All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

1, 1, 2, 11, 12, 13, 112, 113, 114, 1104, 2004, 2012, 1031, 123, ...

Name the next few numbers in the sequence. What is the ultimate fate of this sequence?

 See The Solution Submitted by Tristan No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 Puzzle Solution Comment 5 of 5 |

Let T(n) = nth term of the sequence.

Then,
Units digit of T(n) = # 1's in T(n-1) and T(n-2) taken together.

Tens digit of T(n) = # 2's in T(n-1) and T(n-2) taken together.

Hundred digit of T(n) = # 3's in T(n-1) and T(n-2) taken together, and so on.

Accordingly, we must have:

T(13) = 1031 (given)
T(14) = 123 (given), so that:
T(15) = 213
T(16) = 222
T(17) = 141

T(18) = 1032
T(19) = 1113
T(20) = 214
T(21) = 1114
T(22) = 2014
T(23) = 2014
T(24) = 2022
T(25) = 1041
T(26) = 1031
T(27) = 1032
T(28) = 213
T(29) = 222
T(30) = 141

-----------
----------, and so on.

Consequently, we can now assert that:

(i) The respective missing 15th term, 16th term and the 17th term are 213, 222 and 141.

(ii) From the 18th term onwards, the given sequence will loop indefinitely.

 Posted by K Sengupta on 2008-12-09 06:32:21

 Search: Search body:
Forums (0)