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
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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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Can you form 24 using all the numbers 3, 3, 9, and 11, along with any of the 4 arithmetic operations (addition, subtraction, multiplication, and division) and parentheses?
by
Chung Kevin
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A concave polygon can be equilateral. For example, the concave octagon to the right is equilateral.
What is the least number of sides a concave equilateral polygon can have?
by
Andy Hayes
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One day, Alice, Betty, Cathy, David, and Edward were at home playing hide and seek. Unfortunately, one of them accidentally collided into a flower vase. When their mother came back home and saw the broken vase, she asked them who did it.
Alice: "Betty broke it!"
Betty: "Alice is not telling the truth."
Cathy: "I did it!"
David: "I did not break it and Betty is lying!"
Edward: "David is telling the truth!"
Given that at least three children are telling the truth, who broke the vase?
by
Sheryl-Lynn Tan
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A catalyst is a molecule that can increase the rate of a chemical reaction.
Suppose we have a reaction that releases energy \(E.\) If we introduce a catalyst into the reaction and assume that no other conditions change, does the amount of energy released during any given reaction increase, decrease, or stay the same?
by
Steven Yuan
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You are given a set of cards arranged in a line. Each card is either \(\color{black}{\text{black}}\) or \(\color{red}{\text{red}}\). You may divide the cards into two parts by picking a line before or after the whole cards (so that a part can contain 0 cards), or somewhere between two cards.
No matter how many cards are arranged in whatever manner, can you always ensure the number of \(\color{black}{\text{black}}\) cards in the left part is exactly the same as the number of \(\color{red}{\text{red}}\) cards in the right part?
An example split that fulfills the condition is shown below.
There is 1 \(\color{black}{\text{black}}\) card in the left part and 1 \(\color{red}{\text{red}}\) card in the right part
by
Agnishom Chattopadhyay
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