## Wednesday, July 23, 2008

### Strange Sequence

Here is a sequence of numbers:

1 11 21 1211 111221

It seems to be a strange sequence, but yet there is a system behind it...

First Question: What is the next term in this sequence?

Second Question: Here is another sequence of numbers:

1 11 21 1211 1231 131221

What is the next term in this sequence?

First Answer: The system behind the sequence is that each number (except the first one of the sequence) "describes" the previous number. So 11 means one "1", 21 means two times a "1", 1211 means one "2" and one "1", and 111221 means one "1", one "2", and two times a "1". The number following on 111221 is therefore 312211 (three times a "1", two times a "2", and one "1").

Second Answer: Again, the system behind the sequence is that each number (except the first one of the sequence) "describes" the previous number. Now, however, the number of occurrences of each cipher is counted. So 1231 means one "2" and three times a "1", and 131221 means one "3", one "2", and two times a "1". The number following on 131221 is therefore 132231 (one "3", two times a "2", and three times a "1"). The complete sequence is as follows:

1 11 21 1211 1231 131221 132231 232221 134211 14131231 14231241 24132231 14233221 14233221 etcetera