Jonathan Coxhead wrote (quoting me, snipped)

...

Add 1 minute to 23:59:60 31st December 2003. I assume that this is a valid time and that it will be a leap second; if not choose some other year.

This is complicated since we have multiple overflows. First stage you get the invalid time

23:60:60 31st December 2003.

But **HERE**, you add 60 seconds. Why? If you want to add "1 minute" to 23:59:60 31st December 2003, and assuming still that it is a leap minute, then to be consistent with the rule for months, I think you ought to add **61** seconds---the number of seconds in *this* minute.

If the problem had been to add "60 seconds", I would agree, but if the problem is to add "1 minute", I think there's a flaw here.

Your arithmetic is faulty. Because we are assuming 23:59:60 31st December 2003 is a leap second, there are 61 seconds until 00:01:00 1st January 2004, the time my method (eventually) produces.