mort@ihuxn.UUCP (Having trouble.) (11/27/83)
A friend of mine wrote this puzzle on the board and I haven't found a way to do it except by finding a loophole in the rules. Here is the board: ------------------------------------------- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ------------------------------------------- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ------------------------------------------- The puzzle is to draw a line (please not on your terminal screen) WITHOUT LIFTING THE WRITING INSTRUMENT starting from any point not on an intersection of lines in such a way that every line segment is ONCE AND ONLY ONCE touched by your line. Every segment must be touched once. Look at the middle horizontal line: it has three segments, each of which must be touched once. You may pass through a line as long as yo do it only once. Here is the catch: YOU MUST NOT DRAW OVER YOUR OWN LINE. I hope I have made the directions clear enough. Ted Brown says it's impossible. Joe Slotkowski says it is blatantly obvious, and drew a mess of spaghetti that fit the rules and solved the puzzle, but I couldn't repeat it. -- Mort Dubman AT&T Bell Laboratories ihnp4!ihuxn!mort Naperville, IL.
spaf@gatech.UUCP (11/27/83)
Vg pnaabg or fbyirq nppbeqvat gb gur ehyrf tvira. Va snpg, gur chmmyr
vf onfvpnyyl n irefvba bs gur Oevqtrf bs Xbavtforet ceboyrz fbyirq ol
Rhyre.
Yrg rnpu rapybfrq nern or rdhvinyrag gb n iregrk va n tencu, naq yrg
rnpu yvar frtzrag frcnengvat gjb fhpu nernf or na rqtr va gur
pbeerfcbaqvat tencu. (Gurer vf n iregrk pbeerfcbaqvat gb gur "bhgfvqr"
bs gur svther juvpu vf pbaarpgrq gb nyy gur bgure iregvprf, cbffvoyl ol
zber guna bar rqtr.)
Gur ceboyrz cbfrq vf gurersber rdhvinyrag gb svaqvat n Rhyrevna cngu.
Fhpu n cngu rkvfgf va n pbaarpgrq, aba-qverpgrq tencu vss gur ahzore bs
iregvprf bs bqq qrterr vf 0 be 2. Hasbeghangryl sbe hf, gur tencu
pbagnvaf 4 iregvprf bs bqq qrterr (gur "bhgfvqr" iregrk, gur iregrk
pbeerfcbaqvat gb gur zvqqyr fdhner va gur gbc ebj, naq obgu iregvprf
sebz gur obggbz ebj).
Va n zber vaghvgvir znaare, pbafvqre gung nal obk jvgu na bqq ahzore bs
fvqrf (frtzragf) zhfg unir gur cngu rvgure ortva be raq vafvqr bs vg;
bgurejvfr, lbh arrq na rira ahzore bs fvqrf, orpnhfr rnpu ragenapr gb
gur obk zhfg unir n pbeerfcbaqvat rkvg. Fvapr n pbzcyrgryl pbaarpgrq
cngu guebhtu nyy gur fvqrf pna unir ng zbfg 2 raqcbvagf, gurer pna or
ng zbfg 2 obkrf jvgu na bqq ahzore bs rqtrf. Gurer ner 4 fhpu obkrf,
guhf gur ceboyrz vf vafbyhnoyr.
--
Off the Wall of Gene Spafford
School of ICS, Georgia Tech, Atlanta GA 30332
CSNet: Spaf @ GATech ARPA: Spaf.GATech @ CSNet-Relay
uucp: ...!{akgua,allegra,rlgvax,sb1,unmvax,ulysses,ut-sally}!gatech!spafags@pucc-k (Seaman) (11/28/83)
The puzzle is indeed solvable if you are allowed to pass through a line lengthwise instead of merely crossing it. (This is what the statement of the problem seems to imply.) I won't attempt to draw a solution on the terminal, but it is fairly easy to find once you know that that is the secret. If tracing a line lengthwise is not allowed, then the "Seven Bridges of Konigsberg" reasoning applies and the problem is impossible. Dave Seaman ..!pur-ee!pucc-k!ags
glc@akgua.UUCP (g.l. cleveland ) (11/28/83)
Back in 1982, Martin Gardner had a cute story in "Analog Science
Fiction/Science Fact" on the "box" puzzle. For those who still
wish to play around with it I'll rotate (13) the following comments
he brought out.
Nf unf nyernql orra oebhtug gb gur arjftebhc'f nggragvba, gur
chmmyr pna or rkcynvarq vaghvgviryl nf univat ab fbyhgvba fvapr gur
ahzore bs rkvgf/ragenaprf gb gur svir "obkrf" qbrfa'g unir gur
cebcre rirarff/bqqarff gb vg. Ubjrire, Tneqare cbvagrq bhg gung vs
gur chmmyr jrer qenja ba gur fhesnpr bs n gbehf (qbhtuahg-funcr)
jurer gur "ubyr" bs gur gbehf jnf ragveryl jvguva bar bs gur
"obkrf", gura bar pbhyq pbzr vagb gung "obk" ivn bar bs vgf
ragenaprf, yrnir ol jnl bs gur "ubyr" naq pbzr *onpx* vagb gur fnzr
"obk" ivn nabgure bs vgf ragenaprf!
Cheers,
Lindsay
Lindsay Cleveland (...{ihnp4|mhux?|clyde}!akgua!glc)
AT&T Western Electric/Bell Laboratories ... Atlanta, Ga
(404) 447-3909 ... Cornet 583-3909ss@rabbit.UUCP (11/28/83)
-------------------------
The puzzle is to draw a line (please not on your terminal screen)
WITHOUT LIFTING THE WRITING INSTRUMENT starting from any point not
on an intersection of lines in such a way that every line segment
is ONCE AND ONLY ONCE touched by your line. Every segment must be
touched once. Look at the middle horizontal line: it has three
segments, each of which must be touched once. You may pass through
a line as long as yo do it only once.
-----------------------------
Take the liberty of going OUT of large rectangle. Nothing in the
problem statement prevents this.
Here is one possible solution
-------------------------------------------
! /\_________!_/\ ! /\ !
! / ! \ !/ -----------|
!/ ! \ !\ ! |
!\ ! \---\ ! \ ! |
! \ ! | ! \ ! |
--|---------------------|-------|---------- |
! / ! / ---/ ! /
!/ ! / / !/
!\ !/ / !
! \ ! \ / !
! \ ! \/ !
-------------------------------------------
Just one of the many that can be drawn. Still possible even if you count
the middle horizontal line as four line segments. Note that it is also
possible to make a closed curve without violating the problem statement.
The apparant difficulty comes from the mental block set by the
enclosing rectangle.
Sharad Singhal.
rabbit!ssgandalf@hogpd.UUCP (M.ESTIS) (11/29/83)
Mental block? Go outside the large box? WAIT... Aren't the outside edges line segments too?