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Addition sequence (Posted on 2007-01-09) Difficulty: 2 of 5
1, 1, 2, 11, 12, 13, 112, 113, 114, 1104, 2004, 2012, 1031, 123, ...

Name the next few numbers in the sequence. What is the ultimate fate of this sequence?

  Submitted by Tristan    
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Solution: (Hide)
Each number in the sequence is determined by looking at the previous two numbers in the sequence. The rightmost digit is equal to the number of 1s, the tens digit is equal to the number of 2s, the hundreds digit is equal to the number of 3s, etc.

After a while, the sequence will begin to loop. The sequence begins with the following:

1, 1, 2, 11, 12, 13, 112, 113, 114, 1104, 2004, 2012, 1031, 123, 213, 222, 141,

And then the rest of the numbers loop infinitely:

1032, 1113, 214, 1114, 2014, 2014, 2022, 1041

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2008-12-09 06:32:21
AnswerK Sengupta2008-10-22 05:23:50
No SubjectAnsh2007-02-21 14:19:05
Questionre: next few terms. (No spoiler)David Johnson2007-01-16 09:09:14
next few terms. (No spoiler)Jer2007-01-09 13:02:12
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