This question concerns calendar dates of the form \[d_1d_2/m_1m_2/y_1y_2y_3y_4\] in the order day/month/year.

The question specifically concerns those dates which contain no repetitions of a digit. For example, the date \(23/05/1967\) is such date but \(07/12/1974\) is not such a date as both \(1=m_1=y_1\) and \(7=d_2=y_3\) are repeated digits.

We will use the Gregorian Calendar throughout (this is the calendar system that is standard throughout most of the world; see below.)

  1. Show that there is no date with no repetition of digits in the years from \(2000\) to \(2099\).

Which digits are already in use?