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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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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Tri-Square Trios

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

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Gretel’s Goldfish

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

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Summing Multiples

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Find a pattern in the sum of multiples.

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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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Hypatia’s Triumph

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Take on the Egyptian Hypatia’s challenge about sums 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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Arranging Toothpicks

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

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