This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
Title: Cliff Puzzle 9: 3-Atoms and Growth
If you respond to this puzzle, if possible please send me your name,
address, affiliation, e-mail address, so I can properly credit you if
you provide unique information. PLEASE ALSO directly mail me a copy of
your response in addition to any responding you do in the newsgroup. I
will assume it is OK to describe your answer in any article or
publication I may write in the future, with attribution to you, unless
you state otherwise. Thanks, Cliff Pickover
* * *
Start with 3 digits: 1, 2, and 3.
Each succeding row repeats the previous three rows, in order,
as you can see from the following diagram.
1. What is the sum of digits in the 100th row?
2. Get rid of all the twos. Here I've replaced each of them with a "."