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MathNet 2026 — Part 08 Question 55

Math Olympiad Vault · MathNet 2026 — Part 08

Question 55

Let us call a year *colored* if the decimal representation of its number has no repeating digits. For example, all years from $2013$ to $2019$ are colored, unlike $2020$.


a) Find the nearest chain of seven consecutive colored years in the future.


b) Can a chain of more than seven consecutive years happen in the future?