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MathNet 2019-part-07 — 184 problems (EN–VI) Question 101

Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)

Question 101

Find the average of all 5-digit numbers that satisfy the following:
* The number is of the form $\overline{ab0cd}$, that is, its third digit is zero;
* Digits are pairwise distinct;
* Both numbers $\overline{ab0cd}$, and $\overline{dc0ba}$ are divisible by 7.