5-3-2014: One of only 48 such dates in the 21st century

If the full date of this Saturday, May 3, 2014 is written as 5-3-2014 (or simply, 532014), it only contains sequential digits 0, 1, 2, 3, 4 and 5, where each digit appears only once.

Calendar dates made of sequential digits such as 5-3-2014 are rare because, for example, they didn't occur at all in the 20th century

I got excited about this numerical property and wondered how many more such calendar dates exist in this century.

After a little bit of investigation, I found out that there are a total of 48 such dates in the 21st century.



Note that 24 of the 48 are expressed as six-digit calendar dates (containing digits 0 to 5) indicated in green color and the other 24 are written as seven-digit dates of seven (made of digits 0 to 6) indicated in yellow color.

The first three such six-digit calendar dates made of digits 0 to 5 only already occurred last year (4-5-2013 and 5-4-2013) and early this year (3-5-2014) and mostly went unnoticed.

The fourth one will be 5-3-2014 to occur on Saturday this week.

My hope is to generate some attention to these calendar days because they are not only fun numerically but also possess the potential to serve as brainteasers.

The first such seven-digit calendar date in this century made of digits 0 to 6 only will occur in 2034, on May 16 (5-16-2034). Also, note that 2034 contain four such calendar dates, two six digits, made of only digits 0 to 5, and the other two each having seven digits, made of digits 0 to 6 only.

These calendar dates are still considered to be rare since for example, no such calendar dates exist in this century after 2065.

Here are a few brainteaser questions I constructed related to these sequential-digit dates:

1. Which calendar date will be the first six-digit such calendar date made of only digits 0 to 5 in the next (22nd) century?

2. Which calendar date will be the first seven-digit such calendar date made of only digits 0 to 6 in the next century?

3. Which calendar date will be the first eight-digit such calendar date (made of digits 0 to 7) in this millennium?

4. How many such dates existed in the 20th century?

5. How many such dates exist in the 23rd century?

Answers

1. 4-5-2103
2. 5-06-2134
3. 06-17-2345
4. None
5. None
 

Aziz S. Inan, Ph.D., is professor of Electrical Engineering at the University of Portland