"As Easy As ABC(CD) aka END VIEW method of attack?
Chuck Fresno
several Japanese puzzle magazines and the Puzzle Championships
that has been called END VIEW or EASY AS ABC(DE) as well as
other names. Here's a sample from a recent issue of GAMES:
C A
+---+---+---+---+---+---+
C | | | | | | |
+---+---+---+---+---+---+
C | | | | | | | B
+---+---+---+---+---+---+
A | | | | | | | B
+---+---+---+---+---+---+
| | | | | | | C
+---+---+---+---+---+---+
| | | | | | | B
+---+---+---+---+---+---+
A | | | | | | |
+---+---+---+---+---+---+
The object is to place the letters A, B and C so that each column and
row have exactly one of each letter. The clues along the edges tell
you which letter would be the first you'd see from than vantage point
looking down the row or column.
These seem like simple puzzles, but for some reason, I cannot make any
headway except by trial and error. I want to be able to "if this, then
that, then this" it, but I cannot. What methods of a attack are there?
SPOILER BELOW
The solution to the sample puzzle is below.
The solution to the sample puzzle is below.
The solution to the sample puzzle is below.
The solution to the sample puzzle is below.
The solution to the sample puzzle is below.
The solution to the sample puzzle is below.
The solution to the sample puzzle is below.
The solution to the sample puzzle is below.
C A
+---+---+---+---+---+---+
C | | | | C | B | A |
+---+---+---+---+---+---+
C | | C | A | B | | | B
+---+---+---+---+---+---+
A | | | | A | C | B | B
+---+---+---+---+---+---+
| B | | | | A | C | C
+---+---+---+---+---+---+
| C | A | B | | | | B
+---+---+---+---+---+---+
A | A | B | C | | | |
+---+---+---+---+---+---+
balakumar jothimohan balasubramaniam
--------
Notation used: (a,b)=> a'th row, b'th column.
step 1. Take last column:
(6,6) cant be A
(5,6),(2,6),(3,6) have to be empty or B
(4,6) has to be empty or C
That leaves just (1,6) for A.
(1,6)=A
step 2. similarly attack the 1st column for finding the location of
B(which is the element absent in the set CCAA)
(4,1)=B
step 3. no other A can be found in row 1 and col 6. //ly for B.
step 4. look at elements where all elements are ruled out. at this point,
it is (1,3). therefore it should be empty.
(1,3)=Empty.
step 5. therefore (2,3) should be null or A.
step 6. look at col 2. B is ruled out in all the boxes except (6,2).
(6,2)=B
step 7. looking from row 6's left, we have to see a A. therefore (6,1) is
A.
step 8. rule out A from row 6 and col 1.
(3,1)=A
step 9. now (3,3) can't be B-3 elements cant be filled out
step 10. therefore looking at col 3, we know that (5,3) is B
step 11. therefore (5,4), (5,5), (5,6) are empty.
step 12. therefore (5,2)=A and (5,1)=C
ROW 5 complete
step 13. therefore (1,1),(2,1) and (3,1) are empty
COL 1 complete
keep filling up thus..
at one point of time, you would have the choice of filling one of (2,2)
or (1,2) with C or Empty. filling (2,2) with Empty would lead to a
contradiction in Col 6.
hence (2,2)=C. at this point, you should have rows 1,5,6 filled and
columns 1,2 filled.
column 6 gets filled next. then row 2, col3, row 3,row 4.
now, thats a complete matrix.
Cheers.
Balakumar
Chuck Fresno
didn't see this.
On Sat, 11 Aug 2001 13:25:11 -0500, balakumar jothimohan
balasubramaniam <bbal...@students.uiuc.edu> wrote:
>Spoiler:
>--------
James Dow Allen
Recently Chuck Fresno (chuck...@rocketmail.com) wrote:
> There is a puzzle that has appeared in GAMES magazine as well as
> several Japanese puzzle magazines and the Puzzle Championships
> that has been called END VIEW or EASY AS ABC(DE) as well as
> other names....
>
> The object is to place the letters A, B and C so that each column and
> row have exactly one of each letter. The clues along the edges tell
> you which letter would be the first you'd see from that vantage point
> looking down the row or column.
Here's another example:
A
+---+---+---+---+---+---+
C | | | | | | |
+---+---+---+---+---+---+
| | | | | | | B
+---+---+---+---+---+---+
C | | | | | | |
+---+---+---+---+---+---+
| | | | | | | B
+---+---+---+---+---+---+
C | | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
C B
To save space, the puzzle can be abbreviated by listing
the clues clockwise, here as:
.....A // .B.B.. // .B.C.. // .C.C.C
It's fun to generate these puzzles. Of course there
should be a unique solution and no unnecessary clue.
I've appended several more below, if you can't wait
for GAMES!
I was surprised to find a set of just six clues which
yielded a unique solution. For the Obpuzzle:
Can you find such an arrangement of six clues?
James D. Allen
(Flames to the newsgroup please; spam to the From:
address; personal mail to jamesdowallen at yahoo.)
ACAA.. // .BB.BC // ...... // ..C...
.CB.B. // C.B... // ...... // A.A.A.
...... // .AA.A. // ...BAB // C.B...
....AB // C..... // ..AB.. // ..CBB.
....B. // .B.B.. // ..AB.. // .A.A.A
..A... // AAA... // ..BB.. // CC....
....C. // .CC.C. // .B..B. // ..AABB
...A.. // .BBA.. // .B.BC. // .A..CC
B.C... // .B.AB. // .BA... // ...CCA
.BBB.. // ...CC. // A..... // ....AA
.BBBC. // .A.B.. // A....C // .A....
BABB.. // .C.... // A..A.. // B.B...
B.B..B // .A...B // AC.AA. // ....C.
C..CC. // .A..B. // B..B.. // ..C..B
.A.C.. // .A.... // BA.BB. // .B...C
A.AAA. // ...B.. // C..... // ...BB.
.CAAB. // .BBB.. // C...A. // ..CC..
C..B.. // A..A.. // C..BA. // B..BB.
.B.... // ..CCB. // C.CB.B // A.A.C.
...B.A // ..AA.. // CA...C // .B....
BB.C.. // ....C. // CA.A.. // ..BCBB
..BA.. // ...B.. // CC.... // CB...B
Mark J. Tilford
That was significantly tougher than any of the puzzles in GAMES. Do you
have any puzzles with more than three letters or are larger than side 6?
(I know that issue of GAMES had some, but I misplaced that issue.)
--
------------------------
Mark Jeffrey Tilford
til...@ugcs.caltech.edu
James Dow Allen
> Any puzzles with more than three letters or are larger than side 6?
I'll look into it in my copious spare time. Meanwhile ...
why has no one tackled my Obpuzzle:
> Can you find such an arrangement of six clues
> which yields a unique solution?
I suggest you start with A.B... on one side.
James
Justin Leck
> til...@ralph.caltech.edu (Mark J. Tilford) wrote in message
news:<slrn9ppq1k....@ralph.caltech.edu>...
> > Any puzzles with more than three letters or are larger than side 6?
Here are a few 6x6 puzzles using the letters ABCD. As before, the puzzles
are abbreviated by listing the clues clockwise around the outside of the
grid. Some of these may be a little tedious to do by hand:
..A.B. // C.CBDA // A.ACBD // .BAB..
..ABAB // B.BCDA // .DDC.. // .B.D..
AB.CA. // ..CCDD // .B.BC. // ..B.B.
..AB.. // .CBBDD // .B..A. // AC...B
...A.B // .CB..A // .CDD.. // C...DD
...A.. // BA..C. // ...DBD // .ADA..
.A.AB. // .CBC.B // ..D... // A....B
..A..B // .C..D. // .DD.D. // ...BB.
A...BA // C...D. // .DD..D // .B....
.AAB.. // ....C. // D...CC // .....B
Here are a few 7x7 puzzles using the letters ABC.
.AABCB. // ..CAAB. // C.BCCB. // ..CBAB.
.ABAAC. // ..AA.A. // ABBCC.. // .B.C.BC
.A.B.B. // .AAAC.. // C...BB. // CA.CBBC
A..BBA. // .BBBB.C // .BA.B.. // .C.C.A.
.AA.B.B // ..A.... // AA..CCC // B.AC.A.
AAB.... // B.C.... // .AAAABB // .AA.B..
.AAA..B // ..AAAA. // ..CB... // C....B.
..ABAB. // ..B...B // B.....C // .CCCCB.
.AA.AB. // ..BAB.. // ...CC.B // .CC..C.
A....A. // .AB.A.. // ...CCC. // A.CC...
Here are a few 7x7 puzzles using the letters ABCD.
.ABABC. // ..CAC.. // A.DDCC. // CD.C..C
.A.BC.A // A.DDA.. // ..AA.DA // C..BBB.
AB.ABBC // ..AA.A. // ..A.A.B // .BBCC..
.ABB.A. // ..B.C.A // ..D.ACB // CD.C..C
ABA..CC // .D...B. // .DCDDC. // .C.B.C.
.A.BAC. // .B.CC.. // B...D.. // DBDD.D.
A..B... // BB.B.A. // ..AA.C. // .DACCD.
..A.B.. // C.BB... // BADDD.B // ..D..D.
A.BAB.. // ..CCC.. // .DC.DB. // .C...B.
.A..... // ..BBB.. // ...CCD. // D.CC.CD
.AB.B.A // ..B.... // .C.C..B // AD.C...
I need to write a better solver to construct 8x8 puzzles, or puzzles with
more than 4 letters.
>
> I'll look into it in my copious spare time. Meanwhile ...
> why has no one tackled my Obpuzzle:
>
> > Can you find such an arrangement of six clues
> > which yields a unique solution?
>
> I suggest you start with A.B... on one side.
>
> James
SPOILER
5
4
3
2
1
I haven't found the solution you found, but an alternative is:
....A. // .BB... // B..A.. // .....A
Justin
James Dow Allen
For example, in the 7x7 ABCD problem
...BDC. // ..BB..D // A.BC.D. // ..AA..D
it is possible to derive the following readily:
B D C
+---+---+---+---+---+---+---+
D | | | | | - | C | |
+---+---+---+---+---+---+---+
| | | | | D | A | C |
+---+---+---+---+---+---+---+
| | | | | A | ? | ? | B
+---+---+---+---+---+---+---+
A | | | | * | | ? | ? | B
+---+---+---+---+---+---+---+
A | | | | | | | D |
+---+---+---+---+---+---+---+
| | | | | | | A |
+---+---+---+---+---+---+---+
| | - | | | | D | - | D
+---+---+---+---+---+---+---+
D C B A
Now, it is "illegal" to place a B at the cell marked (*)
without proof, even though the assumption that the puzzle
has a unique solution implies it must be B! (Otherwise,
the four cells marked "?" would be
+---+---+ +---+---+ +---+---+
| ? | ? | | B | - | | - | B |
+---+---+ = +---+---+ or +---+---+
| ? | ? | | - | B | | B | - |
+---+---+ +---+---+ +---+---+
and the two cases are equivalent: if one satisfies the
conditions the other will too, so solution cannot be unique.)
Come to think of it, it's fun to find inferences like this,
so, since it's just a solitaire anyway, go for it!
James D. Allen (jamesdowallen at yahoo)
> I haven't found the solution you found, but an alternative is:
> ....A. // .BB... // B..A.. // .....A
> Justin
Neat! I wonder if there are any more.
Justin Leck
>
> Here are a few 6x6 puzzles using the letters ABCD. As before, the puzzles
> are abbreviated by listing the clues clockwise around the outside of the
> grid. Some of these may be a little tedious to do by hand:
..
> ...A.. // BA..C. // ...DBD // .ADA..
> .A.AB. // .CBC.B // ..D... // A....B
I've just noticed that the above 3 puzzles do not have unique solutions. My
apologies to anyone that has wasted time trying any of them. To make up for
that, here are some (hopefully unique) replacement 6x6 puzzles using the
letters ABCD. As before, the puzzle are abbreviated by listing the clues
clockwise around the grid:
AA.B.. // C.ADC. // A..AB. // DD.BC.
...A.. // BA.C.. // ..BB.C // A..DC.
A.A..A // ..B.C. // BD.... // CD.D..
Here are some 7x7 puzzles using the letters ABCDE:
A..BBA. // CABD.A. // ADCDC.. // B.AB.C.
.ABC.C. // ...ABDA // .ED.DC. // .ED.DAA
A..ABC. // .DCD.C. // ..AE.C. // CDD.BB.
ABA.CDC // .A.B..A // E.B.... // EBE..C.
.A..AA. // .BAB.A. // ...CAC. // .BDDE.B
AABC... // C..BD.A // BE.E... // C..C.A.
..AA.AB // .CB.D.D // ...D.CC // .CC.D..
.ABB.C. // ....AA. // D..D... // .CC.ECA
ABC.DD. // B.B..ED // ..C.... // .AA..D.
.AA.... // .BCCD.B // ..EBE.. // ....A.E
Here are some 8x8 puzzles using the letters ABC:
..ABBCAB // ABCCABA. // ..AA.BAB // ACA..B.C
ABCB..CB // AB.B.ABA // .BB.AA.. // .ABBC.CB
A.BBACCB // CBABBC.C // ..AC..C. // .BA...C.
A.BACAC. // AAB.C.BC // B..BB.C. // ..AAA...
A.AB.B.B // CBCC.... // C..C..AC // A.ACA.C.
.AB.B.A. // B.BBA..A // ....CA.. // .CCCCCB.
A....BAA // ..B..A.. // C..BBBC. // .C.CCC.B
...AA.A. // A.A.B..B // ...BBBB. // ..A.CBB.
.A...BB. // .C.BB.B. // ...CA..B // C...AA.B
..A.A... // A..A.A.. // BB.B...C // B...CCC.
..AB.B.B // .CBBA... // .C.C.... // ..A....B
A..A...B // .AAAA... // A.CA.... // .......C
Here are some 8x8 puzzles using the letters ABCD:
ABBC.BAD // ....CAA. // BBD.AACC // CCBBC..B
.A...BCD // DD.BBBDC // .BDC.BCA // ..CADDB.
A.ABBCDD // .CCD..BB // .AA.AD.. // .DDACA..
.AB.A..C // D.B.CAC. // .CDCA.C. // .DDBAAA.
.ABB.B.C // DA.D..C. // .CCAA.B. // ..AB.BBA
.AA.AB.. // .CDDC..B // D..DBBD. // .CDDCA..
A...B.BC // DD.A.AD. // ..CDC.D. // .ACC.BB.
...A.BA. // CADDD.C. // .DDD..CA // B.A...C.
A....BAB // CD.DCD.. // .D.BD... // .A.AB.A.
.AB.BCB. // AA...... // BD....B. // D.BBDB..
Here are some 8x8 puzzles using the letters ABCDE:
AB.A.CD. // .CAEACE. // ...BDEDE // EC.BCBD.
ABAACDC. // .DEE.AAC // .ECDD... // E..EDC..
.ABCA.BC // .DA.DC.. // ..EDEC.. // AEDCA.E.
A....BC. // .BAD.DAA // .BDEEBA. // .EAA..A.
AAB.CB.B // ..CCD..B // ..DAE... // CAE..EB.
..ABA.B. // .B..CAC. // .C..DED. // DD.BC.CB
..A.B..B // ..CC.CC. // A.AAD.E. // ..A.EEAA
AABCCB.. // .DD.C..A // ...E.A.. // .BAE.BB.
.A.AAB.. // .C.DDE.A // DC..CC.. // ...E.CA.
.A..B... // ...CD.E. // DD..EE.E // ..BE.DDB
And finally some 8x8 puzzles using the letters ABCDEF:
A.BA.CCD // .DCBAC.E // ..AEB.B. // DDFC.A..
ABCDCE.B // ..BAD.FA // ..DDA.F. // .AEB..C.
..ABC.C. // .AD.ED.C // ..FEACB. // FBBA..CE
...AAB.. // B.C.CDD. // EEFC..B. // FBFBA.E.
.AB.CAB. // .AA.DDE. // .D..BCCE // .CB.F.D.
ABCB..D. // BAC.AE.E // ...CFFF. // .A.FE.E.
.A.BBBC. // .D..EBE. // ..DDEEFA // ..F.FE..
A.BCC.D. // ..EFAAE. // ..A.BCF. // C..FB.B.
ABBBCD.. // ..DC.EFD // ..CEFF.. // C..A.E..
.A.BBA.. // .C.DE.BC // .FCC.E.. // .DADA...
"James Dow Allen" asked about 6x6 puzzles using the letters ABC and having
only 6 clues per puzzle. I think that the following are the only ones
possible, ignoring letter changes and various symmetries:
.....A // .BB... // .B.B.. // .....A
....A. // .BB... // B..A.. // .....A
...A.A // .B.... // .B.... // ..B..A
...A.A // B..... // .B.... // ..A.A.
...A.A // B..... // .B.... // ..B.A.
...A.A // .B.... // .B.... // ..A..A
...AA. // .B.... // B..... // ..A..A
...AB. // C.C... // C..... // ....B.
.A.B.. // .....B // .....B // .AA...
.A.... // ....B. // ...C.B // A.A...
Also, the maximum number of essential clues appears to be 18, of which the
only instance I've found is:
AB.B.A // C...B. // CACBAB // BCBACA
Justin