Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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A hollow cylinder is completely filled with frozen water.
Will it take longer to roll down an inclined plane while it’s frozen, or after it melts?
Assume: When frozen, the water does not move relative to the cylinder.
by
Pranshu Gaba
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What is the fewest number of colors needed such that no two adjacent vertices are colored the same?
Note: In graph theory, two vertices are adjacent if they share an edge.
by
Andrew Hayes
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\[\pm1\pm2\pm3\pm \cdots \pm2017\pm2018 = \, ?\]
Using appropriate + and - signs on the left side of the equation, which number can be obtained on the right?
by
Julian Yu
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Triangle \(ABC\) is inscribed in a circle. The angle \(ABC\) is obtuse, and the altitude \(CH\) is tangent to the circle.
If \(HB=10\) and \(BA=8,\) what is the radius of the circle?
by
Jeremy Galvagni
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Tom was born on a Thursday in either 2014, 2015, 2016, or 2017. What is the oldest age Tom can turn on his next Thursday birthday?
Hint: Consider the remainder when the number of days in a year (365) is divided by the number of days in a week (7). But don't forget about leap years!
by
Stephen Mellor
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