCircle WeirdDiceLesson

Möbius WS

Modular Arithmetic

Modular Arithmetic_CAM

MTC upload

Multgraph_2

Multgraph_3

Musical-Symmetry

Music-dance-mix-match

MW 2012 Practice 2 – St_opt

MW 2012 Practice 2 Slns_opt-small_Part2

 

MW 2012 Practice 3 Slns

MW 2012 Practice 3 Slns 1-2

MW 2012 Practice Round 1 – St

MW Golden Section 2012 – Solns

MW Golden Section 2012

NAMC2012-AngleDefect CurvatureAnd TheGaussBonnet FormulaWithAnswers

NATM – Chomp the Graph Description

NATM – Chomp the Graph Description_0

NATM – Student Handout

NaturalMath

Nim and Jim

Nim games

NimHandout

NimHandout_0

NLMTC Polydron Activity

Nim and Jim

Nim games

NimHandout

NimHandout_0

NLMTC Polydron Activity

Number Bracelets NAMC

NumberTheoryABC

Olga_Part1

Olga_Part2

ON REFLECTION_July 2010_MSRI

 

Orbit-Stabilizer-Lesson

Owlnvole

Parity Lesson Plan

ParityProblems

ParityProblems_0

parkingsequences_circleinfo

parkingsequences_handout

Penny

Phizz_dodecahedron_2

Phizz_dodecahedron_2_0

Pile_Spliiting_Script_TANTON

Pile_Spliiting_ Script_TANTON_0

Pilesubdivide

Planar Graph Basics

PointsandLines_Braun

Polya

Polygons

Polynomials as base x

Probability-monty hall worksheet

Problems kids love to solve

 

Protein_Folding_Handout

Public-Key

Puppy-walk

Puzzles

Pythagorean Fractal Auctions Houston handout

Rational-tangles

Regionsofacircle1

Regionsofacirclefinal

Regular

River-set

RSA

Scan_Doc0002

SET_handout with solutions

Shapes Lesson Plan

ShowWhatYouKnow

SJSU Math Circle Content 
Created by Tom Davis 

Ski Jumps

Solnscount

Solvit

Soma Cube

Sona_lesson_0

 

Sound

STERN BROCOT TREE_July 2010_MSRI

Story for Logic Games

Taking Graphs Deeper
Source Unknown

Tangle-dance-guide

Taxicab_geometry_session

Teacher’s Notes

TESSELLATIONS_July 2010_MSRI

The Game of Criss

The time fillers

THEONS LADDER and SQUANGULAR NUMBERS_July 2010_MSRI

Tile problems
Tile-guide

Tiling_0

Tiling-handout

Tiling

Tilinggrid_1in

TILINGS at Berkeley Math Circle

TopologyOfSurfaces And3dSpaces_NAMC

Towers of hanoi lesson plan

Traffic Jam

 

Triominos1

TShubinGridPowerJanuary2012

TubesLesson

Un-Holey

UNIT 16_Counting Principles_July 2010

UNIT 17_A Grid of Numbers

Visualizing Algebra

VoteBeamer

VoteHandout

Warm-up

watermelonProblem 20110621

What-is-a-Matrix

Wright-intro

Wright

Xforms

ZomeIntro