... by: JC Van Hay
C3=4 + B4=1or7 -> contradiction; 3 singles
B4=7 -> contradiction; 5 singles
D3=1 -> contradiction; 6 singles
UR(34)AE12=8A1; singles to the end
... by: newby
10 one cell solutions
7B4, 8(D5, E6)contradiction therefore 1B4.....
7E6>contradiction therefore7D5
2H9>contradiction therefore 2J9
8G8>contradiction therefore 8H9 solves
... by: Terry
This puzzle also has a rational solution. Below is the log from running #152.
Action: 1 Set G5 to 3.
Reason: Cell G5 is the only cell in row G with this candidate (3).
Action: 2 Set G2 to 7.
Reason: Cell G2 is the only cell in column 2 with this candidate (7).
Action: 3 Set G4 to 2.
Reason: Cell G4 has only one candidate (2).
Action: 4 Set G7 to 5.
Reason: Cell G7 is the only cell in row G with this candidate (5).
Action: 5 Set D6 to 5.
Reason: Cell D6 is the only cell in row D with this candidate (5).
Action: 6 Set C2 to 5.
Reason: Cell C2 is the only cell in row C with this candidate (5).
Action: 7 Set A4 to 5.
Reason: Cell A4 is the only cell in row A with this candidate (5).
Action: 8 Set F9 to 5.
Reason: Cell F9 is the only cell in row F with this candidate (5).
Action: 9 Set J1 to 5.
Reason: Cell J1 is the only cell in row J with this candidate (5).
Action: 10 Set F4 to 4.
Reason: Cell F4 is the only cell in column 4 with this candidate (4).
Action: 11 Remove 9 from H6, J5, J6.
Reason: Candidate 9 appears only in sub-column 4-GHJ in column 4.
. Therefore, 9 can be removed from H6, J5, J6.
Action: 12 Remove 2 from J8.
Reason: Candidate 2 appears only in sub-column 8-DEF in block 6.
. Therefore, 2 can be removed from J8.
Action: 13 Remove 4 from C8.
Reason: One of the cells J2, J8 must have the value 4.
Therefore, one of the following must be true,
(1) J2 will be 4 in which case C3 will be 4 (in 1 step(s)).
(2) J8 will be 4 in which case J8 will be 4 (in 0 step(s)).
All alternatives result in 4 being removed from C8.
Action: 14 Remove 4 from H1.
Reason: One of the cells C3, C7 must have the value 4.
Therefore, one of the following must be true,
(1) C3 will be 4 in which case H7 will be 4 (in 1 step(s)).
(2) C7 will be 4 in which case H3 will be 4 (in 1 step(s)).
All alternatives result in 4 being removed from H1.
Action: 15 Remove 8 from J9.
Reason: Cell H1 must be one of the values 2, 8.
Therefore, one of the following must be true,
(1) H1 will be 2 in which case J9 will be 2 (in 1 step(s)).
(2) H1 will be 8 in which case G8 will be 8 (in 1 step(s)).
All alternatives result in 8 being removed from J9.
Action: 16 Remove 6 from A8.
Reason: Cell C3 must be one of the values 1, 2, 4.
Therefore, one of the following must be true,
(1) C3 will be 1 in which case A8 will be 1 (in 1 step(s)).
(2) C3 will be 2 in which case one of the cells (A5, A6) in sub-row A-456 will be 6 (in 2 step(s)).
(3) C3 will be 4 in which case A8 will be 4 (in 1 step(s)).
All alternatives result in 6 being removed from A8.
Action: 17 Remove 8 from E6.
Reason: Cell C5 must be one of the values 1, 7, 9.
Therefore, one of the following must be true,
(1) C5 will be 1 in which case E6 will be 9 (in 4 step(s)).
(2) C5 will be 7 in which case E6 will be 7 (in 1 step(s)).
(3) C5 will be 9 in which case F5 will be 8 (in 1 step(s)).
All alternatives result in 8 being removed from E6.
Action: 18 Remove 8 from J5.
Reason: Candidate 8 appears only in sub-column 5-DEF in block 5.
. Therefore, 8 can be removed from J5.
Action: 19 Remove 8 from F8.
Reason: One of the cells D5, D8 must have the value 7.
Therefore, one of the following must be true,
(1) D5 will be 7 in which case F5 will be 8 (in 1 step(s)).
(2) D8 will be 7 in which case F8 will be 2 (in 1 step(s)).
All alternatives result in 8 being removed from F8.
Action: 20 Remove 8 from F7.
Reason: One of the cells B3, C3, D3 must have the value 1.
Therefore, one of the following must be true,
(1) B3 will be 1 in which case F5 will be 8 (in 3 step(s)).
(2) C3 will be 1 in which case F7 will be 3 (in 3 step(s)).
(3) D3 will be 1 in which case F5 will be 8 (in 2 step(s)).
All alternatives result in 8 being removed from F7.
Action: 21 Remove 8 from D5.
Reason: One of the cells B6, B7, B9 must have the value 6.
Therefore, one of the following must be true,
(1) B6 will be 6 in which case D5 will be 7 (in 3 step(s)).
(2) B7 will be 6 in which case D7 will be 8 (in 3 step(s)).
(3) B9 will be 6 in which case D5 will be 7 (in 2 step(s)).
All alternatives result in 8 being removed from D5.
Action: 22 Set F5 to 8.
Reason: Cell F5 is the only cell in column 5 with this candidate (8).
Action: 23 Remove 9 from F7.
Reason: Cell F3 must be one of the values 2, 6, 9.
Therefore, one of the following must be true,
(1) F3 will be 2 in which case F7 will be 3 (in 4 step(s)).
(2) F3 will be 6 in which case F8 will be 9 (in 4 step(s)).
(3) F3 will be 9 in which case F3 will be 9 (in 0 step(s)).
All alternatives result in 9 being removed from F7.
Action: 24 Remove 8 from A8.
Reason: One of the cells D3, F3, G3, H3 must have the value 6.
Therefore, one of the following must be true,
(1) D3 will be 6 in which case A8 will be 1 (in 3 step(s)).
(2) F3 will be 6 in which case B7 will be 8 (in 3 step(s)).
(3) G3 will be 6 in which case G8 will be 8 (in 1 step(s)).
(4) H3 will be 6 in which case A8 will be 4 (in 2 step(s)).
All alternatives result in 8 being removed from A8.
Action: 25 Remove 6 from H9, J9.
Reason: Cell E9 must be one of the values 3, 7, 8, 9.
Therefore, one of the following must be true,
(1) E9 will be 3 in which case one of the cells (G8, J8) in sub-column 8-GHJ will be 6 (in 2 step(s)).
(2) E9 will be 7 in which case G8 will be 6 (in 3 step(s)).
(3) E9 will be 8 in which case one of the cells (A9, B9) in sub-column 9-ABC will be 6 (in 2 step(s)).
(4) E9 will be 9 in which case G8 will be 6 (in 3 step(s)).
All alternatives result in 6 being removed from H9, J9.
Action: 26 Remove 6 from B7.
Reason: Candidate 6 appears only in sub-column 9-ABC in column 9.
. Therefore, 6 can be removed from B7.
Action: 27 Remove 7 from C6.
Reason: One of the cells B6, B9 must have the value 6.
Therefore, one of the following must be true,
(1) B6 will be 6 in which case C6 will be 2 (in 1 step(s)).
(2) B9 will be 6 in which case one of the cells (B4, B6) in sub-row B-456 will be 7 (in 1 step(s)).
All alternatives result in 7 being removed from C6.
Action: 28 Remove 3 from B9.
Reason: One of the cells B6, C6 must have the value 2.
Therefore, one of the following must be true,
(1) B6 will be 2 in which case B9 will be 6 (in 1 step(s)).
(2) C6 will be 2 in which case one of the cells (C7, C9) in sub-row C-789 will be 3 (in 1 step(s)).
All alternatives result in 3 being removed from B9.
Action: 29 Remove 7 from B9.
Reason: Cell J5 must be one of the values 1, 6.
Therefore, one of the following must be true,
(1) J5 will be 1 in which case B9 will be 6 (in 2 step(s)).
(2) J5 will be 6 in which case B4 will be 7 (in 2 step(s)).
All alternatives result in 7 being removed from B9.
Action: 30 Remove 7 from C5.
Reason: Candidate 7 appears only in sub-row B-456 in row B.
. Therefore, 7 can be removed from C5.
Action: 31 Set D5 to 7.
Reason: Cell D5 is the only cell in column 5 with this candidate (7).
Action: 32 Set E6 to 9.
Reason: Cell E6 has only one candidate (9).
Action: 33 Remove 9 from C7.
Reason: One of the cells A8, C8 must have the value 1.
Therefore, one of the following must be true,
(1) A8 will be 1 in which case C7 will be 4 (in 1 step(s)).
(2) C8 will be 1 in which case C5 will be 9 (in 1 step(s)).
All alternatives result in 9 being removed from C7.
Action: 34 Remove 8 from B9.
Reason: Cell A6 must be one of the values 3, 6.
Therefore, one of the following must be true,
(1) A6 will be 3 in which case B7 will be 8 (in 2 step(s)).
(2) A6 will be 6 in which case B9 will be 6 (in 1 step(s)).
All alternatives result in 8 being removed from B9.
Action: 35 Set B9 to 6.
Reason: Cell B9 has only one candidate (6).
Action: 36 Remove 8 from H3.
Reason: Cell C7 must be one of the values 3, 4.
Therefore, one of the following must be true,
(1) C7 will be 3 in which case H9 will be 8 (in 2 step(s)).
(2) C7 will be 4 in which case H3 will be 4 (in 1 step(s)).
All alternatives result in 8 being removed from H3.
Action: 37 Remove 8 from J8.
Reason: Cell C7 must be one of the values 3, 4.
Therefore, one of the following must be true,
(1) C7 will be 3 in which case H9 will be 8 (in 2 step(s)).
(2) C7 will be 4 in which case J8 will be 4 (in 1 step(s)).
All alternatives result in 8 being removed from J8.
Action: 38 Remove 2 from F3.
Reason: Cell J9 must be one of the values 2, 9.
Therefore, one of the following must be true,
(1) J9 will be 2 in which case one of the cells (D2, F2) in sub-column 2-DEF will be 2 (in 1 step(s)).
(2) J9 will be 9 in which case F3 will be 9 (in 2 step(s)).
All alternatives result in 2 being removed from F3.
Action: 39 Remove 9 from H9.
Reason: Cell A6 must be one of the values 3, 6.
Therefore, one of the following must be true,
(1) A6 will be 3 in which case A9 will be 9 (in 3 step(s)).
(2) A6 will be 6 in which case H4 will be 9 (in 3 step(s)).
All alternatives result in 9 being removed from H9.
Action: 40 Remove 8 from H7, H6.
Reason: Cell H1 must be one of the values 2, 8.
Therefore, one of the following must be true,
(1) H1 will be 2 in which case H9 will be 8 (in 1 step(s)).
(2) H1 will be 8 in which case H1 will be 8 (in 0 step(s)).
All alternatives result in 8 being removed from H7, H6.
Action: 41 Set J6 to 8.
Reason: Cell J6 is the only cell in column 6 with this candidate (8).
Action: 42 Remove 2 from H3.
Reason: Cell H1 must be one of the values 2, 8.
Therefore, one of the following must be true,
(1) H1 will be 2 in which case H1 will be 2 (in 0 step(s)).
(2) H1 will be 8 in which case H9 will be 2 (in 1 step(s)).
All alternatives result in 2 being removed from H3.
Action: 43 Remove 6 from J8.
Reason: Cell H3 must be one of the values 4, 6.
Therefore, one of the following must be true,
(1) H3 will be 4 in which case J8 will be 4 (in 1 step(s)).
(2) H3 will be 6 in which case G8 will be 6 (in 1 step(s)).
All alternatives result in 6 being removed from J8.
Action: 44 Remove 8 from B1.
Reason: Cell H9 must be one of the values 2, 8.
Therefore, one of the following must be true,
(1) H9 will be 2 in which case H1 will be 8 (in 1 step(s)).
(2) H9 will be 8 in which case B7 will be 8 (in 1 step(s)).
All alternatives result in 8 being removed from B1.
Action: 45 Remove 8 from D7.
Reason: One of the cells G8, H7 must have the value 6.
Therefore, one of the following must be true,
(1) G8 will be 6 in which case one of the cells (D8, E8) in sub-column 8-DEF will be 8 (in 1 step(s)).
(2) H7 will be 6 in which case D7 will be 9 (in 1 step(s)).
All alternatives result in 8 being removed from D7.
Action: 46 Set B7 to 8.
Reason: Cell B7 is the only cell in column 7 with this candidate (8).
Action: 47 Remove 2 from D3.
Reason: Cell H1 must be one of the values 2, 8.
Therefore, one of the following must be true,
(1) H1 will be 2 in which case one of the cells (D2, F2) in sub-column 2-DEF will be 2 (in 1 step(s)).
(2) H1 will be 8 in which case D3 will be 8 (in 1 step(s)).
All alternatives result in 2 being removed from D3.
Action: 48 Remove 2 from B1.
Reason: Candidate 2 appears only in sub-column 3-ABC in column 3.
. Therefore, 2 can be removed from B1.
Action: 49 Remove 3 from E1.
Reason: One of the cells A1, A2 must have the value 8.
Therefore, one of the following must be true,
(1) A1 will be 8 in which case E1 will be 4 (in 1 step(s)).
(2) A2 will be 8 in which case one of the cells (A1, B1) in sub-column 1-ABC will be 3 (in 1 step(s)).
All alternatives result in 3 being removed from E1.
Action: 50 Remove 3 from A2.
Reason: Candidate 3 appears only in sub-column 1-ABC in column 1.
. Therefore, 3 can be removed from A2.
Action: 51 Remove 8 from H1.
Reason: One of the cells D1, D3 must have the value 1.
Therefore, one of the following must be true,
(1) D1 will be 1 in which case H1 will be 2 (in 1 step(s)).
(2) D3 will be 1 in which case G3 will be 8 (in 1 step(s)).
All alternatives result in 8 being removed from H1.
Action: 52 Set H1 to 2.
Reason: Cell H1 has only one candidate (2).
Action: 53 Set H9 to 8.
Reason: Cell H9 has only one candidate (8).
Action: 54 Set G8 to 6.
Reason: Cell G8 has only one candidate (6).
Action: 55 Set G3 to 8.
Reason: Cell G3 has only one candidate (8).
Action: 56 Set J9 to 2.
Reason: Cell J9 is the only cell in row J with this candidate (2).
Action: 57 Remove 9 from A8, C8.
Reason: Candidate 9 appears only in sub-column 9-ABC in column 9.
. Therefore, 9 can be removed from A8, C8.
Action: 58 Remove 6 from D2.
Reason: Cell F8 must be one of the values 2, 9.
Therefore, one of the following must be true,
(1) F8 will be 2 in which case D2 will be 2 (in 1 step(s)).
(2) F8 will be 9 in which case D7 will be 6 (in 1 step(s)).
All alternatives result in 6 being removed from D2.
Action: 59 Remove 9 from D7.
Reason: Cell H3 must be one of the values 4, 6.
Therefore, one of the following must be true,
(1) H3 will be 4 in which case H7 will be 9 (in 1 step(s)).
(2) H3 will be 6 in which case D7 will be 6 (in 1 step(s)).
All alternatives result in 9 being removed from D7.
..............................................
All remaining actions are simple sets.
... by: JPF NAPERVILLE
#152 was readily solved by:
1. using just solver steps 1-6 to gain 10 fill-ins.
2, focusing on the sextet in row J and solving it via a 6 in J2 which
yielded 6 fill-ins.
3. then using only solver steps 1-6 then solved the puzzle.
Once again, the use of just basic logic steps 1-6 plus solving a
combination allowed further use of only basic steps 1-6 to solve the
puzzle----no need for solver steps 7-35.
... by: ray
#1. Use basic strategies and bi- location/value tool to get working board.
#2. Choose J2{2468} - bi-location cell for 2 and 4, tri-location cell for 6.
Forcing J2 = 2 or 4 and using basic strategies gives inconclusion or
contradiction; forcing J2 = 6 ,applying basic strategies, gives solution.
#3. Using this solution,with basic strategies,other bi-location 1-cell solutions
are found by forcing the following cell values: B6 = 7, C8 = 7, F3 = 6
E9 = 7: some 2-cell solutions found are: A12 = (8,4), D78 = (6,2),
H9J8 = (8,4).