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MATH / Set R is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are c…

Problem

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

problem

Set RR is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. If RR contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set RR are squares? Express your answer as a common fraction. [asy]import graph; size(50); for(int i = 0; i<5; ++i) for(int j = 0; j<5; ++j) fill(Circle((i,j),.1)); [/asy]
Plain-text mathematical notation (without MathML)
Set R is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. If R contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set R are squares? Express your answer as a common fraction. [asy]import graph;
size(50);
for(int i = 0; i<5; ++i)
for(int j = 0; j<5; ++j)
fill(Circle((i,j),.1));
[/asy]
Original LaTeX notation
Set $R$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. If $R$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $R$ are squares? Express your answer as a common fraction. [asy]import graph;
size(50);
for(int i = 0; i<5; ++i)
for(int j = 0; j<5; ++j)
fill(Circle((i,j),.1));
[/asy]

level

Level 4

type

Counting & Probability

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Source and history

task_id
85e9cff5-67fd-5890-b028-965b99a62a79
task_key
counting~5fand~5fprobability--test--85e9cff5-67fd-5890-b028-965b99a62a79
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import