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MathNet 2018-part-05 — 181 problems (EN–VI) Question 40

Math Olympiad Vault · MathNet 2018-part-05 — 181 problems (EN–VI)

Question 40

Consider integers of the form $\overline{abcd}$ such that:

a) $a \ge b \ge c \ge d$;

b) $a+b+c+d = 11$;

c) $\overline{abcd} - \overline{cba} = 8082$.

Determine integers of the form $\overline{bdca}$ that satisfy all these conditions.