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MATH / Each of the integers 1, 2, 3, …, 16 is written on a separate slip of paper and these slips are placed in a pile. Jillian will randomly draw slips from the pile without replacement …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Each of the integers 1,1, 2,2, 3,3, …,\dots, 1616 is written on a separate slip of paper and these slips are placed in a pile. Jillian will randomly draw slips from the pile without replacement and will continue drawing until two of the numbers she has drawn from the pile have a product that is a perfect square. What is the maximum number of slips that Jillian can draw without obtaining a product that is a perfect square?
Plain-text mathematical notation (without MathML)
Each of the integers 1, 2, 3, …, 16 is written on a separate slip of paper and these slips are placed in a pile. Jillian will randomly draw slips from the pile without replacement and will continue drawing until two of the numbers she has drawn from the pile have a product that is a perfect square. What is the maximum number of slips that Jillian can draw without obtaining a product that is a perfect square?
Original LaTeX notation
Each of the integers $1,$ $2,$ $3,$ $\dots,$ $16$ is written on a separate slip of paper and these slips are placed in a pile. Jillian will randomly draw slips from the pile without replacement and will continue drawing until two of the numbers she has drawn from the pile have a product that is a perfect square. What is the maximum number of slips that Jillian can draw without obtaining a product that is a perfect square?

level

Level 5

type

Number Theory

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Source and history

task_id
4e0d940c-f4a2-5b03-ab4e-c65c370f5041
task_key
number~5ftheory--test--4e0d940c-f4a2-5b03-ab4e-c65c370f5041
task_revision_id
1
config / split
number_theory / test

Official source

initial import