Very good YEAR
Source: IMC 2019 Day 1 P2
July 31, 2019
linear algebracollege contests
Problem Statement
A four-digit number is called very good if the system
\begin{align*}
Yx+Ey+Az+Rw& =Y\\
Rx+Yy+Ez+Aw & = E\\\
Ax+Ry+Yz+Ew & = A\\
Ex+Ay+Rz+Yw &= R
\end{align*}
of linear equations in the variables and has at least two solutions. Find all very good s in the 21st century.(The st century starts in and ends in .)Proposed by Tomáš Bárta, Charles University, Prague