## 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?

## Half-Sums

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.