Raised to the 100th

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

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Squares and Differences

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Determine the relationship of the squares of three consecutive integers. 

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Hypatia’s Triumph

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

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Difference of Squares

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Find positive integers which can be written as sum or difference of squares.

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Choosing an Elevator

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

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Almost a Square

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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 […]

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Minimizing Products

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Find two positive integers with a given sum and who have the smallest product.

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Planning Cruises

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Determine three different length cruises that will leave on the same day.

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Arranging Toothpicks

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

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36 Divisibility

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Explore some numbers divisible by 36. 

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