Through a simple #Lua script we can find that over 1900-2100 there's 730 such dates:
for day=1,365.25*200 do
local time = os.time{year=1900, month=1, day=day}
local d = os.date('*t', time)
if d.year//100 + d.year%100 + d.month + d.day == 68 then
print(os.date('%Y-%m-%d', time))
end
end
Joining these dates back to Wikipedia for "interesting events" is left as an exercise to the reader (as is reimplementing in other languages).