Distinct Past
Number Theory
Level
2
The year 2013 consists of 4 distinct digits. How many years ago, was the previous (most recent) year which consisted of 4 distinct digits?
Details and assumptions
The year 2000 is 2013-2000 = 13 years ago.
The answer is 26.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
We check the cases. This cannot happen in 2012 (digit 2 appears twice), 2011 (digit 1 appears twice) or 2010 (digit 0 appears twice). It cannot happen in any year that starts with 200, since the digit 0 will appear at least twice. It also cannot happen in any year that starts with 199, since the digit 9 will appear at least twice. It also doesn't happen for 1989 (since digit 9 appears twice) or 1988 (since digit 8 appears twice). We see that 1987 does have 4 distinct digits. Hence, the previous time was 1987, which is 2 0 1 3 − 1 9 8 7 = 2 6 years ago.