csc@watmath.UUCP (Computer Sci Club) (02/17/84)
what's the next term
1, 110, 111, 100, 1001, 11010, 11011, 11000, 11001, ?,
William Hughestjl@cbnap.UUCP (02/17/84)
The problem was posted as:
1, 110, 111, 100, 1001, 11010, 11011, 11000, 11001, ?
I think the intended puzzle was:
1, 110, 111, 100, 11001, 11010, 11011, 11000, 11001, ?
-----
If not, I'll stand corrected.
(But my version makes a good puzzle anyway!).tjl@cbnap.UUCP (02/17/84)
> what's the next term > > 1, 110, 111, 100, 1001, 11010, 11011, 11000, 11001, ?, > > William Hughes I think the intended puzzle is: 1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, ?, --- If not, my version is still a good problem. --------------------------------------- A similar problem (if you liked that) is: 1, 1N, 10, 11, 1NN, 1N0, 1N1, 10N, ? ---------------------------------------
johnc@dartvax.UUCP (johnc) (02/18/84)
I think the puzzle was posted right. I'm not sure if I have the right answer, but the original posting was correct. --johnc
csc@watmath.UUCP (02/19/84)
Sorry about that, the sequence I had in mind was indeed
1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, ?
---
William Hughes
(Next time I'll check SIX times)ark@rabbit.UUCP (Andrew Koenig) (02/22/84)
Give some more terms: 14, 23, 28, 34, 42, 50, 59, 66, 72, 79 ...
ols@pyuxmm.UUCP (OL Springer) (02/23/84)
Sequence continues with: 86, 96, 103, 110, 116, etc. Easy if you're from New York City.
ols@pyuxmm.UUCP (OL Springer) (02/23/84)
Sorry, didn't mention original problem: >>Give some more terms: >> >> 14, 23, 28, 34, 42, 50, 59, 66, 72, 79 ... >> >> More terms: 86, 96, 103, 110, 116, etc.
ken@ihuxq.UUCP (ken perlow) (02/24/84)
-- >>> >>Give some more terms: >>> >> >>> >> 14, 23, 28, 34, 42, 50, 59, 66, 72, 79 ... >>> >> >>> >> >>> More terms: 86, 96, 103, 110, 116, etc. Well, I grew up in New York, so I know how typically provincial this puzzle is. If you're tearing your hair out about it and have never ridden the New York City subways, get some sleep-- it's a dirty trick, like New York itself. Look it--some of us LIKE to do puzzles, and would rather not waste time on that kind of cheap pedantry. This is a NET-WIDE newsgroup! Or how would YOU, dear New Yorker who posted that puzzle like to work on 12, 23, 27, 47, 53, 57, ... What? You've never ridden the ICG south from the Loop? How quaint! -- *** *** JE MAINTIENDRAI ***** ***** ****** ****** 23 Feb 84 [4 Ventose An CXCII] ken perlow ***** ***** (312)979-7261 ** ** ** ** ..ihnp4!ihuxq!ken *** ***
amigo2@ihuxq.UUCP (John Hobson) (02/24/84)
Easy, the sequence: 14, 23, 28, 34, 42, 50, 59, 66, 72, 79, 86, 96, 103, 110, 116, ... is Manhattan subway stops (BMT?). John Hobson AT&T Bell Labs--Naperville, IL ihnp4!ihuxq!amigo2
csc@watmath.UUCP (Computer Sci Club) (02/24/84)
1, 110, 111, 100, 11010, 11011, 11000, 11001, 11110 ...
The sequence is the counting numbers written to base (-2).
If you enjoy recreational mathematics you might find negative
bases fun to play with. For instance prove that all integers (positive
and negative) can be repesented base (-2). Generalize to other negative
bases. Study the bijection from the non negative integers to the integers
given by mapping the base two representation to the base (-2) representation.
Find addition, subtraction, multiplication, division, negation rules in
base (-2). Hours of fun for the whole family!
William Hughestjl@cbnap.UUCP (02/27/84)
I haven't seen a solution to the puzzle as origionally posted,
so I'm including the solution to the puzzle in this form...
1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, ?
the sequence continues...
11110, 11111, 11100, 11101, 10010, 10011, 10000, ...
SOLUTION
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The sequence is the counting numbers in negabinary (radix -2).
If you've never tried a negative radix before, it is worth exploring
a little. For example, no unary signs are needed to indicate negative
or positive numbers. The addition table is...
0 1
|---------|
0 | 0 | 1 |
|---------|
1 | 1 | 110 |
|---------|
Try adding one and negative one. (Note what happens to carries.)
11
+ 1
---
0
It should be possible to design a computer to use negabinary
arithmetic instead of one or two's complement arithmetic. (There's
a good master's thesis for some EE.)
Using a decimal point for rational values works fine (as would some
sort of floating point standard).
QUESTION: What happens to logs in negabinary?
By the way, if there is a solution to the problem as origionally
posted (fifth element was 1001 instead of 101), I'd like to see
the solution.wickart@iuvax.UUCP (04/27/84)
SPOILER ! ! ! ! !
Looks to me like you're counting in base -2. The next item would
be 11110. Neat ! I haven't seen a negative base problem since
8th grade anybody have more ?
Bill Wickart