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Digit Sequence (Posted on 2005-06-28) Difficulty: 2 of 5
Find the rule and continue this sequence of digits:

1235813941213533488671216141383377554...

Is there a limit to the number of times in a row a digit can appear?

See The Solution Submitted by Jer    
Rating: 3.6250 (8 votes)

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Some Thoughts Theoretically (growing vs. shrinking patterns) | Comment 9 of 15 |

There is at least one instance of 5 1's in a row in Charlie's printout, but does that create a growing or shrinking pattern?

11111
2222
444
88
16
7

and it dies at 7.  With 6 1's in a row we still get a dying pattern, but at least we do end up back at a series of 1's:

111111
22222
4444
888
1616
777
1414
555
1010
111

However, if there was ever a series of 7 1's, we would get a growing pattern which would lead to an infinite number of 1's, 2's, 4's, and 8's in a row:

1111111
222222
44444
8888
161616
77777
14141414
5555555
101010101010
11111111111

7 1's will grow into 11 1's, thereby creating a growing pattern.  The following single digit pairs can each create 2 1's: 9-2, 8-3, 7-4, 6-5.


Addendum:  After doing searches on Charlie's printout I find 3 cases of 6 1's in a row.  I don't know if there is a repeating pattern going on already which would preclude 7 1's from appearing together, but it seems that the further you go out the more repeated digits you get (duh).

Edited on June 28, 2005, 6:43 pm
  Posted by Erik O. on 2005-06-28 18:36:34

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