# The Common Thread

What common property unites all of the following numbers?

4, 9, 60, 101, 400, 450, 910, 1010

The set of numbers that share this common property is not limited to just these eight, but the list should provide enough information to solve it.

• Can we also assume that no other numbers below 1010 share this commonality? – breadbox Mar 13 '15 at 3:16
• @breadbox I didn't find any more below 1010 but there could have been some that I missed – Ben Mar 13 '15 at 3:50

## 2 Answers

There are the numbers whose roman numeral translations are in strict alphabetical order (so no repetitions).
 4=IV, 9=IX, 60=LX, 101=CI, 400=CD, 450=CDL, 910=CMX, 1010=MX

• If this is correct, then there's also 104, 109, 401, 404, 409, 501, 504, 509, 550, 905, and 1005. – breadbox Mar 13 '15 at 4:59
• You're right, those ones fit too. I wasn't sure if putting a lot of numbers would give it away too quickly so I stopped once I had found 8 :) – Ben Mar 13 '15 at 13:49
• If you take out 450 and 910 from the original list, you get a tighter pattern that also includes 501, 505, 550, 900, 1005, ... – user3294068 Oct 8 '15 at 15:38

I guess it is

Roman numerals with 1 letter, in alphabetical order; then those with 2 letters, etc.

and the source is http://oeis.org/A003588