What row of numbers comes next? (This is a tough one!)

- 1
- 11
- 21
- 1211
- 111221
- 312211
- 13112221

(

*From - http://www.riddlenut.com/*)

(In reply to

answer by K Sengupta)

Number "1" when written in words is "one". Also, the number of times

that "1" appears in the first row is also "1", which when written

in words is "one".

Since the number one appears one times in the first row, thus,

describing the first row in words, we obtain, "one one". This is "11" when

converted back to the number format, which is the number in the 2nd

row.

Thus, we depict the rationale behind the occurence of the numbers in a

given row in terms of the following table:

Row Number Description (in Words)

1 1 One one

2 11 two one

3 21 one two one one

4 1211 one one one two two one

5 111221 three one two two one one

6 312211 one three one one two two two one

7 13112221 one one one three two one three two one one

8 1113213211 ..........................................

and so on

Consequently, the required next row of numbers is 1113213211

*Edited on ***April 18, 2008, 1:29 pm**