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Saturday 25-Oct-2014

... by: TAREK

look for 1 cell with only two possible candidates. Try to finish the puzzle after chosing one candidate. If you cannot finish the puzzle, then restart by chosing the second candidate, and then continue to end the puzzle.
Good Luck
Tarek

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8(E3,D1), 8C8, (3,9)J8>contradiction therefore 6C8
8(E3,D1), 3J8>contradiction therefore 9J8
8E3>contradiction therefore 8D1 solves

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9D9, 4(H7,J7), 2((G7,G8)>contradiction therefore 1D9
3D7, 3F3>contradiction
3D7, 3F1, 6(E7, F9)>contradiction therefore 3F8
8C8, 7(E7, F9)>contradiction therefore 8B9
7F9>contrdiction therefore 9F9 solves

Saturday 4-Oct-2014

... by: JC Van Hay

G7=3/5/7 -> contradiction; G7=2
J8=3 -> contradiction; 5 singles
C8=8 -> contradiction; singles to the end.

Saturday 4-Oct-2014

... by: Terry

A rational solution is shown in the game log below.

Action: 1 Remove 9 from E3, F3.
Reason: Candidate 9 appears only in sub-column 2-DEF in column 2.
. Therefore, 9 can be removed from E3, F3.

Action: 2 Remove 1 from D7.
Reason: Candidate 1 appears only in sub-column 7-ABC in block 3.
. Therefore, 1 can be removed from D7.

Action: 3 Remove 8 from H6.
Reason: One of the cells C3, C8 must have the value 8.
Therefore, one of the following must be true,
(1) C3 will be 8 in which case E6 will be 8 (in 1 step(s)).
(2) C8 will be 8 in which case H9 will be 8 (in 1 step(s)).
All alternatives result in 8 being removed from H6.


Action: 4 Remove 3 from B3.
Reason: One of the cells H1, H3 must have the value 6.
Therefore, one of the following must be true,
(1) H1 will be 6 in which case 3 will be removed from A3, B3, F3 (in 2 step(s)).
(2) H3 will be 6 in which case B4 will be 3 (in 3 step(s)).
All alternatives result in 3 being removed from B3.


Action: 5 Remove 7 from E6.
Reason: One of the cells D1, D5, D6 must have the value 8.
Therefore, one of the following must be true,
(1) D1 will be 8 in which case E6 will be 8 (in 1 step(s)).
(2) D5 will be 8 in which case E6 will be 5 (in 5 step(s)).
(3) D6 will be 8 in which case E7 will be 7 (in 5 step(s)).
All alternatives result in 7 being removed from E6.


Action: 6 Remove 9 from J7.
Reason: Cell H5 must be one of the values 4, 7, 8.
Therefore, one of the following must be true,
(1) H5 will be 4 in which case J7 will be 4 (in 1 step(s)).
(2) H5 will be 7 in which case 9 will be removed from D7, H7, J7 (in 5 step(s)).
(3) H5 will be 8 in which case 9 will be removed from D7, E7, H7, J7 (in 2 step(s)).
All alternatives result in 9 being removed from J7.


Action: 7 Remove 6 from F1.
Reason: One of the cells F1, F3, F8 must have the value 3.
Therefore, one of the following must be true,
(1) F1 will be 3 in which case F1 will be 3 (in 0 step(s)).
(2) F3 will be 3 in which case F1 will be 5 (in 5 step(s)).
(3) F8 will be 3 in which case H1 will be 6 (in 3 step(s)).
All alternatives result in 6 being removed from F1.


Action: 8 Remove 1 from C3.
Reason: Cell G2 must be one of the values 1, 3, 7.
Therefore, one of the following must be true,
(1) G2 will be 1 in which case A3 will be 1 (in 6 step(s)).
(2) G2 will be 3 in which case G3 will be 1 (in 1 step(s)).
(3) G2 will be 7 in which case 1 will be removed from A3, C3 (in 1 step(s)).
All alternatives result in 1 being removed from C3.


Action: 9 Remove 6 from D1.
Reason: One of the cells H3, H7, H9 must have the value 9.
Therefore, one of the following must be true,
(1) H3 will be 9 in which case H1 will be 6 (in 1 step(s)).
(2) H7 will be 9 in which case D4 will be 6 (in 6 step(s)).
(3) H9 will be 9 in which case D1 will be 8 (in 2 step(s)).
All alternatives result in 6 being removed from D1.


Action: 10 Remove 3 from H1.
Reason: Cell J8 must be one of the values 3, 9.
Therefore, one of the following must be true,
(1) J8 will be 3 in which case F1 will be 3 (in 6 step(s)).
(2) J8 will be 9 in which case H1 will be 6 (in 2 step(s)).
All alternatives result in 3 being removed from H1.


Action: 11 Remove 3 from A1.
Reason: Cell J8 must be one of the values 3, 9.
Therefore, one of the following must be true,
(1) J8 will be 3 in which case F1 will be 3 (in 6 step(s)).
(2) J8 will be 9 in which case A1 will be 7 (in 3 step(s)).
All alternatives result in 3 being removed from A1.


Action: 12 Remove 3 from F3.
Reason: One of the cells H3, J3 must have the value 9.
Therefore, one of the following must be true,
(1) H3 will be 9 in which case 3 will be removed from A3, F3 (in 3 step(s)).
(2) J3 will be 9 in which case F1 will be 3 (in 3 step(s)).
All alternatives result in 3 being removed from F3.


Action: 13 Remove 9 from J9.
Reason: One of the cells A1, B1, F1 must have the value 5.
Therefore, one of the following must be true,
(1) A1 will be 5 in which case J3 will be 9 (in 3 step(s)).
(2) B1 will be 5 in which case J9 will be 5 (in 1 step(s)).
(3) F1 will be 5 in which case J8 will be 9 (in 2 step(s)).
All alternatives result in 9 being removed from J9.


Action: 14 Remove 5 from J4.
Reason: One of the cells G7, J7, J9 must have the value 5.
Therefore, one of the following must be true,
(1) G7 will be 5 in which case E4 will be 5 (in 5 step(s)).
(2) J7 will be 5 in which case J7 will be 5 (in 0 step(s)).
(3) J9 will be 5 in which case J9 will be 5 (in 0 step(s)).
All alternatives result in 5 being removed from J4.


Action: 15 Remove 7 from J4.
Reason: One of the cells F9, H9, J9 must have the value 7.
Therefore, one of the following must be true,
(1) F9 will be 7 in which case E4 will be 7 (in 1 step(s)).
(2) H9 will be 7 in which case J4 will be 3 (in 6 step(s)).
(3) J9 will be 7 in which case J9 will be 7 (in 0 step(s)).
All alternatives result in 7 being removed from J4.


Action: 16 Remove 7 from H7.
Reason: One of the cells C2, C4, C5 must have the value 7.
Therefore, one of the following must be true,
(1) C2 will be 7 in which case H1 will be 7 (in 1 step(s)).
(2) C4 will be 7 in which case E7 will be 7 (in 1 step(s)).
(3) C5 will be 7 in which case 7 will be removed from G7, H7, H9 (in 1 step(s)).
All alternatives result in 7 being removed from H7.


Action: 17 Remove 7 from A2.
Reason: One of the cells H7, H9, J8 must have the value 9.
Therefore, one of the following must be true,
(1) H7 will be 9 in which case A6 will be 7 (in 4 step(s)).
(2) H9 will be 9 in which case A2 will be 6 (in 5 step(s)).
(3) J8 will be 9 in which case A1 will be 7 (in 3 step(s)).
All alternatives result in 7 being removed from A2.


Action: 18 Remove 3 from H3.
Reason: One of the cells H7, H9, J8 must have the value 9.
Therefore, one of the following must be true,
(1) H7 will be 9 in which case H6 will be 3 (in 5 step(s)).
(2) H9 will be 9 in which case A3 will be 3 (in 6 step(s)).
(3) J8 will be 9 in which case H3 will be 9 (in 1 step(s)).
All alternatives result in 3 being removed from H3.


Action: 19 Remove 9 from F8.
Reason: Cell J8 must be one of the values 3, 9.
Therefore, one of the following must be true,
(1) J8 will be 3 in which case F8 will be 6 (in 4 step(s)).
(2) J8 will be 9 in which case J8 will be 9 (in 0 step(s)).
All alternatives result in 9 being removed from F8.


Action: 20 Remove 7 from G5, G6.
Reason: Cell J8 must be one of the values 3, 9.
Therefore, one of the following must be true,
(1) J8 will be 3 in which case G7 will be 7 (in 5 step(s)).
(2) J8 will be 9 in which case G2 will be 7 (in 3 step(s)).
All alternatives result in 7 being removed from G5, G6.


Action: 21 Remove 7 from A5.
Reason: Cell H1 must be one of the values 6, 7.
Therefore, one of the following must be true,
(1) H1 will be 6 in which case A1 will be 7 (in 1 step(s)).
(2) H1 will be 7 in which case J5 will be 7 (in 1 step(s)).
All alternatives result in 7 being removed from A5.


Action: 22 Remove 9 from H9.
Reason: One of the cells G2, G7 must have the value 7.
Therefore, one of the following must be true,
(1) G2 will be 7 in which case H3 will be 9 (in 2 step(s)).
(2) G7 will be 7 in which case H9 will be 8 (in 2 step(s)).
All alternatives result in 9 being removed from H9.


Action: 23 Remove 6 from E7.
Reason: Cell H9 must be one of the values 7, 8.
Therefore, one of the following must be true,
(1) H9 will be 7 in which case E7 will be 7 (in 1 step(s)).
(2) H9 will be 8 in which case 6 will be removed from D7, E7 (in 2 step(s)).
All alternatives result in 6 being removed from E7.


Action: 24 Remove 5 from F6.
Reason: Cell F1 must be one of the values 3, 5.
Therefore, one of the following must be true,
(1) F1 will be 3 in which case G6 will be 5 (in 3 step(s)).
(2) F1 will be 5 in which case F1 will be 5 (in 0 step(s)).
All alternatives result in 5 being removed from F6.


Action: 25 Remove 5 from A1.
Reason: Cell H1 must be one of the values 6, 7.
Therefore, one of the following must be true,
(1) H1 will be 6 in which case A1 will be 7 (in 1 step(s)).
(2) H1 will be 7 in which case C3 will be 5 (in 4 step(s)).
All alternatives result in 5 being removed from A1.


Action: 26 Remove 6 from B1.
Reason: Cell A1 must be one of the values 6, 7.
Therefore, one of the following must be true,
(1) A1 will be 6 in which case A1 will be 6 (in 0 step(s)).
(2) A1 will be 7 in which case H1 will be 6 (in 1 step(s)).
All alternatives result in 6 being removed from B1.


Action: 27 Remove 7 from J7.
Reason: One of the cells H7, J7 must have the value 4.
Therefore, one of the following must be true,
(1) H7 will be 4 in which case E7 will be 7 (in 5 step(s)).
(2) J7 will be 4 in which case J7 will be 4 (in 0 step(s)).
All alternatives result in 7 being removed from J7.


Action: 28 Remove 9 from E7.
Reason: Cell A1 must be one of the values 6, 7.
Therefore, one of the following must be true,
(1) A1 will be 6 in which case H7 will be 9 (in 2 step(s)).
(2) A1 will be 7 in which case E7 will be 7 (in 2 step(s)).
All alternatives result in 9 being removed from E7.


Action: 29 Remove 7 from F5.
Reason: One of the cells B9, J9 must have the value 5.
Therefore, one of the following must be true,
(1) B9 will be 5 in which case F5 will be 2 (in 4 step(s)).
(2) J9 will be 5 in which case J5 will be 7 (in 1 step(s)).
All alternatives result in 7 being removed from F5.


Action: 30 Remove 3 from G8.
Reason: Cell F1 must be one of the values 3, 5.
Therefore, one of the following must be true,
(1) F1 will be 3 in which case J8 will be 3 (in 5 step(s)).
(2) F1 will be 5 in which case F8 will be 3 (in 1 step(s)).
All alternatives result in 3 being removed from G8.


Action: 31 Remove 2 from F8.
Reason: Cell C8 must be one of the values 6, 8.
Therefore, one of the following must be true,
(1) C8 will be 6 in which case F8 will be 3 (in 2 step(s)).
(2) C8 will be 8 in which case G8 will be 2 (in 1 step(s)).
All alternatives result in 2 being removed from F8.


Action: 32 Remove 5 from F3.
Reason: Cell J8 must be one of the values 3, 9.
Therefore, one of the following must be true,
(1) J8 will be 3 in which case E3 will be 5 (in 3 step(s)).
(2) J8 will be 9 in which case F1 will be 5 (in 2 step(s)).
All alternatives result in 5 being removed from F3.


Action: 33 Remove 5 from F5.
Reason: Cell H3 must be one of the values 6, 9.
Therefore, one of the following must be true,
(1) H3 will be 6 in which case F5 will be 1 (in 3 step(s)).
(2) H3 will be 9 in which case F1 will be 5 (in 3 step(s)).
All alternatives result in 5 being removed from F5.


Action: 34 Remove 5 from B1.
Reason: Cell H1 must be one of the values 6, 7.
Therefore, one of the following must be true,
(1) H1 will be 6 in which case F1 will be 5 (in 4 step(s)).
(2) H1 will be 7 in which case B5 will be 5 (in 4 step(s)).
All alternatives result in 5 being removed from B1.


Action: 35 Set F1 to 5.
Reason: Cell F1 is the only cell in column 1 with this candidate (5).

Action: 36 Set F8 to 3.
Reason: Cell F8 is the only cell in row F with this candidate (3).

Action: 37 Set J8 to 9.
Reason: Cell J8 has only one candidate (9).

Action: 38 Set H3 to 9.
Reason: Cell H3 is the only cell in row H with this candidate (9).

Action: 39 Set H1 to 6.
Reason: Cell H1 is the only cell in row H with this candidate (6).

Action: 40 Set A1 to 7.
Reason: Cell A1 has only one candidate (7).

Action: 41 Set G2 to 7.
Reason: Cell G2 is the only cell in column 2 with this candidate (7).

Action: 42 Set E7 to 7.
Reason: Cell E7 is the only cell in column 7 with this candidate (7).

Action: 43 Remove 1 from A3.
Reason: Candidate 1 appears only in sub-column 2-ABC in column 2.
. Therefore, 1 can be removed from A3.

Action: 44 Remove 3 from A3.
Reason: Candidate 3 appears only in sub-column 3-GHJ in block 7.
. Therefore, 3 can be removed from A3.

Action: 45 Remove 5 from A7.
Reason: Cell C2 must be one of the values 1, 6.
Therefore, one of the following must be true,
(1) C2 will be 1 in which case A7 will be 1 (in 1 step(s)).
(2) C2 will be 6 in which case A3 will be 5 (in 1 step(s)).
All alternatives result in 5 being removed from A7.


Action: 46 Remove 9 from D7, B9.
Reason: Cell D9 must be one of the values 1, 9.
Therefore, one of the following must be true,
(1) D9 will be 1 in which case F9 will be 9 (in 1 step(s)).
(2) D9 will be 9 in which case D9 will be 9 (in 0 step(s)).
All alternatives result in 9 being removed from D7, B9.


Action: 47 Remove 5 from B3.
Reason: One of the cells C3, C8 must have the value 8.
Therefore, one of the following must be true,
(1) C3 will be 8 in which case B3 will be 4 (in 1 step(s)).
(2) C8 will be 8 in which case B9 will be 5 (in 1 step(s)).
All alternatives result in 5 being removed from B3.


Action: 48 Remove 6 from D2.
Reason: One of the cells D5, F5 must have the value 2.
Therefore, one of the following must be true,
(1) D5 will be 2 in which case D7 will be 6 (in 1 step(s)).
(2) F5 will be 2 in which case F3 will be 6 (in 1 step(s)).
All alternatives result in 6 being removed from D2.


Action: 49 Remove 6 from C3.
Reason: Cell E8 must be one of the values 2, 6.
Therefore, one of the following must be true,
(1) E8 will be 2 in which case C8 will be 6 (in 1 step(s)).
(2) E8 will be 6 in which case F3 will be 6 (in 1 step(s)).
All alternatives result in 6 being removed from C3.


Action: 50 Remove 6 from E2.
Reason: Cell B1 must be one of the values 3, 8.
Therefore, one of the following must be true,
(1) B1 will be 3 in which case E2 will be 9 (in 2 step(s)).
(2) B1 will be 8 in which case E8 will be 6 (in 2 step(s)).
All alternatives result in 6 being removed from E2.


Action: 51 Remove 6 from A3, B3.
Reason: Candidate 6 appears only in sub-column 2-ABC in column 2.
. Therefore, 6 can be removed from A3, B3.

Action: 52 Set A3 to 5.
Reason: Cell A3 has only one candidate (5).

Action: 53 Remove 5 from B7.
Reason: Cell C2 must be one of the values 1, 6.
Therefore, one of the following must be true,
(1) C2 will be 1 in which case B7 will be 9 (in 2 step(s)).
(2) C2 will be 6 in which case B9 will be 5 (in 2 step(s)).
All alternatives result in 5 being removed from B7.


Action: 54 Remove 5 from B4.
Reason: Cell C3 must be one of the values 4, 8.
Therefore, one of the following must be true,
(1) C3 will be 4 in which case B9 will be 5 (in 2 step(s)).
(2) C3 will be 8 in which case E4 will be 5 (in 2 step(s)).
All alternatives result in 5 being removed from B4.


Action: 55 Remove 6 from E4.
Reason: Cell B9 must be one of the values 5, 8.
Therefore, one of the following must be true,
(1) B9 will be 5 in which case E8 will be 6 (in 2 step(s)).
(2) B9 will be 8 in which case E4 will be 5 (in 2 step(s)).
All alternatives result in 6 being removed from E4.


Action: 56 Set E4 to 5.
Reason: Cell E4 has only one candidate (5).

Action: 57 Set G6 to 5.
Reason: Cell G6 is the only cell in column 6 with this candidate (5).

Action: 58 Remove 8 from D5.
Reason: Candidate 8 appears only in sub-column 5-GHJ in block 8.
. Therefore, 8 can be removed from D5.

Action: 59 Remove 6 from C5.
Reason: Cell B9 must be one of the values 5, 8.
Therefore, one of the following must be true,
(1) B9 will be 5 in which case C5 will be 5 (in 1 step(s)).
(2) B9 will be 8 in which case C8 will be 6 (in 1 step(s)).
All alternatives result in 6 being removed from C5.


Action: 60 Remove 2 from D2.
Reason: One of the cells E3, E8 must have the value 6.
Therefore, one of the following must be true,
(1) E3 will be 6 in which case F3 will be 2 (in 1 step(s)).
(2) E8 will be 6 in which case D7 will be 2 (in 1 step(s)).
All alternatives result in 2 being removed from D2.


Action: 61 Remove 9 from A6.
Reason: Cell D2 must be one of the values 3, 9.
Therefore, one of the following must be true,
(1) D2 will be 3 in which case A6 will be 3 (in 1 step(s)).
(2) D2 will be 9 in which case E6 will be 9 (in 1 step(s)).
All alternatives result in 9 being removed from A6.

Saturday 4-Oct-2014

... by: JPF NAPERVILLE

#157 was readily solved by simply:
1, using solver steps1-6 to initiate a candidate reduction-but without
any gain in fill-ins.
2. focusing on the sextet in box 6 and partially solving it via testing
a 6 in cell D7.
3.then using only solver steps 1-6 to solve the puzzle.
ONCE AGAIN, the use of only basic logic steps plus solving a combination allowed steps 1-6 only to solve the puzzle. NO need to
to use solver steps 7-35 with this approach.

Saturday 4-Oct-2014

... by: ray

#1. Use basic strategies and bi-location/value tool to get working board.
#2. Choose cell B2{3568} - bi-location for 2,tri-location for 5 and 8.
Forcing B2 = 3 ,with basic strategies, gives the solution;other bi-location
1-cell solutions found, by forcing the indicated values and using basic
strategies, are: B4 = 6, D2 = 3, D7 = 6, E3 = 6, H9 = 7.
Some 2-cell solutions found are A2B3 = (6,4), DF1 = (8,5), D6 E4 =
(9,5), G56 =(1,5).

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