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Seven Clues for Seven Weddings

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James Dow Allen

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May 17, 2013, 6:12:41 PM5/17/13
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(Here's a puzzle I composed several years ago. I don't think I've
presented it in rec.puzzles before.)

Seven men were best of friends, so when each got married he chose
one of the other six to be his best man and a different one of them
to be his usher. From the clues determine for each wedding, the names of
groom (husband), bride (wife), best man, and usher.

Clue 1: Each of the seven men was married just once, served as best man
just once, and as usher just once.

Clue 2: The groom who chose George as best man, was usher for Rachel's
husband.

Clue 3: Sally's husband was best man for Wilma's husband.

Clue 4: The groom who chose Dan for usher, was himself best man at the
wedding where Edgar ushered.

Clue 5: The seven weddings are the ones where Chuck and Frank were grooms,
the ones where Chuck and George were best men, the ones where Adam and
George were ushers, and the one where Ursula was bride.

Clue 6: The seven brides are Tish, Rachel, Adam's and Bill's wives, the
one at the wedding where Chuck ushered, the one at the wedding where Frank
was best man, and the red-headed lady.

Clue 7: The seven men are Dan, Phoebe's husband, Veronica's husband, the
groom who chose George as usher, the one who was best man at Ursula's
wedding, and the ones who were ushers at Phoebe's and Rachel's weddings.

James Dow Allen

John Jones

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May 21, 2013, 10:30:57 AM5/21/13
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On Fri, 17 May 2013 22:12:41 +0000 (UTC), "James Dow Allen"
<gm...@jamesdowallen.nospam> wrote in article
<XnsA1C43500A20...@178.63.61.175>...
original puzzle as spoiler space
I have never liked logic puzzles and now I know why!
Ingenious set of conditions, went round in circles on my graph paper
for literally days. Oh, and made a malpas in the first hour.

In the end I reverted to form and picked up the prolog.
Have a solution but will leave it to the OP or manual solvers to post.
As proof: Phoebe is the redhead.

PS writing prolog for this was tricky and the runlengths could be high.
I estimated several million possible permutations.
The secret was to avoid expensive operations and filter out the bad
permutations as soon as possible. In the end the solution was found in 3
minutes on a laptop.

Lessons learned:
many relationships in the filters are inverse.
So hold the inverses to be readily accessible.
Use P R etc to hold the groom number 1-7 married to p, r etc.
Use A B etc to hold the groom whose BM is 1 2 etc (eg Bm-1(d)=D)
Use UA UB to hold the groom whose Usher is 1 2 etc
Keep a list of bestmen, and ushers.
Keeping variables as above cuts down on nth_elem calls to extract the
nth element of the list of best men etc.
Also, avoid using uniq in favour of listing the \== truths.
(uniq(List) checks that the list has no duplicates, aka nodups)
(A\==B means A is not B and do not bind variables.)

OP: Well done, and look forward to some insight on how this can be done
by hand. Prolog follows sig FWIW.

HTH
JJ

doit:- /* M phase */
permutation([P,R,S,T,U,V,W],[1,2,3,4,5,6,7],_),
T\==1, T\==2, R\==1, R\==2, P\==4, V\==4,
M=[P,R,S,T,U,V,W],
/* M set up, BM phase */
printf("M = %\n",[M]),
permutation([A,B,C,D,E,F,G],[1,2,3,4,5,6,7],_),
A\==1,B\==2,C\==3,D\==4,E\==5,F\==6,G\==7,
C\==3, G\==3, U\==3, C\==6, G\==6, U\==6,
C\==G,C\==U,G\==U,
F\==1, F\==2, F\==T, F\==R,
BM=[A,B,C,D,E,F,G],
jnth_elem(BM,S,W),
jnth_elem(BM,BMU,U),
BMU\==4,BMU\==P,BMU\==V,
/* BM set up, Ush phase */
printf(" BM = %\n",[BM]),
permutation([UA,UB,UC,UD,UE,UF,UG],[1,2,3,4,5,6,7],_),
UA\==1,UB\==2,UC\==3,UD\==4,UE\==5,UF\==6,UG\==7,
UA\==A,UB\==B,UC\==C,UD\==D,UE\==E,UF\==F,UG\==G,
not member(UA,[3,6,C,G,U]),
not member(UG,[3,6,C,G,U]),
not member(UC,[1,2,T,R,F]),
jnth_elem(BM,UD,UE),
Ush=[UA,UB,UC,UD,UE,UF,UG],
jnth_elem(Ush,G,R),
jnth_elem(Ush,UshP,P),
jnth_elem(Ush,UshR,R),
uniq([4,P,V,UG,BMU,UshP,UshR]),
printf("Solution is % % %\n",[M,BM,Ush]).

James Dow Allen

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May 25, 2013, 10:52:54 AM5/25/13
to
John Jones <a1...@hotamil.com> might have writ, in
news:MPG.2c0595798...@news.eternal-september.org:

Thank you, John, for doing my puzzle!
I should apologize. If I'd remembered how difficult some of these
puzzles are, I'd have included a stern warning, or not submitted it at
all.
I used to provide such puzzles for Dell and PennyPress magazines, which
rate puzzles as 1-star to 5-stars. This one was published by Penny so
rated at most 4-star (only Dell publishes 5-star puzzles), and, with
just seven events and seven clues, likely was awarded just 3 stars by
the editor! It seems that no puzzle is too difficult for Dell, but I
wonder how many readers actually solve the more difficult puzzles.

I found it fun to compose puzzles with a minimal number of clues, and to
try to find relatively brief solution explanations. But given the
effort involved, I barely got minimum wage for my work on a 3-star ($75)
puzzle.

I attach the solution I submitted to Penny Press. As you can see, if
there was a quick path to solution, I didn't find it.

Grooms are Dan, Edgar (4), Chuck, Frank, George, Adam (5), Bill (6).
Each groom was best man once and usher once (1), so participated in
three weddings altogether (intro). Brides are Rachel (2), Sally, Wilma
(3), Ursula (5), Tish (6), Phoebe, Veronica (7). Each bride
participated in just one wedding so ``Sally's usher,'' for example, is
shorthand for Sally's husband's usher.

At the weddings where George is best man or usher, the groom isn't
George (intro), Chuck, Frank (5), Dan (7), so each is Adam, Bill or
Edgar. Phoebe's usher isn't George or Dan (7). George isn't Ursula's
best man (5), so is Phoebe's or Veronica's groom [only possible (7)].
Either Chuck is George's best man [so not his usher (intro)] or Adam is
George's usher [only possibilities for George as groom (5)], in either
case George's usher isn't Chuck, so George [married to Phoebe or
Veronica] is either the one with Frank as best man or the one with
red-headed wife [only possibilities (6)]. Chuck isn't groom where
George is best man or George is usher, so is Phoebe's or Veronica's
groom or Phoebe's usher [only possibilities (7)].

Ursula's groom isn't Chuck, Frank, the grooms where George was best man
or usher (5), Ursula's best man (intro), Phoebe's usher [else, since not
George or Dan (above), he would be Adam, Bill or Edgar, so Adam, Bill
and Edgar would be, in some order, the grooms where Ursula is bride,
George is best man, and George is usher, so Ursula's best man wouldn't
be any of those (7), and isn't Chuck, George (5), Dan (7) so would be
Frank, so George [who had red-headed wife or Frank as best man (above)]
would have the red-headed wife, so Chuck [not Phoebe's usher who would
be Ursula's groom, so Phoebe's or Veronica's groom, but not his own
usher (1), and not married to the red-head [would be George]] could not
be placed (6)], so is Dan [only possible (7)].

Sally isn't married to Ursula's best man [Sally's married to Wilma's
best man (3)], so is either married to Phoebe's usher, Rachel's usher,
or was bride when George was usher [only possibilities (7)]. Chuck
isn't Phoebe's usher [Chuck isn't George's usher (above) so George's
bride [Phoebe or Veronica] would be Veronica, so Phoebe's groom would be
Frank [elimination (5) since she wouldn't be the bride where George is
best man or usher (7) or where Chuck is groom or best man (intro)], so
neither Adam nor Bill would be married to Phoebe [would be Frank],
Veronica [would be George], Ursula [Dan], Tish, Rachel (6), so would be
married to Sally and Wilma in some order, so Wilma's best man would be
Adam or Bill (3), so Adam would be Wilma's groom or best man, so not
usher (intro) so Wilma's usher would be George [only possibility (5)],
so Sally's groom [would be Adam or Bill (above) and also is Phoebe's or
Rachel's usher or the one who picked George as usher (above)] wouldn't
be Phoebe's usher [would be Chuck] or the one who picked George as usher
[would be Wilma's husband] so Rachel's usher, so Ursula's best man would
be Edgar [elimination (7)], Ursula would be the red-head [elimination
(6)], George's best man would be Frank [elimination (6)] and his usher
would be Adam [elimination (5)], Edgar would have Chuck as best man
[only possible (5)] and Dan couldn't be placed as usher [the groom who
chose him for usher wasn't Dan (intro), Edgar (4), Adam or Bill [one of
them would have chosen George for usher, the other was best man when
George was usher] (4), Frank [would have chosen Chuck as usher], George
[would have chosen Adam as usher], Chuck [Chuck would have been best man
when Edgar was groom, so not when Edgar was usher (1)]]], so Chuck is
married to Phoebe or Veronica [only possible (7)]; Chuck and George are
Phoebe's and Veronica's grooms in some order. Neither Chuck nor George
had Chuck for usher (above), so their weddings, in some order, are the
ones with Frank as best man and the red-headed bride [only possible
(6)].

The wedding where Dan and Ursula were bride and groom had Chuck as usher
[only possibility (6)]. Frank's bride is Tish or Rachel [only
possibilities (6)]. Adam and Bill are married to Sally and Wilma in
some order [only possibilities (6)], so Wilma's best man is Adam or Bill
(3). Ursula's [Dan's] best man isn't Frank [Frank is Chuck or George's
best man (above)] so Ursula's best man is Adam, Bill or Edgar. Rachel's
usher, Ursula's best man, and the man who chose George as usher are
Adam, Bill and Edgar in some order, so Phoebe's usher is Frank
[elimination]; Frank is Phoebe's or Veronica's best man (above) but not
Phoebe's (intro) so Veronica's. George's bride is Phoebe or Veronica,
so his usher is either Frank [Phoebe's usher] or Adam [if George's bride
is Veronica, his best man would be Frank (above) and choosing Adam as
usher would be the only possibility (5)]. Wilma [whose groom and best
man are Adam and Bill in some order (above)] has George as usher [only
possibility (5)]. Ursula's best man isn't Wilma's best man (1) so isn't
Sally's husband (3) or Wilma's husband (7) so isn't Adam or Bill, so is
Edgar.

The man who picked Dan as usher isn't Dan (intro), Edgar (4), George
[George's usher is Adam or Frank (above)], Adam or Bill [groom and best
man in some order when George was usher, but the man who picked Dan as
usher would have been best man when Edgar was usher (4)], Chuck
[Phoebe's usher is Frank, so Chuck's wife would have been Veronica, so
George's wife would be Phoebe, his usher Frank, his best man Chuck [only
possible (5)] which wouldn't fit (4)], so was Frank. Frank was best man
when Edgar was usher (4), the groom there would be Chuck [only possible
(5)], so George's wife is Phoebe, usher Frank, and best man Chuck [only
possible (5)].

The usher when George was best man was Bill [only place left (5)], the
groom at that wedding was Rachel's usher (above) who is Adam, Bill or
Edgar (above) but not Bill [wedding's usher] or Edgar [Veronica's usher]
so Adam. Frank's usher is Dan (above) so Frank is married to Tish, not
Rachel. Adam's wife is Sally [elimination], so Wilma's groom is Bill
and best man is Adam (3). Rachel's groom is Edgar [elimination], who is
also Dan's best man [elimination]. Dan's stint as best man wasn't when
he was usher (intro) so was when Adam was usher [elimination]. Frank's
best man was Bill.

In summary:
Adam & Sally wed, George best man, Bill ushered
Bill & Wilma wed, Adam best man, George ushered
Chuck & Veronica wed, Frank best man, Edgar ushered
Dan & Ursula wed, Edgar best man, Chuck ushered
Edgar & Rachel wed, Dan best man, Adam ushered
Frank & Tish wed, Bill best man, Dan ushered
George & Phoebe wed, Chuck best man, Frank ushered

Phoebe is indeed red-haired, by elimination (6).

James Dow Allen

rlw...@sdf.org

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May 25, 2013, 11:05:16 PM5/25/13
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In article <XnsA1CBDE98733...@178.63.61.175>,
James Dow Allen <gm...@jamesdowallen.nospam> wrote:
>John Jones <a1...@hotamil.com> might have writ, in
>news:MPG.2c0595798...@news.eternal-september.org:
>
>I used to provide such puzzles for Dell and PennyPress magazines, which
>rate puzzles as 1-star to 5-stars. This one was published by Penny so
>rated at most 4-star (only Dell publishes 5-star puzzles), and, with
>just seven events and seven clues, likely was awarded just 3 stars by
>the editor! It seems that no puzzle is too difficult for Dell, but I
>wonder how many readers actually solve the more difficult puzzles.

For several years I at least did all the ones in Dell [Official] PP&WG
with regular grids where you could put X's and dots. I hated the ones
that had a write-in table instead. With the note above saying "we didn't
find a standard solving grid helpful". Did you have a say in that?

I always wanted the standard grid, and I suspected that the real reason
it was left out sometimes was that it was too large to fit on a single
page along with the clues. I drew my own grid on graph paper many times.

Now I have a program to generate the full grid in ASCII from a list of
attributes and values... and an editor for the ASCII grid which does the
easy deductions for you, for example:

#################################
# | b | | # | | | #
#---+---+---+---#---+---+---+---#
# b | a | b | b # c | c | c | c #
#---+---+---+---#---+---+---+---#
# | b | | # | | | #
#---+---+---+---#---+---+---+---#
# | b | | # | | | #
#################################
# | d | | #
#---+---+---+---#
# | d | | #
#---+---+---+---#
# | d | | #
#---+---+---+---#
# | d | | #
#################

If you put a dot at 'a', then X's are automatically put into the 'b'
cells, and the 'c' row gets copied to the 'd' column automatically; if
that brings 3 X's together in a row or column then the dot goes into the
last available space automatically.

Or (starting from an empty grid again) if you put X's in the first 2
cells of row 'c' and the last 2 cells of column 'd', the editor notices
that they are mutually exclusive and puts an X at 'a' automatically.

Within a single region, the editor does this transformation
automatically:

##################### #####################
# X | | | | X # # X | | | | X #
#---+---+---+---+---# #---+---+---+---+---#
# X | | | | X # # X | | | | X #
#---+---+---+---+---# #---+---+---+---+---#
# X | | | | X # -----> # X | | | | X #
#---+---+---+---+---# #---+---+---+---+---#
# | | | | # # | X | X | X | #
#---+---+---+---+---# #---+---+---+---+---#
# | | | | # # | X | X | X | #
##################### #####################

And the final feature is an undo stack with a "bookmark" command, so you
can mark your place when you have guess, then proceed until you find a
contradiction and then hit the "undo to mark" key and it will restore
the pre-guess state so you can fill in the opposite of your guess and
move forward. Multiple guess-bookmarks are allowed, so you can go as
deep as you have to with nested gueses.

I tell you all of that so I can tell you this: With this editor doing
all the grunt work, the wedding puzzle was *still* hard. Thanks.

--
Alan Curry
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