Problem Sets

Below you will find some problem sets from previous Julia Robinson Mathematics Festivals.

The difficulty column tells you what range of difficulties you'll find in each activity. Level 1 should be accessible to a typical 6th grader, perhaps with some discussion with a mathematically competent adult. Level 3 is for very strong middle school students, or high school students with some problem solving experience. Level 5 is probably challenging enough for the activity's authors, and may include some unsolved problems.

Name Topic Difficulty
1 2 3 4 5
Area Attack! Area * * *
Bag of Tricks -- Bayesian Statistics Bayes' theorem, probability, judgement * *
Building Blocks Area, volume, binary, optimization * * * * *
Candy Conundrum with Teacher's Guide Counting, probability, ratio, lattice points * * * *
Cardinal Infinity with bonus problems Counting, infinity * * *
Change for a Dollar Counting, recursion * * * * *
Chess Covers and Tours Symmetry, patterns, patience * * *
Coloring Cubes Coloring, counting, cutting * * *
Counting Squares: 2D, 3D, 4D Counting, patterns, geometry * * *
Criss Cross Graph theory, Euler's formula * * *
Cut! Patterns, lines, planes, space * * * *
Derangement Counting, factorial, Pascal's Triangle, statistics * * * *
Difference Engine Subtraction, patterns, parity * * * * *
Diophantine Dilemma Addition, linear equations, integers * * * *
Dissections Geometry, area, cutting, 3D * * *
Divisor Game Game theory * * * *
Dominoes and Rectangles Tiling, recursion, counting, 3D * * *
Euler Phi Fractions, primes, common factors, remainders * * * *
A Fair Coin? Probability * * * *
Fibonacci Flips and Probability Puzzles Probability, counting, recursion, Markov * * *
Folding Fractals Recursion, patterns, fractals, turing machines * * *
Fractal Fiesta Fractals, hands-on, dimension, geometry * * *
Functions Rearranged Algebra, composing functions, maximization * *
Generating with Grammar Recursion, patterns, computer science * * * *
Gossip Recursion, combinatorics * * * *
Making Infinity Finite Recursion, series, limits, probability, Markov chains * *
Light Bulbs Factors, primes, inverses * * * * *
Little Boxes Area, fractions, infinite series * * *
Palindrome Grab! Symmetry, game theory * * *
Partner Puzzles Primes, perfect squares, addition, arrangements * * *
Pick's Theorem Area, lattice polygons, pattern * *
Pirate Puzzles Logic * * *
Prisoner Probabilities, Certainties, and a Paradox Probability, expected value, logic, patterns * * * *
Pythagoras Revisited Geometry * * *
Spider and the Ant Graph theory * * *
Splitting Piles Game theory * * *
Staring Out to Sea Geometry, circle, tangents * *
Teeter Totter Geometry * *
Three Jugs Logic, geometry, trilinear coordinates * * *
Tiling Torment Parity * * *
To Twos, Too! Sums, patterns, recursion, divisibility, binary * * * *
Topology and MySpace Sets, intersection, union, topology * *
Tower of Hanoi Counting, recursion * * *
Who Took the Candy? Game theory * * *
Wolves and Sheep Counting, symmetry * * * *