Excel in math and science
Master concepts by solving fun, challenging problems.
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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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\[ \Huge \color{purple}\sqrt[3]{\color{green}3^{\color{blue}{3}^{\color{red}{3}}}} \color{orange}=\ ?\]
Hint:
- \(\displaystyle \large 3^{3^3} = 3^{ \left(3^3 \right) } \)
- \(\displaystyle \large 3^{3^3} \ne { \left(3^3 \right) }^3 \)
by
Arul Kolla
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\[\large x = \underbrace{11111...11111}_{\text{Number of 1s = 100}} - \underbrace{22222...22222}_{\text{Number of 2s = 50}} \]
What is the sum of digits in \(x?\)
Hint: Try it with smaller numbers first. For example, find the sum of digits in \(111111 - 222.\)
by
Syed Hamza Khalid
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I know that just adding numerators and denominators doesn’t work. For example,
\[\frac{1}{2}+\frac{2}{3} \ne \frac{1+2}{2+3}.\]
Curious if this kind of addition ever works, I look for positive integers \(a,b,c,d\) such that
\[ \dfrac ab + \dfrac cd = \dfrac{a+c}{b+d}.\]
After some searching, I conclude that such numbers don't exist. Am I right?
by
Pi Han Goh
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A system of two symmetrical, identical, water-filled jars is fixed on a turntable. Each jar has a cork—attached to the bottom by a thread—floating vertically.
What will happen to the corks when the turntable starts rotating?
Details and Assumptions:
- The jars are closed so that no water spills out.
by
Rohit Gupta
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What is the length of \(BC?\)
by
Aidan Poor
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