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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
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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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Concept Quizzes
How many solutions are there to the inequality \[3<x+y+z<7,\] when \(x,y,z\) are non-negative integers?
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.
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by Brilliant Staff
How many solutions are there to the inequality \[x+y+z\le6,\] where \(x,y,z\) are non-negative integers?
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
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examples, and problems from the community.
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including olympiad champions, researchers, and professionals.
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by Brilliant Staff
How many solutions are there to the equation \[a+b+c+d=15,\] where \(a,b,c,d\) are integers such that \(a\ge1, b\ge2, c\ge3, d\ge4?\)
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.
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including olympiad champions, researchers, and professionals.
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by Brilliant Staff
Amy is packing up for her camping trip. Her bag can currently fit up to ten bottles of drink. How many ways are there for her to pack her beverages including at least \(4\) water bottles and at least \(1\) bottle of coke?
Note: Her selection must consist of only water and coke.
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
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by Brilliant Staff
How many solutions are there to the equation \[x+y+z=16,\] when \(x,y\) are positive odd numbers and \(z\) is a positive even number?
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.
Your answer seems reasonable.
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That seems reasonable.
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by Brilliant Staff