Problem Solving / General – MathCircles.org

Puzzling Pairs

By:

Topic(s):

Combinatorics, Number Theory, Parity / Invariants, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Lesson Plan, References

Langford pairings are sequences in which a set of N pairs, {1, 1, 2, 2, …, N, N}, is arranged so that every pair, {k, k}, appears in the sequence with k numbers between the pair. Langford pairings have been actively studied by mathematicians since the 1960s for their applications...

Stomachion (Archimedes’ Box)

By:

August Raybould

Topic(s):

Geometry, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Handouts, Lesson Plan, References

The Stomachion puzzle, attributed to the Ancient Greek scholar Archimedes and preserved within the Archimedes Palimpsest, is considered to be the oldest known mathematical puzzle. The puzzle contains 14 pieces in 12 distinct shapes that fit perfectly into a square. Since its discovery, the underlying structure of the puzzle has...

Fold & Cut

By:

Topic(s):

Geometry, Problem Solving / General

Supporting Resources:

Handouts, Photos & Videos, References, Virtual Tools

What shapes can result from the following fold-and-cut process?
Take a piece of paper.
Fold it flat.
Make one complete straight cut.
Unfold the pieces.
Are all shapes possible?

Cup Stacking

By:

Topic(s):

Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides, Handouts, Photos & Videos, References

Begin with a row of cups and end with all of the cups in a single stack. Rules: 1. Count the number of cups in a stack. That stack must jump that number of spaces. For example, 1 cup can only move 1 space; 2 cups have to move 2...

Liar’s Bingo

By:

Bob Klein, Steve Phelps

Topic(s):

Mathematical Games, Number Theory, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Handouts, References

From recognizing a pattern to generating terms, to abstracting and making inferences, tasks based on patterns embody the “low-threshold, high-ceiling” trait of good problems. Liar’s Bingo is all about patterns. This session involves recognizing patterns and searching for underlying structure, number theory, numeration, and potentially binary arithmetic. Sometimes, as in...

Locked Out: A Breakout Box Session for Your Circle

By:

Donna Farrior, Kimberly Adams

Topic(s):

Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, References

Escape Rooms and “Bomb Disposal” activities are growing in popularity as a form of team building and entertainment. This session blends the two ideas to create a cooperative math activity where the challenge is to solve math problems whose solutions generate combinations to open a locked box. The math problems...

Magic, Latin, & Sudoku Squares

By:

Matthias Beck

Topic(s):

Algebra / Arithmetic, Combinatorics, Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides

Squares and numbers, numbers and squares. There is something very satisfying about arranging numbers in a square formation, following specific rules, whether it is a Magic Square, Latin Square or Sudoku. This is probably why Sudoku puzzles are so popular. This session touches on some of the deep mathematics behind...

Mathemagical Card Tricks

By:

Stephanie Santorico

Topic(s):

Algebra / Arithmetic, Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides, References

There are many card tricks based on simple mathematics as opposed to sleight of hand. In this session, participants will play with a number of such tricks, test them out and work on discovering the math underneath, with a goal to formalize the mathematics that makes the trick work.

Mathematical Games

By:

Tatiana Shubin

Topic(s):

Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides

This session includes 15 games using manipulatives or paper and pencil. The goal is to decide which one of the two players has a winning strategy. To solve a game means to find a winning, or a non-losing, strategy for one of the players. An answer must include a detailed...

Mathematical Magic for Muggles

By:

Paul Zeitz

Topic(s):

Mathematical Games, Mathematical Modeling, Number Theory, Parity / Invariants, Problem Solving / General

Supporting Resources:

Facilitator Guides

Presented are several easy-to-perform feats that suggest supernatural powers such as telepathy, “seeing fingers,” predicting the future, photographic memory, etc. Each trick uses simple mathematical ideas that allow information to flow effortlessly and sneakily, among them simple, efficient “coding” parity and other invariants symmetry probability One can approach these activities...

Topic: Problem Solving / General