A quick puzzle

jogger08152 · #1 04-09-2007, 11:17 PM

A friendly acquaintance passed this to me on a small note over cards two weekends ago. Complete the next line, but please don't explain your reasoning. I'll know if you're right:

1
11
21
1211
111221
312211
...

Enjoy.

bigpooch · #2 04-09-2007, 11:27 PM

13112221 and the next line is
1113213211

kyro · #3 04-10-2007, 12:31 PM

[ QUOTE ]
13112221 and the next line is
1113213211

[/ QUOTE ]

31131211131221

UMTerp · #4 04-10-2007, 12:58 PM

[ QUOTE ]
[ QUOTE ]
13112221 and the next line is
1113213211

[/ QUOTE ]

31131211131221

[/ QUOTE ]

13211311123113112211

gumpzilla · #5 04-10-2007, 01:03 PM

Conway proved some crazy, crazy things about this sequence. Here is a reference.

jay_shark · #6 04-10-2007, 01:19 PM

13112221.

I see the pattern now . Any time a row has consecutive one's (1 or more ), you add them and follow that with an additional 1 . If a previous row begins with a non one , then the next row will commence with a 1 . If a previous row commences with a one , then the subsequent row will commence with two 1's .

theweatherman · #7 04-10-2007, 01:34 PM

[ QUOTE ]
13112221.

I see the pattern now . Any time a row has consecutive one's (1 or more ), you add them and follow that with an additional 1 . If a previous row begins with a non one , then the next row will commence with a 1 . If a previous row commences with a one , then the subsequent row will commence with two 1's .

[/ QUOTE ]

no quite. read the string of terms out loud: 13112221 as one 1 one 3 two 1s three 2s one 1 and you get the next entry as 1113213211, then 31131311131221 then 13211311133113112211 then 111312211331232113212221 to infinity

jay_shark · #8 04-10-2007, 01:49 PM

Very nice !

arahant · #9 04-10-2007, 02:50 PM

[ QUOTE ]
Conway proved some crazy, crazy things about this sequence. Here is a reference.

[/ QUOTE ]

wow. that's actually kind of creepy!