Question

the year 2013 contains four digits whose values are consecutive integers. How many years after 2013 will this event occur next

Answer 1

The year 2013 contains four digits {2, 0, 1, 3} that are consecutive.

We want to find the next year such that this happens. We will find that in 18 years this will this event occur next.

The next year that this happens is the year that has the same digits, but the tens and units digits are permuted (as these are the place values with smaller values).

So the next year that this happens is:

2031

It also has the digits {2, 0, 3, 1} which has the same digits as 2013.

To find how many years after this will happen, we just need to find the difference between 2031 and 2013.

This is: 2031 - 2013 = 18

In 18 years this will this event occur next.

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