The Last Digit

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Given a number raised to a large power, find the ones digit of the expansion.

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Half-Sums

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Consider the infinite sums of some numbers.

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Hot Air Balloon

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

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Pascal’s Patterns

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Identify patterns in a triangular array of numbers.

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Infinite Series

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

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Gone Fishing

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

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Fibonacci Extended

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

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Multiplying Rabbits

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

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Nugget Numbers

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

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Fractions into Whole Numbers

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

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