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Have a good day

Some years ago I bought a car which had a digital display on its dashboard. The 10 digits displayed showed the date and time, such as

17:05:86 15:32

A “good day ” was a day during which the 10 digits displayed were all different. In particular, I recall two good days, more than four months apart. The day mid-way between the two was not a good day, but in each month between those two good days there was at least one good day.

What were the dates (day and month) of those two particular good days?

WIN…

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