Grades 11-12 Video Solutions 2013-Grades 11-12 Video Solutions 2013 problem5

Video Transcription

Question number five, the year 2013 has the property that its number is made up of the consecutive digits 0, 1, 2, and 3.  How many years have passed since the last time a year was made up of four consecutive digits?  So what we are looking for is a number as large as possible but less than 2013 made up with four consecutive digits.  What we know at first is that no such number exists.  In the span between 2000 and 2013. So since that's true, we must start with a 1.  We can check by inspection. So let's make a note of that.  By inspection, no such number exists between 2000 and 2012.  So beginning with 1, we use 1, 2, 3, and 4.  And the largest possible number we can come up with is 1432.  And so 1432 was the last year this occurred. And this was by subtracting 581 years ago.

Video Summary

The year 2013 contains consecutive digits 0, 1, 2, and 3. The task is to determine how many years have passed since the last occurrence of a year with four consecutive digits. After examining years before 2013, it was found that the number 1432 is the most recent year composed of four consecutive digits, specifically 1, 2, 3, and 4. Thus, 581 years have elapsed since 1432.