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Trying to wrap my brain around ERs
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=10&t=1066		 Page 1 of 1
Author:  enxio27 [ Fri Oct 26, 2012 4:15 pm ]
Post subject:  Trying to wrap my brain around ERs
Here's the grid as it stands:

Code:
.-------------------------------.-------------------------------.-------------------------------.
| 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         |
'-------------------------------.-------------------------------.-------------------------------'


Sudoku Solver 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?
Author:  HATMAN [ Sat Oct 27, 2012 12:16 pm ]
Post subject:  Re: Trying to wrap my brain around ERs
If you do F10 it becomes clear:

The 7 at r4c3 eliminates the 7s in r13c3 forcing r2c2 and it also eliminates the 7 at r4c8 forcing r2c8 - conflict.

I agree the notation is hard to understand.

Note with Ed's ordering JSudoku give a very obvious two-string kite on 8.
Author:  nj3h [ Sun Oct 28, 2012 6:20 pm ]
Post subject:  Re: Trying to wrap my brain around ERs
1. Look at row 5.
2. Note there are two cells with an 8 pencil mark.
3. If r5c9 is an 8, then r1c9 and r2c9 cannot be an 8.
4. Then r2c8 is an 8 and r2c4 is not an 8.
5. Now let's look at the other 8 in row 5 (r5c4).
6. If this cell is an 8, then r2c4 cannot be an 8.
7. Therefore, whichever cell in row 5 is an 8 yields the situation where r2c4 can never be an 8. Therefore candidate 8 can be removed from r2c4.

I don't know if this is enough to solve the puzzle, but the ER technique works like this. Some things to thing about:

Notice the two 8s in r5 are in different blocks. There must be only 2 candidates with the same value (in this case 8). There are 8s still unplaced in blocks 2 and 3. Without these two situations the ER just won't work.

Good luck with this.
Author:  enxio27 [ Fri Nov 02, 2012 3:11 pm ]
Post subject:  Re: Trying to wrap my brain around ERs
I finally got it. The logic seems backward from what I'm used to, and I think that's what made the concept difficult.

This explanation on The New Sudoku Players' Forum finally got me through it:

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.
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