MathDB
Very good YEAR

Source: IMC 2019 Day 1 P2

July 31, 2019
linear algebracollege contests

Problem Statement

A four-digit number YEARYEAR 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 x,y,zx,y,z and ww has at least two solutions. Find all very good YEARYEARs in the 21st century.
(The 2121st century starts in 20012001 and ends in 21002100.)
Proposed by Tomáš Bárta, Charles University, Prague