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Omni-MATH / A four-digit number YEAR is called very good if the system begin{aligned} & Y x+E y+A z+R w=Y & R x+Y y+E z+A w=E & A x+R y+Y z+E w=A & E x+A y+R z+Y w=R end{aligned} of linear …

Problem

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problem

A four-digit number YEARY E A R is called very good if the system $$\begin{aligned} & Y x+E y+A z+R w=Y \\ & R x+Y y+E z+A w=E \\ & A x+R y+Y z+E w=A \\ & E x+A y+R z+Y w=R \end{aligned}$$ of linear equations in the variables x,y,zx, y, z and ww has at least two solutions. Find all very good YEARs in the 21st century.
Plain-text mathematical notation (without MathML)
A four-digit number YEAR is called very good if the system $$\begin{aligned} & Y x+E y+A z+R w=Y \\ & R x+Y y+E z+A w=E \\ & A x+R y+Y z+E w=A \\ & E x+A y+R z+Y w=R \end{aligned}$$ of linear equations in the variables x,y,z and w has at least two solutions. Find all very good YEARs in the 21st century.
Original LaTeX notation
A four-digit number $Y E A R$ is called very good if the system $$\begin{aligned} & Y x+E y+A z+R w=Y \\ & R x+Y y+E z+A w=E \\ & A x+R y+Y z+E w=A \\ & E x+A y+R z+Y w=R \end{aligned}$$ of linear equations in the variables $x, y, z$ and $w$ has at least two solutions. Find all very good YEARs in the 21st century.

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Source and history

task_id
8b063c34-a840-5902-8f4a-1522812a3fc3
task_key
test--8b063c34-a840-5902-8f4a-1522812a3fc3
task_revision_id
1
config / split
/ test

Official source

initial import