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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1047.0. "next in series" by VIVIAN::MILTON (I'm thinking about it!) Tue Apr 04 1989 04:57

    What are the next terms in the following series?
    
    
    36 91 21 51 82 12
    
    and
    
    18 22 26 21
    
    The latter is said to be temporal.
    
    I'm useless at this sort of thing, can anyone give some good stratagies
    for solving these?
                     
    Thanks
    
    Tony.
T.RTitleUserPersonal
Name		DateLines
1047.1series depending on first number???AISG::MONROETue Apr 04 1989 08:1531
    Well, I have worked with these type of problems a little so I'll
    take a crack at this.
    
    For the first series...
    
    >> 36 91 21 51 82 12
    
    my guess would be that it would continue with
    
    42 73 03 33 64 ...
    
    It seem to add 30 (hence the 3 in 36), mod with 100.  When the digits
    of a number add up to 6 (hence the 6 in 36), we shift increment
    the one's digit.
    
    For the second series...
    
    >> 18 22 26 21 
    
    my guess is to continue it with ...
    
    25 29 33 27 41 45 49 53 51 ...
    
    Here we add 4 to the previous number until the sum of the digits
    add up to 8 (hence the 8 in 18).  When the digits to add up to 8,
    we set the one's digit to 1 (hence the 1 in 18).  This will lead
    to a problem though if the number 71 ever shows up in the series.
    As I said earlier, I've had a "little" practice with these.  I'd
    be glad to see what other possibilities other people come up with.
    
    	-Tod-
1047.2turn it on it's headNEATO::CAMHITue Apr 04 1989 11:1636
    a short version of the solution for 
    
    a. 36 91 21 51 82 12 
    
    comes when you look at it slightly differently (it also explains the
    36): 
    
    push the numbers together:
    
    b.	369121518212
    
    which, when pulled back apart slightly differently gives:
    
    c.	3,6,9,12,15,18,21,2...
    
    so you'd continue (b) with:
    
    d.	42730333639424548...
    
    so you'd get the solution:
    	
    e.	42,73,03,33,63,94,24,54...
    
    which gives you the same solution as .1
    
    where they would possibly diverge is once (c) gets to 3-digit numbers;
    since the series (a) is combining everything into 2-digits, (e)
    would continue:
    
    ...9 1,02, 10,5 1,08, 11,1 1,14...
                               
    but .1 may do something funny.
    
    -Keith
1047.3NEATO::CAMHITue Apr 04 1989 12:578
    in case it wasn't clear what I was doing in .2, its just a series
    of multiples of 3 squooshed together then pulled out in 2-digit
    numbers
    
    re .0
    
    what is meant by "temporal" with regard to series?
1047.4HERON::BUCHANANAndrew @vbo DTN 828-5805Wed Apr 05 1989 09:227
Good on you for solving No.1

"temporal" means "related to the concept of 'time'"

Eg the four numbers given might be days of the month, or something.

Andrew.