Expert: Steve Holleran - 2/27/2008

Question
My son's teacher gave this sequence and asked the class to find the next one.  Believe it or not, I can't even see it.
1, 11, 21, 1211, 11121, 312211.  Can you help?

Answer
Hi Shelley,

Well, unless I'm mistaken, I think there's an omission in one of the terms here.  If not, I don't see the pattern either.

I believe that the fifth term, which you have as "11121"
should be "111221".  If so, then this is what I see:

Each term refers to the preceding term

1        = starting term

11       = the term above contains one "1"   (1-1)

21       = the term above contains two "1"s  (2-1s)

1211     = the term above contains one "2" and one "1"  (1-2,1-1)

111221   = the term above contains one "1", one "2", and two "1"s

312211   = the term above contains three "1"s, two "2"s and one "1"


etc.


If the term I questioned is correct as you have written it, and not as I have interpreted it, then I'm a little stumped too.

Let me know, and if I'm incorrect, I'll have another go at it.

Steve