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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_5 / The textit{taxicab distance} between points (x₁,y₁) and (x₂,y₂) in the coordinate plane is given by |x₁−x₂|+|y₁−y₂|. For how many points P with integer coordinates is the taxicab d…

Problem

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

problem

The $\textit{taxicab distance}$ between points

(x_1, y_1)

and

(x_2, y_2)

in the coordinate plane is given by

|x_1 - x_2| + |y_1 - y_2|.

For how many points

P

with integer coordinates is the taxicab distance between

P

and the origin less than or equal to

20

Plain-text mathematical notation (without MathML)

The $\textit{taxicab distance}$ between points (x₁,y₁) and (x₂,y₂) in the coordinate plane is given by |x₁−x₂|+|y₁−y₂|.
For how many points P with integer coordinates is the taxicab distance between P and the origin less than or equal to 20?

Original LaTeX notation

The $\textit{taxicab distance}$ between points $(x_1, y_1)$ and $(x_2, y_2)$ in the coordinate plane is given by \[|x_1 - x_2| + |y_1 - y_2|.\]
For how many points $P$ with integer coordinates is the taxicab distance between $P$ and the origin less than or equal to $20$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_5
task_id: 6082ccfa-3e2c-5868-b8c1-8e2f3048d724
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f5
task_revision_id: 2
config / split: default / train

Official source

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