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Usenet Newsgroups : rec.puzzles Hall of Fame

The 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.

Hall of Fame
Categories : pickover : pickover.01.p

Title: Cliff Puzzle 1: Can you beat the numbers game?

If you respond to this puzzle, if possible please include your name,
address, affiliation, e-mail address.  If you like, tell me a little bit
about yourself.  You might 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

* * *
At a recent trip to the Ontario Science Center in Toronto, Canada I came
across an interesting puzzle.  The center is located minutes from
downtown Toronto and it's a vast playground of science with hundreds of
exhibits inviting you to touch, try, test, and titillate your curiosity.
The puzzle I saw there can be stated as follows.  In the 10 boxes below,
write a 10-digit number.  The digit in the first box indicates the total
number of zeros in the entire number.  The box marked "1" indicates the
total number of 1's in the number.  The box marked "2" indicates the
total number of 2's in the number, and so on.  For example, the "3" in
the box labeled "0" would indicate that there must be exactly three 0's
in the 10-digit number.

| 0| 1| 2| 3| 4| 5| 6| 7| 8| 9|
| 3|  |  |  |  |  |  |  |  |  |

Stop And Think

1. Is there a solution to this problem?  Are there many solutions to this

2. A more advanced an interesting problem is to continue to
generate a sequence in a recursive fashion such that each row becomes
the sequence for the previous.  For example, start with the usual
0 through 9 digits in row 1:

Row 1: 0 1 2 3 4 5 6 7 8 9

Assume Row 2 is your solution to the puzzle.  I've just inserted random
digits below so as not to give away the solution:

Row 1: 0 1 2 3 4 5 6 7 8 9   S(1)
Row 2: 9 3 2 3 3 1 6 7 8 9   S(2)
Row 3:                       S(3)

Row 2 is now the starting point, and your next job is to form row 3, row 4,
etc. using the same rules.  In the previous example, a digit in the
first box would indicate how many 9's there are in the next 10-digit number,
and so forth.

Contest: I am looking for the longest sequence of numbers users can come
up with using these rules.  Can you find a Row 2 or Row 3?
Is it even possible to generate a "row 2" or "row 3"?


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