Trying to wrap my brain around ERs

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Trying to wrap my brain around ERs

Postby enxio27 » Fri Oct 26, 2012 8:04 pm

Here's the grid as it stands:

Code: Select all
.-------------------------------.-------------------------------.-------------------------------.
| 2         4         78        | 6         3         57        | 9         1         578       |
| 3         79        6         | 489       4578      1         | 25        78        278       |
| 19        5         178       | 89        78        2         | 4         6         3         |
:-------------------------------+-------------------------------+-------------------------------:
| 19        379       17        | 2         578       4         | 35        78        6         |
| 6         37        2         | 38        9         57        | 1         4         578       |
| 5         8         4         | 13        17        6         | 23        9         27        |
:-------------------------------+-------------------------------+-------------------------------:
| 8         1         9         | 5         6         3         | 7         2         4         |
| 7         2         3         | 14        14        8         | 6         5         9         |
| 4         6         5         | 7         2         9         | 8         3         1         |
'-------------------------------.-------------------------------.-------------------------------'


Richard Broughton's SudokuSolver shows this hint:

741. Grid:02 Empty Rectangle on candidate 7 at n1(c3->r2) - r2c8=r4c8

Why? Apparently I'm not getting the logic here, or perhaps it's the notation. Where is the hinge, and where are the other three corners?
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Re: Trying to wrap my brain around ERs

Postby daj95376 » Fri Oct 26, 2012 9:52 pm

There are several ER patterns in this grid. Apparently, the program is identifying the one I marked below on <7>. Personally, I think the solver's notation needs work.

Code: Select all
 +--------------------------------------------------------------+
 |  2     4    *78    |  6     3     57    |  9     1     578   |
 |  3    *79    6     |  489   4578  1     |  25   *78    278   |
 |  19    5    *178   |  89    78    2     |  4     6     3     |
 |--------------------+--------------------+--------------------|
 |  19    379   1-7   |  2     578   4     |  35   *78    6     |
 |  6     37    2     |  38    9     57    |  1     4     578   |
 |  5     8     4     |  13    17    6     |  23    9     27    |
 |--------------------+--------------------+--------------------|
 |  8     1     9     |  5     6     3     |  7     2     4     |
 |  7     2     3     |  14    14    8     |  6     5     9     |
 |  4     6     5     |  7     2     9     |  8     3     1     |
 +--------------------------------------------------------------+
 # 38 eliminations remain

 c8b1    Empty Rectangle                 <> 7    r4c3

 -or-

 (7)r4c8 = r2c8 - r2c2 = (7)r13c3  =>  r4c3<>7

A better suggestion:

Code: Select all
 <58+7>  XYZ-Wing r4c5/r3c5+r5c6         <> 7    r6c5
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Re: Trying to wrap my brain around ERs

Postby enxio27 » Fri Oct 26, 2012 10:09 pm

daj95376 wrote:There are several ER patterns in this grid. Apparently, the program is identifying the one I marked below on <7>. Personally, I think the solver's notation needs work.

It's not really the notation I'm hung up on (actually, I don't understand your notation any better). It's the logic I'm having trouble with. I've been through several ER tutorials, but I'm still not getting it.

Code: Select all
(7)r4c8 = r2c8 - r2c2 = (7)r13c3  =>  r4c3<>7


Which cells constitute the hinge? Which cells constitute the other three corners? Why is 7 eliminated in r4c3?

Code: Select all
 <58+7>  XYZ-Wing r4c5/r3c5+r5c6         <> 7    r6c5


I haven't gotten to XYZ-wings yet.
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Re: Trying to wrap my brain around ERs

Postby daj95376 » Fri Oct 26, 2012 10:43 pm

enxio27 wrote:It's not really the notation I'm hung up on (actually, I don't understand your notation any better). It's the logic I'm having trouble with. I've been through several ER tutorials, but I'm still not getting it.

Which cells constitute the hinge? Which cells constitute the other three corners? Why is 7 eliminated in r4c3?

I haven't gotten to XYZ-wings yet.

Empty Rectangle:

A) A line (row/column) with two cells for a candidate. In this case, r2c8 and r4c8 in [c8].

B) A box where the candidates are confined to one row and one column. In this case, [r2] and [c3] in [b1].

C) One candidate in (A) exists in one line from (B). In this case, r2c8 in [r2].

D)) An elimination can occur in the cell that's in the alternate line of (B) and also sees the alternate cell of (A). In this case, r4c3 is in [c3] and sees r4c8.

My solver identified [c8] for (A) and [b1] for (B). The elimination r4c3<>7 follows.


As for "the hinge", it's [r2] and [c3] in [b1].


More Specifically: r4c3<>7 follows from the fact that r4c3=7 would result in eliminations r13c3<>7 and r4c8<>7 ... leaving r2c2=7 true in [b1] and r2c8=7 true in [c8]. Since both cells can't be true at the same time for <7>, the elimination r4c3<>7 follows from the contradiction.

[Edit: changed the context from singular sense to multiple sense on "candidate" in (B).]
Last edited by daj95376 on Fri Nov 02, 2012 4:23 pm, edited 1 time in total.
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Re: Trying to wrap my brain around ERs

Postby 7b53 » Sat Oct 27, 2012 2:32 am

enxio27 wrote:It's not really the notation I'm hung up on (actually, I don't understand your notation any better). It's the logic I'm having trouble with. I've been through several ER tutorials, but I'm still not getting it.

from the PM grid, look at column 8.
digit 7 can be either at (r2c8 or r4c8). one of them must be true.

if r4c8=7 then r4c3<>7 (easy enough)

if r2c8=7 then r2c2<>7 . now look closely at box 1 .
where can digit 7 be at box 1 ?
digit 7 can only be at column 3 (r1c3 or r3c3).
coincidentally, it will also eliminates digit 7 from r4c3.

so at column 8 , either digit 7 is at (r2c8 or r4c8), r4c3 cannot be a 7 .
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Re: Trying to wrap my brain around ERs

Postby enxio27 » Fri Nov 02, 2012 3:10 pm

daj95376 wrote:Empty Rectangle:

A) A line (row/column) with two cells for a candidate. In this case, r2c8 and r4c8 in [c8].

B) A box where the candidate is confined to one row and one column. In this case, [r2] and [c3] in [b1].

C) One candidate in (A) exists in one line from (B). In this case, r2c8 in [r2].

D)) An elimination can occur in the cell that's in the alternate line of (B) and also sees the alternate cell of (A). In this case, r4c3 is in [c3] and sees r4c8.

I think this explanation finally nailed it for me. Thank you! :D The logic of ERs seems to be backward to what I'm used to, and I think that's what make the concept difficult.
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