T14665_77_01 back to index of examples click here

700000400020070080003008009000500300060020090001007006000300900030040060009001005_77

1 r9c8=3 B

-> row 9 digit 4 in box 7

 

7 158a9k 56z8A |1269 13E569 2R3569 |4 125 123b

14569K 2 4t56 |1469 7 3b4U569|156j 8 1b3B

1456 145 3 |12O4s6 156 8 |1256J7c 1257C 9

-------------------------------------------------------------------

2489 4789 2Q478 |5 1l6d89 46D9 |3 1247 12478

3e458 6 4578 |1L48 2 3E4e |15V78 9 1478

2P3E4589 4589 1 |489 3e89 7 |258 245y 6

-------------------------------------------------------------------

12568 1n578 25678 |3 5X68 256 |9 124f7 124F78

1M258 3 2578 |27i89g 4 25w9G |1278 6 1278

24h68 4H78 9 |267I8 68젠 1 |278 3 5

 

#6r2c6

[]6r2c6 - 6r1c456 = 6r1c3 - 8r1c3 = AC:r1c2r2c1(8r1c2 - 1r1c2r2c1)

= 1r3c12 - 1r3c5 = AC:r146c5(1r14c5 - 6r14c5) = 6r379c5 - 6r4c5 = 6r4c6 - 6r2c6

then

 

2 #8r6c5

#[]8r6c5=>9r6c2

9r6c2

[]9r4c12. - 9r4c5 = AC:r16c5(9r16c5.Z - 8r6c5)

[]9r6c1 - 3r6c1.E = 3r6c5.e - 8r6c5

#[]8r6c5=>5r1c6

5r1c6

[]2r1c6==AC:r89c4(2r89c4.R - 8r89c4) = 8r56c4 - 8r6c5

[]3r1c6 - 3r5c6.E = 3r6c5.e - 8r6c5

[]6r1c6 - 6r123c4 = AC:r8c46r9c4(6r9c4 - 8r89c4) = 8r56c4 - 8r6c5

[]9r1c6 - 9r8c6 = AC:r89c4(9r8c4 - 8r89c4) = 8r56c4 - 8r6c5

#[]8r6c5 - 9r6c2

[]1r2c9==3r2c6.b - 3r5c6 = 3r6c5 - 8r6c5

[]1r2c7 - 1r1c89r2c9 = AC:r23c7r3c8(1r23c7r3c8 - 5r23c7r3c8) = 5r1c8 <=8r6c5

[]1r2c4 - 1r3c5 = AC:r146c5(1r14c5. - 8r46c5.) = 8r56c4. - 8r6c5

[]1r2c1 - 9r2c1.K = 9r1c2.k - 9r6c2

clear []8r6c5 - 9r6c2|# <= 8r6c5

 

3 #1r3c4

#1r3c4=>5r2c3

5r2c3

[]4r2c3 - 4r2c46 = 4r3c4 - 1r3c4

[]6r2c3 - 6r2c7 = AC:r3c78(6r3c7 - 2r3c78) = 2r3c4 - 1r3c4

#[]1r3c4>1r7c8

1r7c8

[]1r4c8 - 1r4c5 = 1r5c4 - 1r3c4

[]1r3c8 - 1r3c4

[]1r1c8 - 1r12c9 = 2r1c9 - 2r1c46 = 2r3c4 - 1r3c4

#[]1r3c4=>6r1c4

6r1c4

[]6r1c3 - 8r1c3 = AC:r1c2r2c1(8r1c2 - 1r1c2r2c1) = 1r3c12 - 1r3c4

[]AC:r16c5(6r1c5 - 9r16c5) = 9r4c5 - 1r4c5.l = 1r5c4.L - 1r3c4

[]6r1c6 - 6r4c6 = 6r4c5 - 1r4c5 = 1r5c4 - 1r3c4

#[]G - 1r3c4

[]5r8c3 - 5r2c3 <=1r3c4

[]5r8c1 - 1r8c1.M = 1r7c12.m - 1r7c8 <=1r3c4

[]5r7c2 - 5r7c56.W = 5r8c6.w - 9r8c6.G

[]5r7c3 - 5r7c56.W = 5r8c6.w - 9r8c6.G

[]5r7c1 - 5r7c56.W = 5r8c6.w - 9r8c6.G

#[]g - 1r3c4

[]2r3c4.O - 1r3c4

[]2r9c4 - 7r9c4.I = 7r8c4.i - 9r8c4.g

[]2r8c4 - 9r8c4.g

[]2r1c4 - 6r1c4 <= 1r3c4

 

7 158a9k 56z8A |1269 13E569 2R3569 |4 125 123b

14569K 2 4t56 |1469 7 3b4U59 |156j 8 1b3B

1456 145 3 |2O4s6 156 8 |1256J7c 1257C 9

-------------------------------------------------------------------

2489 4789 2Q478 |5 1l6d89 46D9 |3 1247 12478

3e458 6 4578 |1L48 2 3E4e |15V78 9 1478

2P3E4589 4589 1 |489 3e9E 7 |258 245y 6

-------------------------------------------------------------------

12568 1n578 25678 |3 5X68 256 |9 124f7 124F78

1M258 3 2578 |27i89g 4 25w9G |1278 6 1278

24h68 4H78 9 |267I8 68젠 1 |278 3 5

 

#[]5r1c35 - 4r3c4 []4r3c4 - 2r3c4 = AC:r23c7r3c8(2r3c78 - 5r23c7r3c8) = 5r1c8 - 5r1c5

 

4 #5r1c3

 

#[]4r6c12 - 5r2c7 []5r2c7 - 6r2c7 = AC:r3c78(6r3c7 - 2r3c78)

= 2r3c4 - 4r3c4 = 4r2c46 - 4r2c3 = 4r45c3 - 4r6c12

#[]5r1c3=>6r2c3

6r2c3

[]4r2c3 - 4r2c46 = 4r3c4 - 5r1c3

[]5r2c3 - 5r1c3

#[]5r2c7=>4r6c4

4r6c4

[]4r6c12 - 5r2c7|#

[]4r6c8 - 5r6c8.y = 5r56c7.Y - 5r2c7

#[]5r2c7 - 5r1c3

[]4r6c2 - 5r2c7|#

[]5r6c2 - 5r5c13 = 5r5c7 - 5r2c7

[]8r6c2 - 8r1c2 = 8r1c3 - 5r1c3

[]9r6c2 - 9r6c5 = 4r5c6 - 4r6c4 <=5r2c7

clear

[]6r2c7 - 6r2c3 <=5r1c3

[]1r2c7 - 1r1c89r2c9 = AC:r23c7r3c8(1r23c7r3c8 - 5r23c7r3c8) = 5r1c8 - 5r1c3

[]5r2c7 - 5r1c3|#

5 #5r3c7

#[]5r1c5=>4r6c8

4r6c8

[]4r6c12 - 4r45c3 = 4r2c3 - 4r2c46 = 4r3c4.s - 5r1c5

[]4r6c4 - 4r5c6.e = 3r1c5.E - 5r1c5

#[]5r3c8=>5r2c3 #[]5r3c7=>5r2c3

5r2c3

[]4r2c3 - 4r2c46.S = AC:r3c478(4r3c4.s - 5r3c78) = 5r3c125. - 5r3c78

[]6r2c3 - 6r2c7.j = 6r3c7.J - 7r3c7.c = 7r3c8.C - 5r3c8

[]6r2c3 - 6r2c7.j = 6r3c7.J - 5r3c7

#[]5r3c7 - 5r8c3 []5r3c7 => 5r2c3 - 5r8c3

#[]5r8c6.w - 5r3c7

[]5r1c5 => 4r6c8 - 5r6c8.y = 5r56c7.Y - 5r3c7

[]5r12c6 - 5r8c6.w

[]5r3c5 - 5r3c7

#[]5r3c78 - 5r8c3

[]5r3c8 => 5r2c3 - 5r8c3

[]5r3c7 - 5r8c3|#

[]5r3c125 - 5r3c78

#[]5r3c7 - 5r8c1

[]5r5c1 - 5r8c1

[]5r6c12 - 5r5c13.v = 5r5c7.V - 5r3c7

[]5r5c3 - 5r2c3 <=5r3c7

#[]5r3c7 - 5r3c7

[]5r7c123==5r8c6.w - 5r3c7|#

[]5r8c3 - 5r3c7|#

[]5r8c1 - 5r3c7|#

 

7 158a9k 6a8A |1269 13E569 2R3569 |4 125 123b

14569K 2 4t56 |1469 7 3b4U59 |15y6j 8 1b3B

1456 145 3 |2O4s6 156 8 |126J7c 1257C 9

------------------------------------------------------------------

2489 4789 2Q478 |5 1l6d89 46D9 |3 1247 12478

3e458 6 4578 |1L48 2 3E4e |15V78 9 1478

2P3E4589 4589 1 |489 3e9E 7 |258 245y 6

------------------------------------------------------------------

12568 1n578 25678 |3 5X68 256 |9 124f7 124F78

1M258 3 2578 |27i89g 4 25w9G |1278 6 1278

24h6Z8 4H78 9 |267I8 68렠 1 |278 3 5

6 #5r1c5

 

#[]y - 5r1c5 []5r6c8.y - 4r6c8 <= 5r1c5 5

#[]5r1c5=>1r8c7

1r8c7

[]1r23c7 - 1r1c89r2c9 = AC:r23c7r3c8(1r23c7r3c8 - 5r2c7r3c8) = 5r1c8 - 5r1c5

[]1r5c7 - 1r5c4.L = 1r4c5.l - 1r3c5 = AC:r146c5(1r14c5 - 5r1c5)

#[]5r1c5=>4r4c3

4r4c3

[]4r2c3 - 4r2c46 = 4r3c4 - 5r1c5 4

[]4r5c3 - 4r5c6 = 3r1c5 - 5r1c5

#[]5r1c5=>7r9c4

7r9c4.I

[]6r9c4 - 6r79c5 = AC:r1346c5(6r134c5 - 5r13c5) = 5r7c5 - 5r1c5

[]2r9c4 - 2r3c4 = AC:r23c7r3c8(2r3c78 - 5r2c7r3c8) = 5r1c8 - 5r1c5

[]8r9c4 - 8r56c4 = AC:r146c5(8r4c5 - 5r1c5)

#[]5r1c5=>5r2c3

5r2c3

[]5r2c7.y - 5r1c5|#

[]5r2c6 - 5r1c5

[]5r2c1 - 5r2c3r3c12 = AC:r1c23r2c1(5r1c2r2c1 - 1r1c2r2c1)

= 1r3c12 - 1r3c5 = AC:r146c5(1r14c5 - 5r1c5)

#[]6r7c5=>6r3c47

6r3c47

[]6r3c5 - 6r7c5

[]6r3c1 - 6r9c1 = 6r7c13 - 6r7c5

#[]5r1c5=>5r3c8

5r3c8

[]5r2c7.y - 5r1c5|#

[]5r1c8 - 5r1c5

#[]v - 5r1c5

[]5r5c1 - 3r5c1.e = 3r1c5.E - 5r1c5

[]5r6c1 - 5r5c13.v

[]5r5c3 - 5r2c3 <= 5r1c5

[]5r6c2 - 5r5c13.v

#[]Z - 5r1c5

[]6r4c5 - 6r379c5 = AC:r146c5(6r14c5 - 5r1c5)

[]6r9c5 - 6r7c56.Z

[]6r13c5 - 6r123c4 = 6r9c4 - 6r7c56.Z

[]6r7c5 => = AC:r3c478(6r3c47 - 5r3c8)<=5r1c5

#[]5r1c5=>8r9c12 thru AC:r9c12

8r9c12

[]6r9c1.Z - 5r1c5|#

[]2r9c1 - 2r46c1.q = 2r4c3.Q - 4r4c3 = 9##[]4r4c12r5c13r6c12.&m - 5r1c5 UREM=3 |#

[]7r9c2 - 7r9c4.I = 9##[]7r9c27.i - 5r1c5 UREM=1 |#

#[]5r1c5=>

8r89c7.

[]8r5c7 - 5r5c7.V = v - 5r1c5|#

[]8r6c7 - 8r6c4 = AC:r4c5r5c4(8r4c5r5c4 - 9r4c5) = AC:r16c5(9r16c5 - 5r1c5)

#[] - 5r1c5

[]8r9c7 - 8r9c12 <= 5r1c5

[]8r8c7 - 1r8c7 <= 5r1c5

[]8r56c7 - 8r89c7.

 

7 #4r2c1

#[]4r6c4 - 4r2c1 []4r2c1 - 4r2c46 = 4r3c4 - 4r6c4

#[]6r2c3 - 4r2c1 []4r2c1 - 4r2c46 = 4r3c4 - 2r3c4

= AC:r3c78(2r3c78 - 6r3c7) = 6r2c7 - 6r2c3

#[]4r4c6 - 4r2c1 []AC:r1c23r2c1(4r2c1 - 1r1c2r2c1) = 1r3c12 - 1r3c5

= AC:r146c5(1r14c5 - 6r14c5) = 6r379c5 - 6r4c5 = 6r4c6 - 4r4c6

#[]4r6c2 - 4r2c1 []4r2c1 - 4r9c1 = 4r9c2 - 4r6c2

#[]4r2c1=>8r6c4

8r6c4

[]4r6c4 - 4r2c1|#

[]9r6c4 - 9r46c5 = 9r1c5 - 9r1c2 = 9r2c1 - 4r2c1

#[]4r2c1=>

6r23c1.

[]6r1c3==AC:r1c2r2c1(8r1c2.a - 4r2c1)

[]6r2c3 - 4r2c1|#

#[]4r2c1=>e

4r5c6.e

[]4r2c6 - 4r2c1

[]4r4c6 - 4r2c1|#

#[]4r2c1=>5r2c3

5r2c3

[]4r2c3 - 4r2c1

[]6r2c3 - 4r2c1|#

#[]4r2c1=>4r6c8

4r6c8

[]4r6c1 - 4r2c1

[]4r6c4 - 4r2c1|#

[]4r6c2 - 4r2c1|#

#[]v - 4r2c1

[]5r5c1 - 3r5c1.e <= 4r2c1

[]5r6c1 - 5r5c13.v

[]5r5c3 - 5r2c3 <= 4r2c1

[]5r6c2 - 5r5c13.v

#[]2r9c1 - 4r2c1

[]4r4c6 - 4r2c1|#

[]4r4c2 - 4r9c2 = 4r9c1 - 2r9c1

[]4r4c3 - 2r4c3 = 2r46c1 - 2r9c1

[]4r4c89 - 4r6c8 <=4r2c1 UREM=2 |#

[]4r4c1 - 4r2c1

#[]4r2c1 - 1r5c7

[]4r6c2 - 4r2c1|#

[]5r6c2 - 5r5c13 = 5r5c7 - 1r5c7

[]8r6c2 - 8r6c4 <=4r2c1

[]9r6c2 - 9r1c2 = 9r2c1 - 4r2c1

#[]4r2c1=>8r9c12 thru AC:r9c12

8r9c12

[]6r9c1==6r7c56.Z - 6r7c3. <= 4r2c1

[]2r9c1 - 4r2c1|#

[]7r9c2 - 4r9c2 = 4r9c1 - 4r2c1

#[]4r2c1=>1r8c7

1r8c7

[]1r23c7 - 1r12c9 = 2r1c9 - 2r1c46 = 2r3c4 - 4r3c4 = 4r2c46 - 4r2c1

[]1r5c7 - 4r2c1|#

#[]4r2c1=>

8r89c7.

[]8r5c7 - 5r5c7 = v - 4r2c1|#

[]8r6c7 - 8r6c4 <=4r2c1

#[] - 4r2c1

[]8r9c7 - 8r9c12 <=4r2c1

[]8r8c7 - 1r8c7 <= 4r2c1

[]8r56c7 - 8r89c7.

8 #5r1c2

 

#[]5r1c2=>y

5r2c7.y

[]5 5r3c8 <= 5r2c3 - 5r1c2

[]5r1c8 - 5r1c2

#[]y=>8r6c2

8r6c2

[]4r6c2 - 4r6c4 <= 5r6c8.y 4

[]5r6c2 - 5r6c8.y

[]9r6c2 - 9r6c5 = 4r5c6 - 4r6c4 <= 5r6c8.y 4

#[]y=>2r6c7

2r6c7

[]2r4c89==2r6c1.P - 3r6c1 = 4r5c6 - 4r6c4 <= 5r6c8.y 4

[]2r6c8 - 5r6c8.y

#[]5r1c2=>2r9c1

2r9c1

[]2r9c7 - 2r6c7 <= 5r6c8.y <=5r1c2

[]2r9c4 - 2r3c4 = AC:r23c7r3c8(2r3c78 - 5r2c7r3c8) = 5r1c8 - 5r1c2

#[]y - 5r1c2

[]2r4c1 - 2r9c1<= 5r1c2

[]4r4c1 - 4r45c3 = 4r2c3 - 4r2c46 = 4r3c4 - 4r6c4 <= 5r6c8.y 4

[]8r4c1 - 8r6c2 <= y

[]9r4c1 - 9r2c1 = 9r1c2 - 5r1c2

clear []5r1c2=>y - 5r1c2|#

 

9 #4r5c4

 

#[]4r6c2 - 4r5c4 []4r5c4 - 4r3c4 = 4r2c46 - 4r2c3 = 4r45c3 - 4r6c2

#[]1r4c8 - 4r5c4 []1r4c8 - 1r4c5 = 1r5c4 - 4r5c4

#[]4r5c4=>4r6c8

4r6c8

[]4r6c1 - 3r6c1 = 4r5c6 - 4r5c4

[]4r6c4 - 4r5c4

[]4r6c2 - 4r5c4|#

#[]4r5c4=>4r4c3

4r4c3

[]4r2c3 - 4r2c46 = 4r3c4 - 4r5c4

[]4r5c3 - 4r5c4

#[]4r5c4=>5r6c2

5r6c2

[]4r6c2 - 4r5c4|#

[]8r6c2 - 8r6c4 = AC:r4c5r5c4(8r4c5r5c4 - 4r5c4)

[]9r6c2 - 9r6c5 = 4r5c6 - 4r5c4

#[]1r5c7 - 4r5c4 []4r5c4 => 5r6c2 - 5r5c13 = 5r5c7 - 1r5c7

#[]o - 4r5c4 #[] - 4r5c4

[]1r4c8 - 4r5c4|#

[]1r45c9 - 1r12c9. = 2r1c9 - 2r1c46.o

[]1r5c7 - 4r5c4|#

#[]4r5c4=>2r7c8

2r7c8

[]2r6c8 - 4r6c8 <= 4r5c4

[]2r4c8 - 2r4c13 = 2r6c1- 3r6c1 = 4r5c6 - 4r5c4

[]2r3c8 - 2r1c89.O =o - 4r5c4|#

[]2r1c8 - 2r1c9. = - 4r5c4|#

#[]4r5c4=>2r9c7

2r9c7

[]2r9c1 - 2r46c1 = 2r4c3 - 4r4c3 <=4r5c4

[]2r9c4 - 2r3c4.O = o - 4r5c4|#

clear []4r5c4 => 2r7c8 - 2r9c7 <=4r5c4

 

10 #4r5c1

Explication Eliminations

 

#[]4r5c1=>d thru AC:r4c5r56c4

6r4c5.d

[]4r2c6 - 4r2c3 = 4r45c3 - 4r5c1

[]9r4c5r6c4 - 9r6c5 = 3r5c1 - 4r5c1

#[]4r5c1=>1r1c9

1r1c9

[]3r1c9==3r2c6.b - 3r5c6 = 3r5c1 - 4r5c1

[]2r1c9. - 2r1c46 = 2r3c4 - 4r3c4 = 4r2c46 - 4r2c3 = 4r45c3 - 4r5c1

#[]N - 4r5c1

[]1r1c2 - 1r1c9 <= 4r5c1

[]1r2c1 - 1r78c1.N

[]1r3c2 - 1r3c5 = AC:r146c5(1r14c5 - 6r14c5) = 6r379c5 - 6r4c5.d <= 4r5c1

[]1r3c1 - 1r78c1.N

#[]4r5c1=>7r4c2.Ġ

7r4c2.Ġ

[]7r9c2 - 4r9c2 = 4r9c1 - 4r5c1

[]7r7c2 - 1r7c2 = 1r7c189.N - 4r5c1|#

#[]d - 4r5c1

[]AC:r1c2r2c1(8r1c2 - 1r1c2r2c1) = 1r3c12 - 1r3c5

= AC:r146c5(1r14c5 - 6r14c5) = 6r379c5 - 6r4c5.d

[]8r9c2 - 8r9c5 = 6r9c5 - 6r4c5.d

[]8r6c2 - 8r6c4 = AC:r4c5r5c4(8r4c5r5c4 - 6r4c5.d)

[]8r7c2 - 1r7c2 = 1r7c189 - 4r5c1|#

[]8r4c2 - 7r4c2. <= 4r5c1

clear []4r5c1 => d - 4r5c1|#

 

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