Review question

# Which dates contain no repetitions of a digit? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5212

## Suggestion

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?