The first puzzle has a long solution path but after the MSLS, the next hardest step is a Death Blossom :

- Code: Select all

..3....8..5....2.17...........5.8..6.9.12....8....3....6.9....5..4....7.....1.6.2

Locked Candidates 1 (Pointing): 7 in b3 => r1c4<>7,r1c5<>7,r1c6<>7

Locked Candidates 1 (Pointing): 9 in b5 => r1c5<>9,r2c5<>9,r3c5<>9

MSLS:16 Cells r2579c1368, 16 Links 69r2,56r5,12r7,59r9,34c1,78c3,47c6,34c8

18 Eliminations: r7c7<>1,r4c18,r3c8,r8c1<>3,r346c8,r1c16,r3c6, r4c1<>4,r5c7<>5,r2c45<>6,r46c3<>7,r3c3<>8

Locked Pair: in r4c1,r4c3 => r4c2<>12,r6c2<>12,r6c3<>12,r4c2<>12,r4c7<>1,r4c8<>12,

Hidden Single: 2 in b6 => r6c8=2

Hidden Single: 1 in b6 => r6c7=1

Hidden Single: 1 in b9 => r7c8=1

Hidden Single: 5 in b6 => r5c8=5

Hidden Single: 5 in b4 => r6c3=5

Naked Single: r4c8=9

Hidden Single: 9 in b5 => r6c5=9

Hidden Single: 6 in r6 => r6c4=6

Naked Single: r3c8=6

Locked Candidates 1 (Pointing): 9 in b9 => r8c1<>9

Empty Rectangle : 4 in b5 connected by c1 => r2c5 <> 4

Finned X-Wing:4c48\r29 fr13c4 => r2c6<>4

Finned Swordfish:4c168\r259 fr7c6 => r9c4<>4

Locked Candidates 2 (Claiming): 4 in c4 => r1c5<>4,r3c5<>4

AIC Type 2: 3r4c2 = r5c1 - (3=2)r7c1 - (2=1)r4c1 - r8c1 = 1r8c2 => r8c2<>3

MSLS:13 Cells r48c457+r123c45,r4c2,r8c9,13 Links 347r4,389r8,2c4,56c5,3478b2

2 Eliminations: r2c6<>7,r8c2<>8

Almost Locked Set XZ-Rule: A=r45c7,r6c9 {3478},B=r7c7,r9c8 {348}, X=8, Z=3 => r8c7<>3

Almost Locked Set XY-Wing: A=r1c24{124}, B=r48c1{125}, C=r8c245679{1235689}, X,Y=1, 5, Z=2 => r1c1<>2

Almost Locked Set XY-Wing: A=r1c24{124}, B=r579c6{2457}, C=r8c245679{1235689}, X,Y=1, 5, Z=2 => r1c6<>2

Death Blossom Complex Type 2: Set have degrees of freedom of 0-23478{r7c13567} => r4c2<>4

3r7c1-(3=12478){r13689c2}

3r7c5-(3=45678){r12348c5}

3r7c7-(3=47){r4c57}

W-Wing: 47 in r5c6,r6c9 connected by 4r4 => r5c79<>7

Grouped 2-String Kite: 7 in r5c6,r9c2 connected by r46c2,r5c3 => r9c6 <> 7

Death Blossom Complex Type 2: Set have degrees of freedom of 2-3469{r2c18} => r5c9<>4

6r2c1,9r2c1-(69=12345){r145789c1}

3r2c8-(3=479){r136c9}

Region Forcing Chain: Each 4 in r1 true in turn will all lead r1c2<>1

(4-1)r1c2

(4-2)r1c4 = (2-1)r1c2

4r1c7 - r2c8 = r9c8 - (4=5)r9c6 - r8c56 = (5-1)r8c1 = r8c2 - 1r1c2

4r1c9 - r2c8 = r9c8 - (4=5)r9c6 - r8c56 = (5-1)r8c1 = r8c2 - 1r1c2

Naked Pair: in r1c2,r1c4 => r1c7<>4,r1c9<>4,

WXYZ-Wing: 5679 in r1c579,r2c6,Pivot Cell Is r1c5 => r1c6<>9

Almost Locked Set XY-Wing: A=r1c1579{15679}, B=r9c23468{345789}, C=r4789c1{12359}, X,Y=1, 9, Z=5 => r1c6<>5

Region Forcing Chain: Each 7 in r9 true in turn will all lead r2c5<>3

7r9c2 - r6c2 = (7-4)r6c9 = r3c9 - (4=3)r2c8 - 3r2c5

(7-9)r9c3 = (9-5)r9c1 = (5-4)r9c6 = r9c8 - (4=3)r2c8 - 3r2c5

7r9c4 - r2c4 = (7-3)r2c5

Death Blossom Complex Type 2: Set have degrees of freedom of 1-34578{r2347c5} => r1c7<>9

3r3c5-(3=479){r136c9}

5r3c5-(5=169){r1c156}

3r7c5-(3=125689){r8c124567}

AIC Type 2: 9r1c1 = (9-7)r1c9 = (7-4)r6c9 = r6c2 - r5c1 = 4r2c1 => r2c1<>9

AIC Type 2: 5r8c1 = (5-9)r9c1 = r1c1 - (9=7)r1c9 - (7=5)r1c7 - (5=6)r1c5 - r8c5 = 6r8c6 => r8c6<>5

Death Blossom Complex Type 2: Set have degrees of freedom of 2-12358{r8c124} => r2c8<>4

5r8c1-(5=34789){r9c12348}

3r8c4-(3=46789){r2c13456}

8r8c4-(8=349){r8c79,r9c8}

Hidden Single: 4 in c8 => r9c8=4

Full House: r2c8=3

Naked Single: r9c6=5

Hidden Single: 5 in b7 => r8c1=5

Hidden Single: 1 in b7 => r8c2=1

Locked Candidates 1 (Pointing): 4 in b3 => r3c2<>4,r3c4<>4

Locked Candidates 1 (Pointing): 2 in b7 => r7c6<>2

Locked Candidates 2 (Claiming): 2 in c2 => r3c3<>2

Hidden Pair: 38 in r5c9,r8c9 => r8c9<>9

Hidden Single: 9 in b9 => r8c7=9

AIC Type 2: 2r1c2 = r1c4 - r3c6 = (2-6)r8c6 = r8c5 - (6=5)r1c5 - (5=7)r1c7 - r1c9 = (7-4)r6c9 = 4r6c2 => r1c2<>4

Hidden Single: 4 in b1 => r2c1=4

Hidden Single: 4 in b4 => r6c2=4

Full House: r6c9=7

Hidden Single: 7 in b3 => r1c7=7

Hidden Single: 5 in b3 => r3c7=5

Hidden Single: 4 in b3 => r3c9=4

Full House: r1c9=9

Hidden Single: 4 in b2 => r1c4=4

Hidden Single: 5 in b2 => r1c5=5

Hidden Single: 6 in c5 => r8c5=6

Hidden Single: 9 in c1 => r9c1=9

Hidden Single: 2 in r1 => r1c2=2

Naked Single: r3c2=8

Naked Single: r3c5=3

Naked Single: r3c4=2

Hidden Single: 2 in b8 => r8c6=2

Skyscraper : 3 in r4c2,r7c1 connected by r47c7 => r5c1,r9c2 <> 3

[stte]

The second puzzle is essentially cracked with an early MSLS :

- Code: Select all

.2...67..4...8......9.......3.....7.5.8....4..1.3....2....9..5....6.1..3...2..6.7

Hidden Single: 3 in b6 => r5c7=3

Locked Candidates 1 (Pointing): 2 in b4 => r4c5<>2,r4c6<>2

Locked Candidates 2 (Claiming): 4 in c2 => r7c3<>4,r8c3<>4,r9c3<>4

MSLS:16 Cells r1689c1358, 16 Links 13r1,67r6,27r8,13r9,89c1,45c3,45c5,89c8

19 Eliminations: r1c49<>1,r8c7<>2,r9c6<>3,r346c5,r4c3,r6c6<>4,r34c5,r2c3<>5, r6c6,r8c2<>7,r3c18,r7c1<>8,r2c8,r4c1<>9

Hidden Single: 4 in b4 => r6c3=4

Locked Pair: in r4c1,r4c3 => r5c2<>6,r6c1<>6,r4c5<>6,r4c9<>6,

Naked Single: r4c5=1

Hidden Single: 1 in b6 => r5c9=1

Hidden Single: 6 in b6 => r6c8=6

Hidden Single: 6 in b5 => r5c5=6

Hidden Single: 2 in b5 => r5c6=2

Hidden Single: 2 in b2 => r3c5=2

2-String Kite: 8 in r6c7,r7c4 connected by r4c4,r6c6 => r7c7 <> 8

Empty Rectangle : 7 in b8 connected by r6 => r7c1 <> 7

Sue de Coq: r23c7 - {124589} (r23c8 - {123}, r468c7 -{4589}) => r1c8<>1 r1c8<>3 r7c7<>4

Locked Candidates 2 (Claiming): 1 in r1 => r2c3<>1,r3c1<>1

AIC Type 1: 4r3c7 = r8c7 - (4=8)r7c9 - r7c4 = (8-4)r4c4 = 4r4c6 => r3c6<>4

AIC Type 2: 4r3c7 = r8c7 - (4=8)r7c9 - r7c4 = r4c4 - r6c6 = 8r6c7 => r3c7<>8

AIC Type 1: 4r4c6 = (4-8)r4c4 = r7c4 - (8=4)r7c9 => r7c6<>4

Grouped AIC Type 2: 9r2c6 = r46c6 - (9=7)r5c4 - (7=5)r6c5 - r89c5 = 5r9c6 => r2c6<>5

Grouped AIC Type 2: 4r4c6 = (4-5)r9c6 = r89c5 - (5=7)r6c5 - (7=9)r5c4 => r4c6<>9

Almost Locked Set XY-Wing: A=r7c49{478}, B=r469c6{4589}, C=r5c4{79}, X,Y=7, 9, Z=8 => r7c6<>8

AIC Type 2: 3r1c5 = r9c5 - (3=7)r7c6 - r8c5 = r6c5 - (7=9)r6c1 - r6c6 = 9r2c6 => r2c6<>3

Almost Locked Set XY-Wing: A=r19c3{135}, B=r7c7{12}, C=r2c234679{1235679}, X,Y=3, 2, Z=1 => r7c3<>1

Almost Locked Set XY-Wing: A=r2c236789{1235679}, B=r23469c6{345789}, C=r3c8{13}, X,Y=1, 3, Z=7 => r2c4<>7

Almost Locked Set XY-Wing: A=r6c167{5789}, B=r123c4,r1c5,r3c6{134579}, C=r5c4,r6c5{579}, X,Y=5, 9, Z=7 => r3c1<>7

X-Wing:7c15\r68 => r8c3<>7

AIC Type 2: 1r1c3 = r9c3 - r9c8 = (1-2)r7c7 = r8c8 - (2=5)r8c3 => r1c3<>5

Locked Candidates 1 (Pointing): 5 in b1 => r8c2<>5,r9c2<>5

AIC Type 2: 5r2c2 = (5-8)r3c2 = (8-6)r3c9 = 6r2c9 => r2c9<>5r2c2<>6

AIC Type 1: (2=6)r4c1 - (6=3)r3c1 - r2c3 = (3-2)r2c8 = 2r8c8 => r8c1<>2

WXYZ-Wing: 4789 in r8c12,r6c1,r9c2,Pivot Cell Is r8c1 => r9c1<>9

Hidden Pair: 79 in r6c1,r8c1 => r8c1<>8

Uniqueness Test 7: 26 in r47c13; 2*biCell + 1*conjugate pairs(2c1) => r7c3 <> 6

Sashimi X-Wing:8r38\c29 fr8c78 => r7c9<>8

Naked Single: r7c9=4

Hidden Single: 4 in b3 => r3c7=4

Hidden Pair: 12 in r2c7,r7c7 => r2c7<>59

Locked Candidates 2 (Claiming): 5 in c7 => r4c9<>5

AIC Type 2: 4r1c4 = (4-3)r1c5 = r9c5 - (3=7)r7c6 - (7=9)r2c6 => r1c4<>9

Locked Candidates 2 (Claiming): 9 in r1 => r2c9<>9

Naked Single: r2c9=6

Hidden Single: 6 in c3 => r4c3=6

Hidden Single: 2 in b4 => r4c1=2

AIC Type 2: (8=9)r1c8 - r9c8 = r9c2 - (9=7)r8c1 - r7c3 = (7-3)r2c3 = (3-2)r2c8 = 2r8c8 => r8c8<>8

X-Wing:8c18\r19 => r9c26,r1c9<>8

Hidden Single: 8 in b8 => r7c4=8

W-Wing: 45 in r1c4,r9c6 connected by 4r4 => r3c6<>5

Naked Pair: in r3c6,r7c6 => r2c6<>7,

Naked Single: r2c6=9

Locked Candidates 2 (Claiming): 7 in r2 => r3c2<>7

XYZ-Wing: 489 in r8c2 r8c7 r9c2 => r8c1 <> 9

[stte]

The third puzzle has an early MSLS but remains unsolved without 'Brute Force'.