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...
