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MathNet 2021 — Part 05 Question 21

Math Olympiad Vault · MathNet 2021 — Part 05

Question 21

Integers $0 \leq a, b, c, d \leq 9$ satisfy
$$
\begin{gathered}
6a + 9b + 3c + d = 88 \\
a - b + c - d = -6 \\
a - 9b + 3c - d = -46
\end{gathered}
$$
Find $1000a + 100b + 10c + d$.