Proper Patterns

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Given some of the proper factors of a number, what could the number be?

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Partial Sum of Consecutive Integers

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

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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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Double Trouble

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Find a number that fits this description.

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Sum of Infinite Fractions

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

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The Frog Race

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Two frogs have a race. Determine which frog wins the race.

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Perfecting 90

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How can 90 become a perfect square? a perfect cube?

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Three Daughters

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Determine the age of each daughter.

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Multiples of 72

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What is the relationship between two divisors and their product, sum, difference, and quotient?

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Choose an Elevator

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Determine which of two elevators reaches the lobby first.

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