It has the appeal of patterns that seem almost visible and yet slip away for a moment longer. There is no hidden algebra: the key is in how each term is observed.
The "look and say" sequence
Riddle statement
Observe the sequence:
\[
1,\ 11,\ 21,\ 1211,\ 111221,\ 312211,\ 13112221
\]
What is the next term?
Show solution
Solution
Answer: the next term is 1113213211.
Each term describes the previous one by listing its groups of consecutive equal digits: first how many there are, then what the digit is.
Thus, 13112221 is read by groups:
un 1 → 11
a 3 → 13
two 1 → 21
three 2 → 32
a 1 → 11
Concatenating: 11 13 21 32 11 → 1113213211.
This sequence is known as look-and-say (or Morris sequence).