Maths Question

What row of numbers comes next 1 11 21 1211 111221 312211 13112221?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ans:

1113213211
The first row - 1 - contains one 1 -> 11
11 contains two 1's -> 21
21 contains one 2, one 1 ->1211
1211 contains one 1, one 2, two 1's ->111221
etcetera.
Building on that theory, it would go
111221 contains three 1's, two 2's, one 1-> 312211
312211 contains one 3,one 1,two 2's two 1's->13112221
13112221 contains one 1,one 3,three 2's, one 1,
therefore the next sequence of numbers would be ->1113213211
Note that even if this sequence was continued infinitely, you would never get 4 or more as a sequence, as this would require you to have two sets of the same number next to each other, which is impossible.