[Guest]

Consider the following sequence of numbers:

...

12334444

11122344

31221324

...

1. What is the next number in the sequence?
   
2. What was the previous number in the sequence?
   
3. Is it possible for any sequence following the same rule to have a beginning (A number that can be "sequenced" no further back)? If so, which numbers could possibly fill this role?
   
4. Is it possible for any sequence following the same rule to have an end (A number that can be "sequenced" no further forward)? If so, which numbers could possibly fill this role?
   

Edited January 2, 2009 by Llam4

[bonanova]

Consider the following sequence of numbers:

...

12334444

11122344

31221324

...

1. What is the next number in the sequence?
   
2. What was the previous number in the sequence?
   
3. Is it possible for any sequence following the same rule to have a beginning (A number that can be "sequenced" no further back)? If so, which numbers could possibly fill this role?
   
4. Is it possible for any sequence following the same rule to have an end (A number that can be "sequenced" no further forward)? If so, which numbers could possibly fill this role?
   

1. 13112211131214
   
2. 23334444[blank]4444
   
3. Yes. 1 or any single number:
   1
   1 1
   2 1
   1 2 1 1
   1 1 1 2 2 1
   3 1 2 2 1 1
   ...
   
4. No. It would have to be an empty sequence, which could have no non-empty predecessor.
   

[Guest]

1. 13112211131214
   
2. 23334444[blank]4444
   
3. Yes. 1 or any single number:
   1
   1 1
   2 1
   1 2 1 1
   1 1 1 2 2 1
   3 1 2 2 1 1
   ...
   
4. No. It would have to be an empty sequence, which could have no non-empty predecessor.
   

2. There aren't any spaces in the numbers (They're only one number)

3. Including only single digit numbers your range would be -9 to 9, giving you 19 (including 0) possibilities. However, there are an infinite amount of possible beginning numbers if you consider the rules that you know. There are two more ways to make a "beginning" number.