Where one number describes the previous number. Basically to get the next number in a sequence, look at the last number, then group all the digits in repeating groups.
For example:
Take the number: 1111333211233311222
Group it as follows:
(1111) (333) (2) (11) (2) (333) (11) (222)
Now count the number of times each digit appears in each group.
(1111) has 4 ones
(333) has 3 threes
(2) has 1 two
(11) has 2 ones
(2) has 1 two
(333) has 3 three
(11) has 2 ones
and
(222) has 3 two
or:
(4 ones) (3 threes) (1 two) (2 ones) (1 two) (3 three) (2 one) (3 twos)
which can be:
(4 1) (3 3) (1 2) (2 1) (1 2) (3 3) (2 1) (3 2)
Now write all the digits as one number:
4133122112332132
Hence, if the sequence started with 1111333211233311222, the next number is:
4133122112332132, Which would be followed by: 141123112221122312111312, and then 11142112132132212213111231131112 and so on
Ok, that's a complicated example, so lets apply this to the test sequences you asked about
:
11 21 1211
Take the first number, and group common digits.
(11)
Now count the digits in each group:
(2 ones)
Now rewrite as a single number:
21.... check
repeat:
(2) (1)
(1 two) (1 one)
1211 check.
Now for the answer to the test:
(1) (2) (11)
(1 one) (1 two) (2 ones)
And the answer becomes:
111221
Originally Posted by JPaul
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