Just to clarify….I never meant to SKIP zero. The two options I was thinking of were either to have zero only count as the low end of the string, because zero is actually the smallest value digit, so the only options would be numbers that contain 0-1-2-3, 1-2-3-4, 2-3-4-5, 3-4-5-6, 4-5-6-7, 5-6-7-8, and 6-7-8-9, OR to allow zero to connect the lowest digits to highest digits (kind of like an ace connects the lows and the highs in the card game spit), which would also allow 7-8-9-0, 8-9-0-1, and 9-0-1-2. There are 24 possible orders for any four unique digits, so that would be 168 possibilities if zero only counts low, 240 possibilities if zero can “string”. There are 9,000 positive integers that contain 4 digits, so that’s 168/9000 or 1.8667% if zero is low, 240/9000 or 2.6667% if zero strings. To have two such numbers independently, you just square the odds, so 0.0348% if zero is low, 0.0711% if zero strings.
My sentence “The year 2,013 is the first year since 1,987 to have all unique digits, and when rearranged they are also consecutive” was admittedly confusing lol. ‘They are also consecutive’ was not referring to the 1,987; following either of the two possibilities, 1987 would not be consecutive (and I think just deciding to “ignore” zero wouldn’t be a very fair move, saysme, but thanks for the thought). The only commonality between 1987 and 2013 is the uniqueness of digits, which none of the years between them have.