Logic Challenge 3
RamkinLady
LOGIC CHALLENGE 3
Now for something completely different, I will do more of the previous
challenges in the future.
I hope this is not too easy or too hard, get those brain cells buzzing.
And Thank you all for the great response
I call this challenge Learning your abc's.
I have drawn a grid 6x6 and numbered it just like a crossword. You also
have clues just like a crossword.
Each of the small squares below contains either A, B, or C. Each row and
column and each of the two long diagonals contains exactly two of each
letter. The information from each clue refers only to the squares in that
row or column. From the clues below, can you tell the letter in each
square?
Down
| 1 | 2 | 3 | 4 | 5 | 6 |
1 | | | | | | |
across 2 | | | | | | | right
left 3 | | | | | | |
4 | | | | | | |
5 | | | | | | |
6 | | | | | | |
Clues for ACROSS
1.(across) The As are between the Bs.
2.(across) No two squares containing the same letters are adjacent.
3.(across) The Cs are further right than the Bs.
4.(across) Every B is immediately to the right of a C
5.(across) The As are further left than the Cs
6.(across) The Cs are between the As
Clues for DOWN
1.(down) No two squares containing the same letter are adjacent.
2.(down) The As are between the Cs
3.(down) The As are between the Bs
4.(down) The Bs are lower than the As
5.(down) The Cs are higher than the Bs
6.(down) The Bs are adjacent
Good Luck, Look out in the future for more LOGIC CHALLENGES from me. You
can either keep an eye out in the newsgroups for them, or when you send
the answers to me, put an end note telling me you would like future LOGIC,
and I can email them directly to you.
Email me your answers at Ramki...@aol.com, DO NOT POST TO THIS
NEWSGROUP. You can post to the newsgroup, but please put spoiler on it,
dont ruin it for others, it has been pointed out to me.
With regards
Tracey
Ramki...@aol.com
Ian Lynagh
Once upon a time, in the land of rec.puzzles, RamkinLady eloquently
composed:
>DO NOT POST TO THIS
>NEWSGROUP. You can post to the newsgroup
Beautiful contradiction :)
Half a spoiler below - I have got stuck. Have I gone wrong,
am I missing something obvious or is the puzzle impossible?
I have got stuck. Have I gone wrong, am I missing something
obvious or is the puzzle impossible?
| 1 | 2 | 3 | 4 | 5 | 6 |
1 | BC| BC| BC| A | A | B |
2 |ABC|ABC| BC| A | C | B |
3 |AB |AB | A | B | C | C |
4 | C | B | C | B | A | A |
5 | B | A | A | C | B | C |
6 | A | C | B | C | B | A |
--
Ian Lynagh - i...@lynagh.demon.co.uk
http://www.sn.no/~balchen/igloo/
"Daddy, what does FORMATTING DRIVE C mean?"
Matthew Daly
Ian Lynagh <i...@lynagh.demon.co.uk>, if that is your REAL name, said:
>Once upon a time, in the land of rec.puzzles, RamkinLady eloquently
>composed:
>>DO NOT POST TO THIS
>>NEWSGROUP. You can post to the newsgroup
>
>Beautiful contradiction :)
>
>Half a spoiler below - I have got stuck. Have I gone wrong,
>am I missing something obvious or is the puzzle impossible?
Don't know if it was stated in the puzzle or not, but the rule about
2 A's, 2 B's, and 2 C's in each row and column also extends to the
two main diagonals, which clears up the multiple solutions that you
were noticing.
BTW, anyone who enjoyed the puzzle would be wise to check out Dell's
various variety puzzle books. If I had the inclination, I have a funny
feeling that I would find this specific puzzle in the latest issue
of "Math Puzzles & Logic Problems".
-Matthew
--
Matthew Daly I feel that if a person has problems communicating
mwd...@kodak.com the very least he can do is to shut up - Tom Lehrer
My opinions are not necessarily those of my employer, of course.
--- Support the anti-Spam amendment! Join at http://www.cauce.org ---
Ian Lynagh
Once upon a time, in the land of rec.puzzles, Matthew Daly eloquently
composed:
>Don't know if it was stated in the puzzle or not, but the rule about
>2 A's, 2 B's, and 2 C's in each row and column also extends to the
>two main diagonals, which clears up the multiple solutions that you
>were noticing.
*sigh*. I knew there must be something obvious I was missing.
Thanks :)
Ian
--
Ian Lynagh - i...@lynagh.demon.co.uk
http://www.sn.no/~balchen/igloo/
A conference is a gathering of important people who singly can do
nothing but together can decide that nothing can be done.
Courtenay Footman
In article <5pqmtc$mgi$1...@kodak.rdcs.Kodak.COM>,
Matthew Daly <da...@PPD.Kodak.COM> wrote:
>Ian Lynagh <i...@lynagh.demon.co.uk>, if that is your REAL name, said:
>>Once upon a time, in the land of rec.puzzles, RamkinLady eloquently
>>composed:
>>>DO NOT POST TO THIS
>>>NEWSGROUP. You can post to the newsgroup
>>
>>Beautiful contradiction :)
>>
>>Half a spoiler below - I have got stuck. Have I gone wrong,
>>am I missing something obvious or is the puzzle impossible?
>
>2 A's, 2 B's, and 2 C's in each row and column also extends to the
>two main diagonals, which clears up the multiple solutions that you
>were noticing.
>
>various variety puzzle books. If I had the inclination, I have a funny
>feeling that I would find this specific puzzle in the latest issue
>of "Math Puzzles & Logic Problems".
>
for Dell's "Math Puzzles & Logic Problems"; the harder cross sums are
a particular treat.
I just noticed an add in the back of the latest issue for a book of
one hundred cross sums for $6; I have the horrible feeling I am
actually going to buy it.
--
-------------------------------------------------------------------------------
Courtenay Footman I have again gotten back on the net, and
c...@lightlink.com again I will never get anything done.
jupiter
Ian Lynagh <i...@lynagh.demon.co.uk> wrote:
>Once upon a time, in the land of rec.puzzles, RamkinLady eloquently
>composed:
>>DO NOT POST TO THIS
>>NEWSGROUP. You can post to the newsgroup
>
>Beautiful contradiction :)
>
>Half a spoiler below - I have got stuck. Have I gone wrong,
>am I missing something obvious or is the puzzle impossible?
>
>
>
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>I have got stuck. Have I gone wrong, am I missing something
>obvious or is the puzzle impossible?
>
> | 1 | 2 | 3 | 4 | 5 | 6 |
>1 | BC| BC| BC| A | A | B |
>2 |ABC|ABC| BC| A | C | B |
>3 |AB |AB | A | B | C | C |
>4 | C | B | C | B | A | A |
>5 | B | A | A | C | B | C |
>6 | A | C | B | C | B | A |
>
>
Yes, you missed the exact same thing I missed until I went back and
carefully re-read the problem statement. Spoiler to your spoiler
below:
The two major diagonals each must also have two of each letter.
--
Greg
jup...@mastnet.net
Matthew Daly
c...@light.lightlink.com (Courtenay Footman), if that is your REAL name, said:
>
>Not that I saw. However, I just want to add a hearty recommendation
>for Dell's "Math Puzzles & Logic Problems"; the harder cross sums are
>a particular treat.
Be careful. The last time we talked about hard Cross Sums, Wei-Hua
posted a Japanese CS puzzle that I'm STILL trying to solve....
But I'll go out on a limb and say that Champion Variety Puzzle has
even harder Cross Sums than MP&LP. I'd love to know how people
write those puzzles -- I tried it myself and found that I didn't
have any notion of how to make them remotely interesting.
(I'm excited that I was thumbing through old disks last week and
came across my old BASIC and Pascal program library, including my
Cross Sums solver and my Paint By Numbers player.)
>I just noticed an add in the back of the latest issue for a book of
>one hundred cross sums for $6; I have the horrible feeling I am
>actually going to buy it.
I've got a 20-year collection of Dell puzzle magazines in my living
room -- very handy for keeping me from buying collections of Cross
Sums, Word Arithmetics, or Cryptograms. I would pay that kind of
money for hard CS puzzles or varieties though.
I'm very glad that I decided several years ago to solve the Logic
Problems on scratch paper so that I'd be able to resolve them later
if I wanted to. Now I'm starting to do the same thing with variety
cryptic crosswords.
-Matthew, who buys MP&LP for the Trigons more than anything.
Wei-Hwa Huang
da...@PPD.Kodak.COM (Matthew Daly) writes:
>Ian Lynagh <i...@lynagh.demon.co.uk>, if that is your REAL name, said:
>>Once upon a time, in the land of rec.puzzles, RamkinLady eloquently
>>composed:
>>>DO NOT POST TO THIS
>>>NEWSGROUP. You can post to the newsgroup
>BTW, anyone who enjoyed the puzzle would be wise to check out Dell's
>various variety puzzle books. If I had the inclination, I have a funny
>feeling that I would find this specific puzzle in the latest issue
>of "Math Puzzles & Logic Problems".
And you would be wrong.
It's in the issue before the latest one. ;-)
ObPuzzle (stolen from the latest issue):
Label three six-sided dice with letters so that you can roll the
following words:
ARM, ORB, FEZ, CRY, GNU, GYP, MIL, JIB, ZIP, PUT, FOG, GEL
ObHardPuzzle (not in the issue):
Is this puzzle solvable if only a subset of the above words were given?
--
Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
-------------------------------------------------------------------------------
"Oh, that was when the sand was so hot we were each hopping on one foot."
Matthew Daly
whu...@ugcs.caltech.edu (Wei-Hwa Huang), if that is your REAL name, said:
>It's in the issue before the latest one. ;-)
>
>ObPuzzle (stolen from the latest issue):
>
>Label three six-sided dice with letters so that you can roll the
>following words:
>
>ARM, ORB, FEZ, CRY, GNU, GYP, MIL, JIB, ZIP, PUT, FOG, GEL
>
>ObHardPuzzle (not in the issue):
>
>Is this puzzle solvable if only a subset of the above words were given?
I suspect you mean "Does the puzzle have a unique solution if only
a subset of the above words were given."
SPOILER
Just a hint for part 1: the sort of question you want to ask yourself
is "Which letter from FEZ goes on the same cube as the G?"
For the second part, there is a mathematical algorithm that allows
you to solve these problems. Assume that there are N words. Assign
the i'th word the value 2^(i-1) for each of the words. Then, assign
each letter a value equal to the sum of the values of each of the words
that it is contained in. To give you an example, GNU is the fifth
word in the list, so it is worth 16 points, and the value of I is
equal to MIL + JIB + ZIP = 64 + 128 + 256 = 448.
So, our quest for sets of six letters which are in each of the words
exactly once is now mathematically equivalent to finding 6 numbers in
the list that are pairwise distinct (that is, X AND Y = 0 in bitwise
arithmetic) and sum to 2^N - 1. A solution to the problem is a partition
of the available letters into sets of "cubes" that fulfill that requirement.
It is fairly elementary to write a computer program to perform this
task.
Having done so, here is how removing each of the words affects the solution:
ORB, GYP, MIL, PUT: Removing these creates two letters with the same
value -- this very obviously creates the necessity of multiple solutions
without further checks.
GEL: This has non-trivial multiple solutions: {AEIOUY, BCGMTZ, FJLNPR}
and {AEIOUY, BCFMNP, GJLRTZ}.
ARM, CRY, GNU, JIB: These maintain the unique solution, but they are
less than optimal in that they each contain a letter that appears in no
other words. For example, if the word ARM were removed, you could place
the remaining 17 letters on three cubes in a unique way, but you
would have latitude in filling the last blank unless the problem
specified that the letter A was one of the eighteen letters.
FEZ, ZIP, FOG: These have a unique solution when removed, and all 18
letters are still in the remaining words, so they are the optimal
words for removal.
The only candidate for removing two words that would keep all eighteen
letters and a hope for a unique solution is ZIP and FOG, but it turns
out that two letters have the same value under that scheme, so only
one word can be removed safely.
-Matthew
Jim Yingst
In article <5pto0a$h...@gap.cco.caltech.edu>,
Wei-Hwa Huang <whu...@ugcs.caltech.edu> wrote:
>Label three six-sided dice with letters so that you can roll the
>following words:
>
>ARM, ORB, FEZ, CRY, GNU, GYP, MIL, JIB, ZIP, PUT, FOG, GEL
Three dice: BCGMTZ, AEIOUY, FJLNPR. Not sure if this is unique.
>ObHardPuzzle (not in the issue):
>
>Is this puzzle solvable if only a subset of the above words were given?
I must be missing something here. The above solution can roll any subset
of the above words, therefore it would be a solution, given any such
subset. Right?
- Jim Yingst <ha...@u.arizona.edu>
slab
Courtenay Footman wrote:
> >
> Not that I saw. However, I just want to add a hearty recommendation
> for Dell's "Math Puzzles & Logic Problems"; the harder cross sums are
>
> a particular treat.
>
> I just noticed an add in the back of the latest issue for a book of
> one hundred cross sums for $6; I have the horrible feeling I am
> actually going to buy it.
I got hooked on Cross Sums a few months ago ... excellent puzzles. I'll
have to check out the ad and think about buying that book also, just to
further torture myself.
--
Shawn Labounty labo...@mail.dec.com
Materials Analyst Excess Materials Group
Digital Equipment Corporation Marlboro, MA
slab
Matthew Daly wrote:
> Be careful. The last time we talked about hard Cross Sums, Wei-Hua
> posted a Japanese CS puzzle that I'm STILL trying to solve....
If you've got a blank copy of that puzzle on-line, I'd love to receive a
copy ... thanks!!
Wei-Hwa Huang
slab <labo...@mail.dec.com> writes:
>Matthew Daly wrote:
>> Be careful. The last time we talked about hard Cross Sums, Wei-Hua
>> posted a Japanese CS puzzle that I'm STILL trying to solve....
>If you've got a blank copy of that puzzle on-line, I'd love to receive a
>copy ... thanks!!
It's still available on my web pages.
http://www.ugcs.caltech.edu/~whuang/gp/xsum.gif
--
Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
-------------------------------------------------------------------------------
Better a genial genius than a prodigal prodigy.
Ian Lynagh
Once upon a time, in the land of rec.puzzles, Wei-Hwa Huang eloquently
composed:
>Label three six-sided dice with letters so that you can roll the
>following words:
>
>ARM, ORB, FEZ, CRY, GNU, GYP, MIL, JIB, ZIP, PUT, FOG, GEL
>Is this puzzle solvable if only a subset of the above words were given?
I reckon you could be it without JIB (assuming you were
told that J was the 18th letter).
SPOILER
DICE 1
G
T
Z
M
C
B
DICE 2
U
Y
O
E
I
A
DICE 3
N
P
F
L
R
J
TTFN
Ian
--
Ian Lynagh - i...@lynagh.demon.co.uk
http://www.sn.no/~balchen/igloo/
If your answer and the teachers answer do not match, you have obviously
left out the fudge factor.
Ian Lynagh
Once upon a time, in the land of rec.puzzles, Wei-Hwa Huang eloquently
composed:
What do you have to do?
--
Ian Lynagh - i...@lynagh.demon.co.uk
http://www.sn.no/~balchen/igloo/
In the beginning the Universe was created. This has made a lot of people
very angry and been widely regarded as a bad move.
slab
Wei-Hwa Huang wrote:
> slab <labo...@mail.dec.com> writes:
> >Matthew Daly wrote:
> >> Be careful. The last time we talked about hard Cross Sums, Wei-Hua
>
> >> posted a Japanese CS puzzle that I'm STILL trying to solve....
>
> >If you've got a blank copy of that puzzle on-line, I'd love to
> receive a
> >copy ... thanks!!
>
> It's still available on my web pages.
>
> http://www.ugcs.caltech.edu/~whuang/gp/xsum.gif
>
Wow, after studying the puzzle for about fifteen minutes I've
concluded that one of the squares contains either a five or a seven.
slab
> Wei-Hwa Huang wrote:
>
> >
> > It's still available on my web pages.
> >
> > http://www.ugcs.caltech.edu/~whuang/gp/xsum.gif
> >
>
> Wow, after studying the puzzle for about fifteen minutes I've
> concluded that one of the squares contains either a five or a seven.
Well, another 45 minutes of studying and I've actually got about eight
digits placed. This is going to take a LONG time to finish, if I ever
do.
Matthew Daly
slab <labo...@mail.dec.com>, if that is your REAL name, said:
>> Wow, after studying the puzzle for about fifteen minutes I've
>> concluded that one of the squares contains either a five or a seven.
I hate to give too much away, but one of the squares DOES contain
either a five or a seven, so you must be on the right track.
>Well, another 45 minutes of studying and I've actually got about eight
>digits placed. This is going to take a LONG time to finish, if I ever
>do.
Uh oh, following up on your own messages? That's the first sign of
impending mental collapse. :-)
After about six months of on-again-off-again false starts on this
puzzle, I sat down yesterday and wrote down my logic so that I would
be able to tell when my thoughts ran astray. Doing that, I have about
a third of the squares filled in and another third that is partially
filled in with two or three possible values. (If people want to see
my "walkthrough" as it currently stands, feel free to email me and
I'll email you a copy.)
Small hint
The lower-left corner of the grid is relatively easy to penetrate, at
least compared to the rest. That's probably where most of your eight
digits are already But, for me at least, getting the lower parts of
that section involved developing a heuristic that I've never had to
use in a Cross Sums puzzle before.
Larger hint
Let's say that you wanted to solve a grid that looked partially like
this: (only relevant sums and parts of the board filled in)
3 4 6 ...
41 X X X X X X X X
45 X X X X X X X X X
X X X ...
...
You know that the 3 is made up of a 1 and a 2, and the 4 is made up of
a 1 and a 3. The two 1's cannot be in the same row, so the top two
rows already have their allotment of 1's for them. Specifically, the
6 is not made up of any 1's, so it must be a 2 and a 4. A little more
thought reveals that the corner must be:
1 3 2 ...
2 1 4 ...
Hope this helps! I have never seen a Cross Sums puzzle even remotely
in this league of difficulty before, so I'm hardly even giving
anything away in this post (although the walkthrough is pretty
explicit in giving away the parts that I've solved so far).
Wei-Hwa Huang
Ian Lynagh <i...@lynagh.demon.co.uk> writes:
>Once upon a time, in the land of rec.puzzles, Wei-Hwa Huang eloquently
>composed:
>What do you have to do?
Whoops -- assumed that everyone knows what a cross-sum is.
A cross-sum is like a crossword, except with the digits instead of
letters. Only the digits from 1-9 are allowed, and in no "word"
is the same digit allowed to appear more than once. (However,
the same digit can appear in the same row or column as long as they
are in different "words".) The sum of the digits in each "word" is
provided in the grid -- decent cross-sums have a unique solution,
although it is often frowned down upon to use this fact to help
solve the puzzle.
A sample cross-sum (yes, I wrote this off-the-cuff):
7 19 4
+--+--+--+
9| | |XX|
+--+--+--+
15| | | |
+--+--+--+
6|XX| | |
+--+--+--+
<SPOILER>
+--+--+--+
| 3| 6|XX|
+--+--+--+
| 4| 8| 3|
+--+--+--+
|XX| 5| 1|
+--+--+--+
Ian Lynagh
Once upon a time, in the land of rec.puzzles, Wei-Hwa Huang eloquently
composed:
Thanks.
Hey man, this is easy. Less than 30 minutes and I've already
done 2 whole digits!
Only 131 to go now :)
And 1.5 hours in and I think I've found the
5 or 7 square :)
Now 6 hours in, 14 digits done and I am thinking of ways to
inflict pain on 2 Chinese guys :)
If I have made a mistake...
In anguish
Ian
--
Ian Lynagh - i...@lynagh.demon.co.uk
http://www.sn.no/~balchen/igloo/
Don't you just hate rhetorical questions?
Wei-Hwa Huang
mwd...@kodak.com (Matthew Daly) writes:
>slab <labo...@mail.dec.com>, if that is your REAL name, said:
>>> Wow, after studying the puzzle for about fifteen minutes I've
>>> concluded that one of the squares contains either a five or a seven.
>I hate to give too much away, but one of the squares DOES contain
>either a five or a seven, so you must be on the right track.
No, can't be. More than one of the squares contains a five or a seven.
:-)
>After about six months of on-again-off-again false starts on this
>puzzle, I sat down yesterday and wrote down my logic so that I would
>be able to tell when my thoughts ran astray. Doing that, I have about
>a third of the squares filled in and another third that is partially
>filled in with two or three possible values. (If people want to see
>my "walkthrough" as it currently stands, feel free to email me and
>I'll email you a copy.)
It took me three days (not all of the days, but about two hours or so
per) to solve it -- but I used one "unsavory" technique (adding a LOT
of columns and row together) and one "illegal" technique (assuming that
the solution was unique). Intwo less hectic days, I'd eliminated the
need for that "illegal" technique, and then I wrote a full walk-through.
But now I can't find it. (This was about 6 months ago.)
>Small hint
>The lower-left corner of the grid is relatively easy to penetrate, at
>least compared to the rest. That's probably where most of your eight
>digits are already But, for me at least, getting the lower parts of
>that section involved developing a heuristic that I've never had to
>use in a Cross Sums puzzle before.
Odd. In retrospection, the upper right is actually easier, although
I did the lower left first as well. Both corners can be done
independently.
The upper left needs the information from the upper right and the
lower left to be finished, and the lower right is the hardest because
it relies heavily on number uniqueness and very little on bounds.
>Let's say that you wanted to solve a grid that looked partially like
>this: (only relevant sums and parts of the board filled in)
> 3 4 6 ...
>41 X X X X X X X X
>45 X X X X X X X X X
> X X X ...
> ...
>You know that the 3 is made up of a 1 and a 2, and the 4 is made up of
>a 1 and a 3. The two 1's cannot be in the same row, so the top two
>rows already have their allotment of 1's for them. Specifically, the
>6 is not made up of any 1's, so it must be a 2 and a 4. A little more
>thought reveals that the corner must be:
>1 3 2 ...
>2 1 4 ...
I've used this technique in Dell's puzzles before.
It may not be necessary, but it does save a lot of work.
--
Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
---------------------------------------------------------------------------
Courtenay Footman
In article <33CA1FF4...@mail.dec.com>,
slab <labo...@mail.dec.com> wrote:
>Ian Lynagh wrote:
>
>> Hey man, this is easy. Less than 30 minutes and I've already
>> done 2 whole digits!
>>
>> Only 131 to go now :)
>>
>> And 1.5 hours in and I think I've found the
>> 5 or 7 square :)
>>
>> Now 6 hours in, 14 digits done and I am thinking of ways to
>> inflict pain on 2 Chinese guys :)
>> If I have made a mistake...
>
>
>I'm ready to give up after filling in seventeen digits. But luckily it
>only took me about two hours to get that far. 8^)
>
I solved it, but took me longer than I thought it should.
(At least twelve hours, probably fifteen, maybe twenty. The addition
mistake did _not_ help.)
SPOILER warning for method;
A question of what constitutes an adequate solution is raised at end.
In an ordinary cross sum, I prove that certain digits must be certain
numbers, which constrains other numbers, and so on. With this one, I
found after the first few numbers, a different technique was required:
I assumed that this was a valid cross sum, with a unique solution.
This provided enough of a constraint to eliminate enough numbers
to allow me to proceed.
An example, (not from the puzzle): Suppose that two spaces add up
to three. Clearly, the two numbers are 2 and 1. Suppose there is
a parallel group of three spaces, that add up to say, nine:
3 A B
9 C D E
If the puzzle is a valid one, than E can not be six, because then
there is no way to determine A B C D; 1 2 2 1 and 2 1 1 2 are
both possible solutions, with no way to distinguish between them.
If one knows that E is either five or six, then one can say it must be
five, and C D must be 1 3 or 3 1, and go on from there.
I used this technique in at least four different places in this puzzle.
Each time I did so, I felt uneasy about it, because I was not proving
the puzzle valid, just assuming it.
As far as validating the puzzle goes, my end game solution was equally
unsatisfactory: I found one number to be either X or Y, so I said,
"What happens if I try X? Well then these three squares must be that,
so these other squares must be this, which fixes this whole chain
of paired possibilities, which constrains those other squares, and...
hey, I just filled in all the squares!" I still have no idea what
would have happened if I filled in the critical square with Y, but I
assume something somewhere would have been impossible.
Thus I can demonstrate that there is a solution; I can not demonstrate
that it is unique. Does this qualify as a satisfactory solution to a
cross sum or a logic puzzle? It leaves me feeling a trifle unhappy,
but not unhappy enough to try and prove the solution unique.
What are other people's opinions on this point?
TRM
I've never done one of these before:
Is each square a digit or can it be 12?
Are there any rules about how many of each digit can be in a particular
sum? (i.e., 1+1+2+4+4+4+3)
Thanks,
Toby
Wei-Hwa Huang
c...@light.lightlink.com (Courtenay Footman) writes:
>As far as validating the puzzle goes, my end game solution was equally
>unsatisfactory: I found one number to be either X or Y, so I said,
>"What happens if I try X? Well then these three squares must be that,
>so these other squares must be this, which fixes this whole chain
>of paired possibilities, which constrains those other squares, and...
>hey, I just filled in all the squares!" I still have no idea what
>would have happened if I filled in the critical square with Y, but I
>assume something somewhere would have been impossible.
>Thus I can demonstrate that there is a solution; I can not demonstrate
>that it is unique. Does this qualify as a satisfactory solution to a
>cross sum or a logic puzzle? It leaves me feeling a trifle unhappy,
>but not unhappy enough to try and prove the solution unique.
>What are other people's opinions on this point?
As I mentioned in my last post, I do not consider a cross-sum solved
unless I have shown deductively that the solution is unique. I mean,
what if I had the same attitude with crosswords? "Well, these words fit,
so that MUST be the solution, and to heck with the clues I can't figure
out!" (Actually, I do this a lot to hard crosswords.)
In any case, this Xsum IS solvable by deductive methods.
Matthew Daly
whu...@ugcs.caltech.edu (Wei-Hwa Huang), if that is your REAL name, said:
>>Thus I can demonstrate that there is a solution; I can not demonstrate
>>that it is unique. Does this qualify as a satisfactory solution to a
>>cross sum or a logic puzzle? It leaves me feeling a trifle unhappy,
>>but not unhappy enough to try and prove the solution unique.
>>What are other people's opinions on this point?
>
>As I mentioned in my last post, I do not consider a cross-sum solved
>unless I have shown deductively that the solution is unique. I mean,
>what if I had the same attitude with crosswords? "Well, these words fit,
>so that MUST be the solution, and to heck with the clues I can't figure
>out!" (Actually, I do this a lot to hard crosswords.)
I think that one needs to differentiate between two different techniques:
A) Saying "If a 3 went here, then you would have to have an 8 here and a 4
there and ... well, that finishes the grid so I've found a solution."
B) Saying:
45 45
4 X X 11
6 X X X
...X X X
...X X
"If the third number in the '6' row were a 2, then the upper four numbers
could either be 1 3 / 3 1 or 3 1 / 1 3. Since I know that Cross Sums
puzzles all have unique solutions, this cannot be. Therefore, the third
number in the '6' row must be a 3...."
I think that A is pretty okay, but B is pretty not okay. In other words, I
don't need to prove that a solution is unique, but it isn't fair to assume
that such is the case.
>In any case, this Xsum IS solvable by deductive methods.
grumble grumble mutter upper right hand corner....
Matthew Daly
whu...@ugcs.caltech.edu (Wei-Hwa Huang), if that is your REAL name, said:
>mwd...@kodak.com (Matthew Daly) writes:
>>I think that one needs to differentiate between two different techniques:
>
[A: Accidentally coming up with "a" correct answer and not checking to see
if it's unique]
[B: Making the logical assumption that a solution is unique to weed out
cases]
>>I think that A is pretty okay, but B is pretty not okay. In other words, I
>>don't need to prove that a solution is unique, but it isn't fair to assume
>>that such is the case.
>
>When I solve cross sums, I think that A is pretty not okay, and B is
>very not okay. It's a matter of giving yourself restraints to enjoy
>the puzzle more, like solving the Rubik's cube with one hand or
>solving a crossword puzzle without writing in any vowels (both of which
>I do). Cross sums are usually designed to that if you attack it the right
>way, you'll NEVER need to use trial and error. Finding the right
>location to attack is a challenge.
Yeah, different strokes. I find that I like the closure of knowing that my
solution is complete, but for some puzzles it's hard to look at a completed
puzzle and say "Well, that assumption worked, so I'll erase all my pencil
work and make the opposite assumption to find out where it fails". I do
that for some puzzles (like Paint By Numbers and the "split the 8x7 grid
into a complete set of domino's" puzzle), but not for others (especially
variety cryptics that involve bizarre grid filling rules).
>>>In any case, this Xsum IS solvable by deductive methods.
>>grumble grumble mutter upper right hand corner....
>
>Is that all you have left? Funny, I could've sworn that was the
>easiest corner!!
Come closer and tell me again about how "funny" it is. :-) No, it isn't
all that I have left, but I can see how it would be the keystone for what I
have left. If I had that, the upper-left and lower-right sections would be
split into two separate puzzles, and I think that I'd be able to work
through them with the center completely filled in.
MILD SPOILERS ON THE UPPER-RIGHT HAND CORNER FOR THOSE WHO STILL HAVEN'T
FIGURED IT OUT AND ARE TRYING TO
I know that the "32 down" is .98.. and the "31 down" is 7xxyy where the x's
are 3 and 4 in some order and the y's are 8 and 9 in some order. And in
the upper-right corner of the center section, I know that "19 across" is
397 and "13 down" is 7231 and "37 across" is 6.5.2.". But everything else
that I have pencilled in is a very basic deduction from those facts, and it
doesn't seem to be enough to get me any further along.
Since I'm in desperation mode, I thought that I would make a few
photocopies of the grid as I have it so far and make wild guesses in some
key squares and find out if certain squares are all forced to have the same
output in all cases. That's REALLY REALLY not all right in my view, but
hopefully it will give me an inkling of where to focus my deductive
reasoning efforts.
Ian Lynagh
Once upon a time, in the land of rec.puzzles, Joseph W. DeVincentis
eloquently composed:
>I drew my own diagram for this, rather than printing out the picture...
>I used graph paper, and gave myself 1/2-inch squares -- lots of room
>to make notes...
I used the original gif, put
123
456
789
in each square and then just erased them
as I eliminated possibilities.
Just in case anyone cared :)
Ian
--
Ian Lynagh - i...@lynagh.demon.co.uk
http://www.sn.no/~balchen/igloo/
I'm not good in groups. It's difficult to work in a group when you're
omnipotent.
Wei-Hwa Huang
mwd...@kodak.com (Matthew Daly) writes:
>Yeah, different strokes. I find that I like the closure of knowing that my
>solution is complete, but for some puzzles it's hard to look at a completed
>puzzle and say "Well, that assumption worked, so I'll erase all my pencil
>work and make the opposite assumption to find out where it fails".
I never have to do this for Cross Sums, since I don't write in assumptions.
(Unless, of course, I'm timing myself; then I don't worry about uniqueness.)
> I do
>that for some puzzles (like Paint By Numbers and the "split the 8x7 grid
>into a complete set of domino's" puzzle), but not for others (especially
>variety cryptics that involve bizarre grid filling rules).
For PBN's, I've had to resort to lots of other techniques to challenge
myself. In order of difficulty:
(1) Don't mark the blank (white) squares.
(2) Don't fill in or mark the black squares either. Instead,
only mark those edges where a black square meets a white square.
(3) Fill in the WHITE squares, and leave the black squares blank
-- a "reverse video" effect.
>>>>In any case, this Xsum IS solvable by deductive methods.
>>>grumble grumble mutter upper right hand corner....
>>
>>Is that all you have left? Funny, I could've sworn that was the
>>easiest corner!!
>Come closer and tell me again about how "funny" it is. :-) No, it isn't
>all that I have left, but I can see how it would be the keystone for what I
>have left. If I had that, the upper-left and lower-right sections would be
>split into two separate puzzles, and I think that I'd be able to work
>through them with the center completely filled in.
>MILD SPOILERS ON THE UPPER-RIGHT HAND CORNER FOR THOSE WHO STILL HAVEN'T
>FIGURED IT OUT AND ARE TRYING TO
>I know that the "32 down" is .98.. and the "31 down" is 7xxyy where the x's
>are 3 and 4 in some order and the y's are 8 and 9 in some order. And in
>the upper-right corner of the center section, I know that "19 across" is
>397 and "13 down" is 7231 and "37 across" is 6.5.2.". But everything else
>that I have pencilled in is a very basic deduction from those facts, and it
>doesn't seem to be enough to get me any further along.
Hmmm. Here's a hint. You should be able to position 1-5 in "45 across",
finish "11 down", and finish "11 across". After you get that far, look
carefully at the missing numbers in "37 across" and "45 across" --
AND TAKE INTO ACCOUNT "4 across".
>Since I'm in desperation mode, I thought that I would make a few
>photocopies of the grid as I have it so far and make wild guesses in some
>key squares and find out if certain squares are all forced to have the same
>output in all cases. That's REALLY REALLY not all right in my view, but
>hopefully it will give me an inkling of where to focus my deductive
>reasoning efforts.
No, no, no. Making photocopies is a good idea if you're prone to
arithmetical errors, but they shouldn't be used for that.
--
Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
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