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Latest past date with eight different digits

Question

Writing dates as MM/DD/YYYYMM/DD/YYYY, find the most recent date (up to today) in which all eight digits are different, such as 01/23/456701/23/4567 would be if it were in the past. Give it as MMDDYYYYMMDDYYYY.

Short answer

0625198706251987. A year beginning with 22 leaves no valid month-day combination without repeating 00, 11 or 22, so the year starts with 11 and the month with 00. Maximising the rest gives year 19871987, then month 0606 and day 2525; a scan of all dates confirms it.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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