Games, Puzzles and Quizzes

Aanchal Malhotra's Avatar
Moderator
Joined: 26 Jul 2011
Post: 664
29 Sep 2011 12:21:02 IST
6 People liked this
13
1350 View Post
What's the next number?
Engineering Entrance , JEE Main , JEE Main & Advanced

Hey guys....

Its time for teasing your brains a bit and answer the question...

Here is a series of numbers. What is the next number in the sequence?
1
11
21
1211
111221
312211
13112221

Lets see what you come up with



Comments (13)


New kid on the Block

Joined: 25 Dec 2009
Posts: 3
6 Oct 2011 00:23:17 IST
0 people liked this

1.

Priyank Kumar's Avatar

Hot goIITian

Joined: 29 Sep 2009
Posts: 165
6 Oct 2011 03:47:04 IST
1 people liked this

INDUCTION IS IMPOSSIBLE
Abhishek Gorai's Avatar

Cool goIITian

Joined: 3 Jun 2011
Posts: 37
6 Oct 2011 18:39:40 IST
0 people liked this

??? How to do ??? Don't see any pattern

New kid on the Block

Joined: 7 Oct 2011
Posts: 7
7 Oct 2011 23:01:23 IST
0 people liked this

1 is the answer

New kid on the Block

Joined: 18 Oct 2011
Posts: 3
18 Oct 2011 20:07:26 IST
0 people liked this

3.


Cool goIITian

Joined: 18 Oct 2011
Posts: 91
18 Oct 2011 22:00:27 IST
1 people liked this

1113213211
The first row - 1 - contains one 1 -> 11
11 contains two 1's -> 21
21 contains one 2, one 1 ->1211
1211 contains one 1, one 2, two 1's ->111221
etcetera.
Building on that theory, it would go

111221 contains three 1's, two 2's, one 1-> 312211
312211 contains one 3,one 1,two 2's two 1's->13112221
13112221 contains one 1,one 3,three 2's, one 1,

therefore the next sequence of numbers would be ->1113213211


Aakanksha Sangwan's Avatar

Cool goIITian

Joined: 26 Jan 2012
Posts: 53
5 Feb 2012 13:49:51 IST
0 people liked this

1 ?

New kid on the Block

Joined: 8 Apr 2012
Posts: 4
8 Apr 2012 11:38:40 IST
0 people liked this

1

New kid on the Block

Joined: 8 Apr 2012
Posts: 4
8 Apr 2012 11:38:59 IST
0 people liked this

1

Hot goIITian

Joined: 11 Mar 2012
Posts: 124
8 Apr 2012 12:39:16 IST
0 people liked this

I think 1.....


Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
8 Apr 2012 13:15:46 IST
3 people liked this

 I will tell you what this is 

first just write 1
now read (You can see a single(one) one)
Hence read one one
and write it . Now you get 
11
Now again read
there are two(ones) hence say two 1
write
21
Now read
one two one 1
1211
now read 
111221
go onnn continuing....... You wiil get this 
pLEASE CLICK LIKE

A small history of this sequence
This sequence is called asA005150
 

A005150 as a simple table

n   a(n)
1   1
2   11
3   21
4   1211
5   111221
6   312211
7   13112221
8   1113213211
9   31131211131221
10   13211311123113112211
11   11131221133112132113212221
12   3113112221232112111312211312113211

[1,11,21,1211,111221,312211,13112221,1113213211, 31131211131221,13211311123113112211, 11131221133112132113212221, 3113112221232112111312211312113211]

 

 

Look and Say Sequence

DOWNLOAD Mathematica Notebook

The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. Starting with 1, the sequence would be defined by "1, one 1, two 1s, one 2 one 1," etc., and the result is 1, 11, 21, 1211, 111221, .... Similarly, starting the sequence instead with the digit d for 2<=d<=9 gives d, 1d, 111d, 311d, 13211d, 111312211d, 31131122211d, 1321132132211d, ..., as summarized in the following table.

d Sloane sequence
1 A005150 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
2 A006751 2, 12, 1112, 3112, 132112, 1113122112, 311311222112, ...
3 A006715 3, 13, 1113, 3113, 132113, 1113122113, 311311222113, ...
LookAndSaySequenceDigits

The number of digits in the nth term of the sequence for d=1 are 1, 2, 2, 4, 6, 6, 8, 10, 14, 20, 26, 34, 46, 62, ... (Sloane's A005341). Similarly, the numbers of digits for the nth term of the sequence for d=2, 3, ..., are 1, 2, 4, 4, 6, 10, 12, 14, 22, 26, ... (Sloane's A022471). These sequences are asymptotic to Clambda^n, where

C_1  approx 1.567...
(1)
C_d  approx 1.814...
(2)
lambda = 1.303577269034296....
(3)
LookAndSaySequenceRoots

The quantity lambda is known as Conway's constant (Sloane's A014715), and amazingly is given by the unique positive real root of the polynomial

 0=x^(71)-x^(69)-2x^(68)-x^(67)+2x^(66)+2x^(65)+x^(64)-x^(63)-x^(62)-x^(61)-x^(60)-x^(59)+2x^(58)+5x^(57)+3x^(56)-2x^(55)-10x^(54)-3x^(53)-2x^(52)+6x^(51)+6x^(50)+x^(49)+9x^(48)-3x^(47)-7x^(46)-8x^(45)-8x^(44)+10x^(43)+6x^(42)+8x^(41)-5x^(40)-12x^(39)+7x^(38)-7x^(37)+7x^(36)+x^(35)-3x^(34)+10x^(33)+x^(32)-6x^(31)-2x^(30)-10x^(29)-3x^(28)+2x^(27)+9x^(26)-3x^(25)+14x^(24)-8x^(23)-7x^(21)+9x^(20)-3x^(19)-4x^(18)-10x^(17)-7x^(16)+12x^(15)+7x^(14)+2x^(13)-12x^(12)-4x^(11)-2x^(10)-5x^9+x^7-7x^6+7x^5-4x^4+12x^3-6x^2+3x-6,
(4)

all of whose roots are illustrated above.

In fact, the constant is even more general than this, applying to all starting sequences (i.e., even those starting with arbitrary starting digits), with the exception of 22, a result which follows from the cosmological theorem. Conway discovered that strings sometimes factor as a concatenation of two strings whose descendants never interfere with one another. A string with no nontrivial splittings is called an "element," and other strings are called "compounds." It is postulated that every string of 1s, 2s, and 3s that does not contain four of the same number in succession eventually "decays" into a compound of 92 special elements, named after the chemical elements.

 


Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
27 Apr 2012 12:53:50 IST
0 people liked this

are everybody okk with my solution

Hot goIITian

Joined: 29 May 2012
Posts: 139
5 Jun 2012 12:19:14 IST
1 people liked this

cool copied solution..



Quick Reply


Reply

Some HTML allowed.
Keep your comments above the belt or risk having them deleted.
Signup for a avatar to have your pictures show up by your comment
If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team
Free Sign Up!
Sponsored Ads

Preparing for JEE?

Kickstart your preparation with new improved study material - Books & Online Test Series for JEE 2014/ 2015


@ INR 5,443/-

For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
Altitude - 16545 m
Post - 7958
2. Himanshu
Altitude - 10925 m
Post - 3836
3. Hari Shankar
Altitude - 10085 m
Post - 2217
4. edison
Altitude - 10825 m
Post - 7804
5. Sagar Saxena
Altitude - 8635 m
Post - 8064
6. Yagyadutt Mishr..
Altitude - 6330 m
Post - 1958

Find Posts by Topics

Physics

Topics

Mathematics

Chemistry

Biology

Parents Corner

Board

Fun Zone