Topic: Has anyone seen this?
 Message: Posted by: James F (Jun 27, 2005 07:14PM)
I don't remember where I saw this and I don't know if it is supposed to be a puzzle or not. When I was shown it I think it was presented as a "find the pattern" but Im not sure. Here it is:

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221

As you can see, it starts growing quickly. I know it has no relations to Pascal's Triangle, but it always reminds me of it. Ive wondered if this could have ANY ties to usefull mathematics.

James
 Message: Posted by: JackTrumper (Jun 27, 2005 08:32PM)
Each line is describing the line above.
1
There is one 1. (11)
There is two 1's. (21)
There is one two and one one. (1211)
etc
etc

:)
 Message: Posted by: Stephen Buxton (Jun 28, 2005 01:41PM)
I'm not sure if it is true for all starting values, however, I have found that there is a point when it cycles - either by repeating the same line over and over again, or by repeating a the last few lines over and over.

BTW - there is a mistake in the 5th line: Shouldn't the description of 1211 be 1231, not 111221?
 Message: Posted by: Jonathan Townsend (Jun 28, 2005 02:30PM)
[quote]
On 2005-06-28 14:41, Stephen Buxton wrote:
...Shouldn't the description of 1211 be 1231, not 111221?
[/quote]

one 1, one 2 two 1s ?
 Message: Posted by: James F (Jun 28, 2005 07:05PM)
Jack got it right.

Stephen:

1211 is correctly described with 111221. I see what youre saying but the pattern is not to describe the total amount of numbers. (As you did by saying three ones) you go in order from left to right. Jonathan put it into words correctly.

By the way, at what point did it start repeating? I was playing around with it to see if it can reach higher than the number 3 but you never have 4 of any number.

James
James
 Message: Posted by: JackTrumper (Jun 28, 2005 08:32PM)
Is their a line that describes itself?
 Message: Posted by: Jonathan Townsend (Jun 28, 2005 09:35PM)
I believe Kurt Goodel showed that there can be such a line thanks to a trick of Quinn's.
 Message: Posted by: Stephen Buxton (Jun 29, 2005 12:45AM)
If you follow the method of counting that I used, rather than the method you described, it will start repeating after about twenty or so lines (I'm going from memory here, btw)
 Message: Posted by: Jonathan Townsend (Jun 29, 2005 07:02AM)
[quote]
On 2005-06-29 01:45, Stephen Buxton wrote:
If you follow the method of counting that I used, rather than the method you described, it will start repeating after about twenty or so lines (I'm going from memory here, btw)
[/quote]

Yeah, got you. combinations versus permutations?
 Message: Posted by: James F (Jun 29, 2005 10:14AM)
Ah I see. Ill have to play with describing each line the way you did. I wonder if it will repeat using the method I posted... Interesting...

James
 Message: Posted by: mxmln (Jun 29, 2005 10:35AM)
This is a logic sequence. What you see is what you got reading from left to right. There are no mathematical functions involved. This actually appeared in an ACT test about 15 or 20 years ago. It is an absolutely great puzzle because virtually everyone will assume there is some type of mathematical function involved. Have fun with it!!!!!!!
 Message: Posted by: Jonathan Townsend (Jun 29, 2005 10:52AM)
[quote]
On 2005-06-29 11:35, mxmln wrote:... It is an absolutely great puzzle because virtually everyone will assume there is some type of mathematical function involved. [/quote]

Good puzzles/questions discriminate. Much depends on the traits you wish to select for. One of my favorite is to ask someone what form of government we have here in the USA. The correct answer is of course "republic". If one wishes to be mean about it, one can ask the victim to recite our pledge of allegiance, and after they finish, ask them the question again. You see, sometimes you want to find people who are clever working in the box you want them inside, and sometimes you want people who can build workable boxes for ventures. Sometimes you want folks who can maintain a box and sometimes you want folks to teach others to maintain a box. Good questions/puzzles can help you find the right person for the task at hand.
 Message: Posted by: Stephen Buxton (Jun 29, 2005 05:33PM)
It's a bit late at night, so if this is wrong, please forgive me...

1
11
21
1211
1231
131221
132221
133221
232221
134211
14131231
14231241
24132231
14233221
14233221
etc etc
 Message: Posted by: James F (Jun 29, 2005 06:35PM)
On line 7 shouldnt it be: 132231? Also, In what order do you desribe the numbers? Is it always largest number to smallest?

James
 Message: Posted by: RiffClown (Jun 29, 2005 06:40PM)
Looks Familiar. To see how far it goes quickly try

http://themagiccafe.com/forums/viewtopic.php?topic=100169&forum=101
 Message: Posted by: mxmln (Jun 29, 2005 08:26PM)
The "greatness" in a puzzle is the ability to force someone to think OUTSIDE the box. If the puzzle fits within an individuals comfort zone in terms of their mental prowess (notice I am not using the word intelligence) then it really doesn't intrigue the individual because it doesn't tax their mind. Making someone think differently about something expands their mind. Giving someone information fills their mind. When you think outside the box you are opening your mind to different views, concepts, possibilities, etc. Then you will willingly want to fill it with information about these new ideas. A good logic puzzle can make you think outside the box but still keep you grounded to reality. It will help you realize just how unfocused one can become due to assumption. Assume nothing, just what exactly is the puzzle asking you to do. Don't go down any tangents that really aren't there. Think clearly and logically before embarking on a solution.
 Message: Posted by: Stephen Buxton (Jun 30, 2005 01:10PM)
As I said, it was late, and I was tired... trying again

1
11
21
1211
1231
131221
132231
232221
134211
14131231
14231241
24132231
14233221
14233221

Well, it gravitates to the same number - I guess that must be one of them there mathematical black holes that you hear talk about