Partial Sum of Consecutive Integers

Can a partial sum of consecutive positive integers equal a number with identical digits?

Sum of Infinite Fractions

Determine the sum of an infinite geometric series that begins with the number one.

Tri-Square Trios

Explore whether the sum of two triangular numbers can equal a square number.

Gretel’s Goldfish

When will Hansel and Gretel have the same number of goldfish?

Summing Multiples

Find a pattern in the sum of multiples.

Raised to the 100th

Use patterns to determine the units digit for numbers raised to the 100th power.

Hypatia’s Triumph

Take on the Egyptian Hypatia’s challenge about sums of squares.

Choosing an Elevator

Based on certain criteria, determine which of two elevators reaches the lobby first.

Almost a Square

A square with sides of integral length (i.e., the side lengths are integers) could be made with 25 square units. Make a rectangle with sides of integral length and an area of 24 square units, but construct the rectangle so it comes as close as possible to being a square. What are the dimensions of […]

Arranging Toothpicks

What is the total number of toothpicks used to build a rectangular grid?


Consider the infinite sums of some numbers.

Hot Air Balloon

Determine the height of a hot air balloon over time based on a recursive condition.

Pascal’s Patterns

Identify patterns in a triangular array of numbers.

Infinite Series

Determine the sum of various infinite series and investigate how to tell if a series will converge.

Gone Fishing

Determine the terms of an arithmetic sequence given its constant difference, number of terms, and sum.

Fibonacci Extended

Identify an explicit pattern between terms in a group of numbers that are generated recursively.

Multiplying Rabbits

Examine how the family tree of a rabbit forms the Fibonacci sequence and the golden ratio.

Nugget Numbers

Find combinations of McDonald’s Chicken McNugget orders that will and will not generate different natural numbers.

Fractions into Whole Numbers

Find three whole numbers that can be substituted into a fractional expression so that the expression evaluates to a whole number.

Patterns in a Table

Investigate numeric relationships in a two dimensional matrix generated by a polynomial function with two variables.

Consecutive Odds and Evens

Determine a rule that relates arithmetic operations on four consecutive odd and even numbers.