The New Sudoku Players' Forum

[borescoper]

if there is a loop with odd number grids(5 or 7 or 9...), and candidates in every grids is same "ab", it's a "deadly loop".for example, a 5 grids loop, all of the grids with candidates "ab", every 4 "ab" can formed a "remote pair", delete the 5th grid "ab" to nothing. so, we must avoid the "deadly loop" apear, then we can find some strong links.
this technique is similar to the technique "oddagon" and "guardian", but there is difference between them. every grid on loop has two candidates, whole loop has two-type of candidates, but not one-type candidate as a normal oddagon. so i call this "bivalue oddagon".
for example, if we delete r6c3(5) and r9c3(5) together, grids with the "#" will constitute a "bivalue oddagon" with candidates "29" in all of the grids on the loop, and the loop will die. so, we can NOT delete r6c3(5) and r9c3(5) together.it means r6c3(5)==r9c3(5), strong link between them.so, r2c3<>5, r2c3=1.

Code: Select all

*--------------------------------------------------------------------------------------------*
|         2         6         8|         7         9         5|         3         4         1|
|         9       135        15|         6        34       348|         2         7        58|
|        57       357         4|         1        23       238|         9         6        58|
|------------------------------+------------------------------+------------------------------|
|        56      1259      1259|       259         7      1269|         8         3         4|
|       468        14         3|      2489       246     12469|         7         5       #29|
|      4578     24579      #259|    234589      2345      2349|         1       #29         6|
|------------------------------+------------------------------+------------------------------|
|        14        29         6|      2349         8      2349|         5       129         7|
|        15         8         7|       259       256       269|         4       129         3|
|         3      2459      #259|        45         1         7|         6         8       #29|
*--------------------------------------------------------------------------------------------*

chinese edition:
附上中文版：
如果有由奇数个格子组成的闭环（5、7、9……），并且所有格子候选数都是ab，那么这是一个“死环”。比如，一个5格的环，所有格都是ab，那么，任意四个ab可构成一个“远程数对”的结构，将第五格删空。所以，我们必须避免“死环”出现。
例如图中，如果同时删除r6c3(5)和r9c3(5)，打#号的格子将会构成一个“奇数双值环”，所有格都是29，这个环就死了。所以，我们不能同时删去r6c3(5)和r9c3(5)，即 r6c3(5)==r9c3(5)，二者构成强链。所以，r2c3<>5，r2c3=1

[Leren]

This is a well known but not often used strategy called oddagons on this forum. Strictly speaking what you have is two almost oddagons in digits 2 and 9. An oddagon is a closed loop of Strong links on a single digit with an odd number of nodes. The two 5's you mention are the Guardians, which prevent this form of Deadly pattern from being exposed. Here is an article on Guardians here or you can type oddagon into the search box in this forum and read the posts on this topic.

Leren

[borescoper]

This is a well known but not often used strategy called oddagons on this forum. Strictly speaking what you have is two almost oddagons in digits 2 and 9. An oddagon is a closed loop of Strong links on a single digit with an odd number of nodes. The two 5's you mention are the Guardians, which prevent this form of Deadly pattern from being exposed. Here is an article on Guardians here or you can type oddagon into the search box in this forum and read the posts on this topic.

Leren

thank you very much for your reply!
i think there is difference between this bivalue loop technique and the oddagon. oddagon is a single-type candidate loop, but bivalue loop is double-type candidates. i will post more example tomorrow, some puzzle is hard to observe if using the oddagon and "guardian", but easy if using the bivalue loop.

[borescoper]

This is a well known but not often used strategy called oddagons on this forum. Strictly speaking what you have is two almost oddagons in digits 2 and 9. An oddagon is a closed loop of Strong links on a single digit with an odd number of nodes. The two 5's you mention are the Guardians, which prevent this form of Deadly pattern from being exposed. Here is an article on Guardians here or you can type oddagon into the search box in this forum and read the posts on this topic.

Leren

and then i searched oddagon in the forum, clicked several URLs, and found that the oddagon is single-type candidate loop, with single-type candidate guardians. maybe we can call the technique "bivalue oddagon", LOL. it is more easy finding than a oddagon, because the bivalue grids with same "ab" always attract more focus; BTW, single-type candidate oddagon always can be replaced with two strong-link chains!

[borescoper]

some examples:

1.bivalue oddagon with missing candidates, and also diagonal strong link guardian:
the 5 "#" grids formed a "bivalue oddagon"(missing candidate "9" in r1c5 but doesn't matter), we can NOT delete r9c1(1) and r1c5(23) together, otherwise, 5 "#" grids will become a "deadly loop". then, r1c5(23)==r9c1(1)--r9c4(1)==r7c6(1)--r1c6(1)==r12c6(6), so, r1c5<>6

Code: Select all

*--------------------------------------------------------------------------------------------*
|         7         4       #69|      1268      #236       168|         5      3689      3689|
|       269       269         3|         5         7        68|        89         4         1|
|         8         1         5|        46       346         9|         2         7        36|
|------------------------------+------------------------------+------------------------------|
|        69       369         1|       268       256       568|         7       389         4|
|         4         7         8|         9         1         3|         6         2         5|
|         5       369         2|       468        46         7|         1       389       389|
|------------------------------+------------------------------+------------------------------|
|      1269      269         4|         3       569       156|        89       689         7|
|         3         5       #69|         7         8         2|         4         1        69|
|      #169         8         7|        16       #69         4|         3         5         2|
*--------------------------------------------------------------------------------------------*

2.bivalue oddagon with 7 grids(and also missing candidate):
the 7 grids with "#" formed a "bivalue oddagon"(missing candidate 5 in r8c3 but doesn't matter), we can NOT delete r8c3(8) and r8c7(1) together, otherwise, 7 "#" grids will become a "deadly loop". then, r8c3(8)==r8c7(1)--r8c1(1)==r8c1(6), so, r8c3<>6, r8c3=8.

Code: Select all

*--------------------------------------------------------------------------------------------*
|         2         8         4|         7       #56         9|       #56         1         3|
|       #56         7         1|         4         3       #56|         8         9         2|
|         3         9       #56|         1         2         8|         7       456        46|
|------------------------------+------------------------------+------------------------------|
|       156       136       356|     23568      4568     24567|         9     34678      1468|
|         4         2         9|       368         1        67|        36      3678         5|
|         8       136         7|       356         9       456|         2       346       146|
|------------------------------+------------------------------+------------------------------|
|         7         5      2368|       268       468         1|       346      3468         9|
|        16         4       #68|         9       568         3|      #156         2         7|
|         9       136      2368|      2568         7      2456|     13456     34568      1468|
*--------------------------------------------------------------------------------------------*

3.bivalue oddagon mixed with other advanced techniques:
the 5 "#" grids formed a "bivalue oddagon", and the 6 "*" grids formed a UR (69). if r9c2<>6, then r8c23={69}(hidden pair), to avoid the 6 "*" grids formed a "deadly pattern(69)", we can find r3c1=78, then, look at the 5 "#" grids, r34c7=6(otherwise the 5 "#" grids will formed a deadly loop 78). so, r9c2(6)==r34c7(6), so, r9c7<>6, r9c2=6.
Once you have used this technique, all solved.

Code: Select all

*--------------------------------------------------------------------------------------------*
|       678       678         5|         4         3         9|         1       678         2|
|         3         1         4|       267         8        27|         5        67         9|
|    #*6789         2       *69|        67         5         1|      #678         4         3|
|------------------------------+------------------------------+------------------------------|
|         1         4        78|         3         2         5|      #678         9       678|
|       *69       *69         2|         1         7         8|         3         5         4|
|       #78         5         3|         9         4         6|         2         1       #78|
|------------------------------+------------------------------+------------------------------|
|         4         3        78|         5         6        27|         9       278         1|
|         5     *6789       *69|       278         1         3|         4      2678       678|
|         2       678         1|        78         9         4|       678         3         5|
*--------------------------------------------------------------------------------------------*

4.complex bivalue oddagon:
look at all 7 grids with symbols. if r4c1<>5, the two "%" grids r4c12 will formed a strong link(r4c1(7)==r4c2(2)). we can use r4c12 as a bivalue grid "27" in this example. on the other hand, the two "*" grids r56c3 formed another strong link(r56c3(2)==r56c3(7)), we can use r56c3 as a bivalue grid "27" in this example.
so, if we delete r4c1(5) and r4c9(5) together, all of the "#" grids will formed a "deadly loop".(r4c12(2==7), r56c3(2==7), r7c3(27), r7c9(27), r4c9(27)). it means r4c1(5)==r4c9(5). so, r4c5<>5, r6c5=5.

Code: Select all

*--------------------------------------------------------------------------------------------*
|         2         7         3|         5         9         6|         4         1         8|
|         9         5         6|         8         1         4|         2         7         3|
|         1         4         8|         3         2         7|         6         5         9|
|------------------------------+------------------------------+------------------------------|
|     %#578      %#28         9|         6      4587         1|         3       248      #257|
|       578         6     *#127|      2479         3       289|     15789      2489      1257|
|         4         3     *#127|       279       587       289|     15789       289         6|
|------------------------------+------------------------------+------------------------------|
|         3         1       #27|        49        48         5|       789         6       #27|
|        78       289         4|      1297         6         3|     15789       289      1257|
|         6       289         5|      1297        78       289|      1897         3         4|
*--------------------------------------------------------------------------------------------*

[eleven]

Nice moves !

There is a typo in the last one, r9c1(5) should be r4c9(5).

[borescoper]

Nice moves !

There is a typo in the last one, r9c1(5) should be r4c9(5).

yes! thank you very much for point it out! i have already modified it!