Christmas Streak 01/88: EINS + EINS + EINS + EINS = VIER!

Logic Level 2

In a cryptogram, each symbol represents a distinct, non-negative, single digit, and all leading digits are non-zero.

Solve the cryptogram below, and submit your answer as the 4-digit integer \(\overline{VIER}. \) \[{\begin{array}{cccccc} && &\color{red}E&\color{orange}I&\color{green}N&\color{blue}S \\ && &\color{red}E&\color{orange}I&\color{green}N&\color{blue}S \\ && &\color{red}E&\color{orange}I&\color{green}N&\color{blue}S \\ +&& &\color{red}E&\color{orange}I&\color{green}N&\color{blue}S \\ \hline && &\color{violet}V&\color{orange}I&\color{red}E&\color{pink}R \end{array}}\]

Note: In German, eins means one and vier means four. So this cryptogram is "doubly true": 1+1+1+1=4.

This problem is a part of <Christmas Streak 2017> series.


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