# MATHEMATICAL PROBLEM SETS

## Example Sets

Below are some problem sets from Julia Robinson Mathematics Festivals. The rightmost column indicates the level of challenge for 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 |
Challenge |
||||

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 | * | * | * | * |