Usenet Newsgroups : rec.puzzles Hall of FameThe rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided. Many of these puzzles also appear in Braingle's own collection. |
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Title: Cliff Puzzle 9: 3-Atoms and Growth
From: cliff@watson.ibm.com
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
2
3
123
23123
312323123
12323123312323123
2312331232312312323123312323123
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 "."
1
.
3
1.3
.31.3
31.3.31.3
1.3.31.331.3.31.3
.31.331.3.31.31.3.31.331.3.31.3
In the last row of this diagram, there are three different species: 31,
331 and 3. How many different species are there in row 30?
3. When the sequence first hits a three, it now undergoes an enzymatic
cleavage, and the digits on the right of the 3 are swapped with the
digits on the left.
1
2
3
123
23123 now becomes 12323
312312323 now becomes 123123233
Now answer the question posed in question 2.
Solution
