It is very common in maths to study certain sequences of numbers and try to guess if they keep some kind of logic, or even if they follow a rule. There are some easy examples you know from class:
The series 2, 4, 6, 8, 10, 12, 14, ... and so on, is the ordered series of even numbers. If I asked you how to follow with it, you would answer immediately: ...16, 18, 20, 22 and so on.
It happens the same with 1, 3, 5, 7, 9, 11, 13, ... etc. (odd numbers).
And this one is one of the most important in arithmetics: 2, 3, 5, 7, 11, 13, 17, 19, ... (prime numbers).
But sometimes, the logic behind some series is not that simple, and could depend not just on math concepts, but in language instead. The following example is a bit astonishing until you understand the way numbers are used in this series:
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
Have you figured out how is this series developed? It's much easier than it seems. Each number of the series DESCRIBES the previous one, as follows:
1 could be described as '
once "one" ' (in a pattern that mentions
number-of-repetitions and
digit), so the next in the series is 11, the first '1' standing for 'once' and the second '1' standing for 'one'. If you described '11' just with this method you'd say '
twice one', so you'd get 21, and then you'd describe '21' as '
once two, once one' that drives to write 1211, which is described as '
once one, once two, twice one', which abbreviation through this method is '111221', and this time you'd say '
three times one, twice two, and once one', that is '312211'... Curious, isn't it?
Anyway, the ones I wanted you to guess their logic (same logic for both, depending on if the series have to do with English or Spanish) were the following two:
English: 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8, 7, 7, 9, 8, 6, 9, 9, 11, ...
Spanish: 3, 3, 4, 6, 5, 4, 5, 4, 5, 4, 4, 4, 5, 7, 6, 9, 10, 9, 10, 6, 9, 9, ...
Do you think you will guess? Think about number-related vocabulary...
