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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When you roll 2 fair dice, is the total more likely to be odd or even?
by
Winston Choo
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A full can of soda's center of mass is approximately at its center.
What happens to the center of mass of the (can + soda) system as part of the soda is consumed and the can is placed back on the table, until eventually all of the soda is consumed?
Assume that the soda can is in the shape of a uniform cylinder.
by
Anuj Shikarkhane
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The 2 diagonals of this rectangle divide it into 4 triangles.
If the area of the shaded region is 42, then what is the area of the rectangle?
by
Magdalena Gradek
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In each square, the blue and red areas are equal.
If \(R\) is the radius of the quarter-circle on the left and \(r\) is the radius of the circle on the right, what is \(\frac{R}{r}?\)
by
Jeremy Galvagni
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I've designed a system which only takes in a prime number as an input and outputs the final digit sum of that number. For example, if I input 997 (a prime), the system will output 7:
\[ 997\ \ \longrightarrow \ \ 9 + 9 + 7 = 25 \ \ \longrightarrow \ \ 2+5=7.\]
How many single-digit positive integers cannot be an output of this system?
A positive number is a number that is greater than zero. (Zero itself is neither positive nor negative.)
A prime number is an integer greater than 1 that has no positive integer divisors other than 1 and itself.
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by
Pi Han Goh
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