Joshua Zucker – MathCircles.org

Primes, Divisibility, and Modular Arithmetic

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Number theory is all about adding and multiplying integers: pretty simple stuff, good for elementary school or for PhD mathematicians. Dr. Arnold Ross says of number theory, that the purpose is “to think deeply of simple things.” So let’s do that together. This session includes multiple problem sets beginning with...

Coins in Twoland

By:

Joshua Zucker

Topic(s):

Algebra / Arithmetic, Combinatorics, Number Theory

Supporting Resources:

In Twoland, the only money is coins with value 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and so on. How many ways can change be given, following Twoland’s strict rules? In this whimsical session, participants will practice precision and organizational skills. This session is also suitable...

Wolves and Sheep

By:

Joshua Zucker, Spencer Bowen

Topic(s):

Combinatorics, Geometry, Problem Solving / General

Supporting Resources:

Facilitator Guides, Handouts, Photos & Videos, References, Virtual Tools

The rules are simple: you want to place the sheep on the board so that the wolves can’t eat them. A wolf can eat a sheep if it has a direct path to it – or is in same row, column, or diagonal as that sheep. Can you place all...

The 1-to-100 problem

By:

Joshua Zucker

Topic(s):

Algebra / Arithmetic, Problem Solving / General

Supporting Resources:

Facilitator Guides

This exercise can be used for middle school students and older. The original problem seems almost impossibly difficult, but there are obviously many ways to approach it by considering simpler problems. As they investigate it, students are actually drilling their multiplication and addition facts. In addition, depending on how detailed...

Activity Database

Primes, Divisibility, and Modular Arithmetic

Coins in Twoland

Wolves and Sheep

The 1-to-100 problem