Difference between revisions of "2024 USAMO Problems/Problem 4"
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Let <math>m</math> and <math>n</math> be positive integers. A circular necklace contains <math>m n</math> beads, each either red or blue. It turned out that no matter how the necklace was cut into <math>m</math> blocks of <math>n</math> consecutive beads, each block had a distinct number of red beads. Determine, with proof, all possible values of the ordered pair <math>(m, n)</math>. | Let <math>m</math> and <math>n</math> be positive integers. A circular necklace contains <math>m n</math> beads, each either red or blue. It turned out that no matter how the necklace was cut into <math>m</math> blocks of <math>n</math> consecutive beads, each block had a distinct number of red beads. Determine, with proof, all possible values of the ordered pair <math>(m, n)</math>. | ||
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| + | ==Video Solution== | ||
| + | https://youtu.be/ZcdBpaLC5p0 [video contains problem 1 and problem 4] | ||
Revision as of 20:55, 29 March 2024
Let 
and 
be positive integers. A circular necklace contains 
beads, each either red or blue. It turned out that no matter how the necklace was cut into blocks of consecutive beads, each block had a distinct number of red beads. Determine, with proof, all possible values of the ordered pair 
.
Video Solution
https://youtu.be/ZcdBpaLC5p0 [video contains problem 1 and problem 4]
