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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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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Linear Diophantine Equations
What amounts of money can you make with only $5 and $7 bills? Can you make $23 with those 2 types of bills?
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Concept Quizzes
A vote to elect the class president is being held in a classroom with \(8\) students. There are \(3\) nominees, who do not get to vote. If the vote is a secret vote, i.e. the people do not know who voted for whom, what is the number of possible vote count results?
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
How many ordered sets of non-negative integers \( (a, b, c, d) \) are there such that \( a + b +c+d =13\)?
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Consider the two sets \(A=\{1,2,3,4\}\) and \(B=\{5,6,7,8\}.\) How many possible functions \(f:A\rightarrow B\) are there such that if \(i<j\) then \(f(i)\le f(j)?\)
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Calvin took a trip to the store to purchase some lightbulbs. His choices at the store were \(25W, 40W, 60W, \mbox{ and } 100W\) lightbulbs. If Calvin purchased \(13\) lightbulbs, how many different combinations of bulbs could he have purchased?
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
A vote to elect the class president is being held in a classroom with \(10\) students. There are \(3\) nominees, who do not get to vote. If the vote is a secret vote, i.e. the people do not know who voted for whom, what is the number of possible vote count results?