Medium Puzzle #43 - One Possible Solution Approach…
	NB:  There is only one final solution to this Sudoku puzzle…
	A	B	C	D	E	F	G	H	I
1
2	AA			BB			CC				Reference to 3x3 Blocks AA, BB & CC
3
4
5	DD			EE			FF				Reference to 3x3 Blocks DD, EE & FF
6
7
8	GG			HH			II				Reference to 3x3 Blocks GG, HH & II
9
	A	B	C	D	E	F	G	H	I
1	6	2						8	9		Medium Puzzle #43 - November 12, 2005
2			1	9		2	6				Original puzzle as published © joe-ks.com
3	3				5				1
4	5	1						9
5	8	7	6				2	3	5
6		3						4	6
7	7				6				2
8			3	4		5	9
9	2	6						1	4
	A	B	C	D	E	F	G	H	I
1	6	2						8	9		Step 1: #2 is in Rows 1 & 2: #2 MUST go in Cell H3
2			1	9		2	6				(cf #2 in Column G @ G5 excludes use of Cell G3)
3	3				5			2	1
4	5	1	4					9			Step 2: #2 is in Rows 7 & 9: #2 MUST go in Cell E8...
5	8	7	6				2	3	5
6		3						4	6		Step 3: Block DD needs #4: #4 MUST go in Cell C4
7	7				6				2		(#4 in Row 6 @ H6 excludes use of Cells A6 & C6)
8			3	4	2	5	9
9	2	6						1	4
	A	B	C	D	E	F	G	H	I
1	6	2						8	9		Step 4: Complete Block DD: need #s 2 & 9…
2			1	9		2	6				#2 can't go in Cell A6 (cf #2 in Column A @ A9), so
3	3				5			2	1		#2 MUST go in Cell C6, & therefore #9 MUST go in Cell A6
4	5	1	4	2				9
5	8	7	6				2	3	5		Step 5: #2 is in Columns E & F: #2 MUST go in Cell D4
6	9	3	2					4	6		(#2 in Row 5 @ G5 excludes use of Cell D5, &
7	7				6				2		(#2 from Step 4 in Row 6 @ C2 excludes use of Cell D6)
8			3	4	2	5	9
9	2	6						1	4
	A	B	C	D	E	F	G	H	I
1	6	2						8	9		Step 6: #5 is in Columns E & F: #5 MUST go in Cell D6
2			1	9		2	6				(#5 in Row 5 @ I5 excludes use of Cell D5)
3	3				5			2	1
4	5	1	4	2				9			Step 7: #1 is in Columns B & C: #1 MUST go in Cell A8...
5	8	7	6				2	3	5
6	9	3	2	5				4	6
7	7				6				2
8	1		3	4	2	5	9
9	2	6						1	4
	A	B	C	D	E	F	G	H	I
1	6	2						8	9		Step 8: Complete Column A: #4 MUST go in Cell A2...
2	4		1	9		2	6
3	3				5			2	1		Step 9: #4 is now in Columns A & C: #4 MUST go in Cell B7
4	5	1	4	2				9			(#4 in Row 8 @ D8 excludes use of Cell B8)
5	8	7	6				2	3	5
6	9	3	2	5				4	6		Step 10: #6 is in Columns G & I: #6 MUST go in Cell H8
7	7	4			6				2		(#6 in Row 7 @ E7 excludes use of Cell H7)
8	1		3	4	2	5	9	6
9	2	6						1	4
	A	B	C	D	E	F	G	H	I
1	6	2						8	9		Step 11: Complete Row 8: need #s 7 & 8…
2	4		1	9	8	2	6				#7 can't go in Cell B8 (cf #7 in Column B @ B5), so
3	3		8		5			2	1		#7 MUST go in Cell I8, & therefore #8 MUST go in Cell B8
4	5	1	4	2				9
5	8	7	6				2	3	5		Step 12: #8 is now in Columns A & B: #8 MUST go in Cell C3
6	9	3	2	5				4	6		(#8 in Row 1 @ H1 excludes use of Cell C1)
7	7	4			6				2
8	1	8	3	4	2	5	9	6	7		Step 13: #8 is now in Rows 1 & 3: #8 MUST go in Cell E2...
9	2	6						1	4
	A	B	C	D	E	F	G	H	I
1	6	2					5	8	9		Step 14: Complete Column H: need #s 5 & 7…
2	4	5	1	9	8	2	6	7			#7 can't go in Cell H7 (cf #7 in Row 7 @ A7) so
3	3		8		5			2	1		#7 MUST go in Cell H2, & therefore #5 MUST go in Cell H7
4	5	1	4	2				9
5	8	7	6				2	3	5		Step 15: #5 is now in Columns H & I: #5 MUST go in Cell G1
6	9	3	2	5				4	6		(#5 in Row 3 @ E3 excludes us of Cell G3)
7	7	4			6			5	2
8	1	8	3	4	2	5	9	6	7		Step 16: #5 is now in Rows 1 & 2: #5 MUST go in Cell B2...
9	2	6						1	4
	A	B	C	D	E	F	G	H	I
1	6	2					5	8	9		Step 17: Complete Column I: need #s 3 & 8…
2	4	5	1	9	8	2	6	7	3		#8 can't go in Cell I2 (cf #8 in Row 2 @ E2), so
3	3		8		5		4	2	1		#8 MUST go in Cell I4, & therefore #3 MUST go in Cell I2
4	5	1	4	2				9	8
5	8	7	6				2	3	5		Step 18: Completet Block CC: #4 MUST go in Cell G3...
6	9	3	2	5				4	6
7	7	4			6			5	2
8	1	8	3	4	2	5	9	6	7
9	2	6						1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7				5	8	9		Step 19: Complete Block AA: need #s 7 & 9…
2	4	5	1	9	8	2	6	7	3		#9 can't go in Cell C1 (cf #9 in Row 1 @ I1), so
3	3	9	8		5		4	2	1		#9 MUST go in Cell B3, & therefore #7 MUST go in Cell C1
4	5	1	4	2				9	8
5	8	7	6				2	3	5		Step 20: Complete Block GG: need #s 5 & 9…
6	9	3	2	5				4	6		#5 can't go in Cell C7 (cf #5 in Row 7 @ H7), o
7	7	4	9		6			5	2		#5 MUST go in Cell C9, & thererfore #9 MUST go in Cell C7
8	1	8	3	4	2	5	9	6	7
9	2	6	5					1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7				5	8	9		NB: Block II needs 2 more #s: #3 & 8 - but note that both #3 & 8
2	4	5	1	9	8	2	6	7	3		both go in Column G…
3	3	9	8		5		4	2	1		Step 21: Complete Column G in Block FF: aside from #s 3 & 8
4	5	1	4	2			7	9	8		needed in Column G (for Block II), the 2 #s needed for Col G
5	8	7	6				2	3	5		in Cells G4 & G6 are #s 1 & 7:  #1 cant' go in Cell G4 (cf #1
6	9	3	2	5			1	4	6		in Row 4 @ B4), so #1 MUST go in Cell G6. & #7 MUST go
7	7	4	9		6			5	2		in Cell G4
8	1	8	3	4	2	5	9	6	7
9	2	6	5					1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7				5	8	9		Step 22: Comlpete Row 4: need #s 3 & 6…
2	4	5	1	9	8	2	6	7	3		#6 can't go in Cell E4 (cf #6 in Column E @ E7), so
3	3	9	8	6	5	7	4	2	1		#6 MUST go in Cell F4, & therefore #3 MUST go in Cell E4
4	5	1	4	2	3	6	7	9	8
5	8	7	6				2	3	5		Step 23: #6 is now in Columns E & F: #6 MUST go in Cell D3
6	9	3	2	5			1	4	6		(#6 in Row 1 @ A1 excludes use of Cell D1)
7	7	4	9		6			5	2
8	1	8	3	4	2	5	9	6	7		Step 24: Complete Row 3: #7 MUST go in Cell F3…
9	2	6	5					1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7				5	8	9		Step 25: Block EE needs #8: #8 MUST go in Cell F6
2	4	5	1	9	8	2	6	7	3		(#8 in Row 5 @ A5 excludes use of Cells D5, E5 & F5,
3	3	9	8	6	5	7	4	2	1		& #8 in Column E @ E2 further exlcudes use of Cell E6)
4	5	1	4	2	3	6	7	9	8
5	8	7	6				2	3	5		Step 26: Block EE also needs #7: #7 MUST go in Cell E6
6	9	3	2	5	7	8	1	4	6		(#7 in Row 5 @ B5 excludes use of Cells D5, E5 & F5)
7	7	4	9		6			5	2
8	1	8	3	4	2	5	9	6	7		Step 27: #7 is now in Columns E & F: #7 MUST go in Cell F9
9	2	6	5	7				1	4		(#7 in Row 7 @ A7 excludes use of Cell D7)
	A	B	C	D	E	F	G	H	I
1	6	2	7				5	8	9		Step 28: Look specifically at Cell E9 - and look at the only
2	4	5	1	9	8	2	6	7	3		possible #s for E9 (look at all #s in Row 9, Column E AND
3	3	9	8	6	5	7	4	2	1		Block HH): only #9 can go in Cell E9…
4	5	1	4	2	3	6	7	9	8
5	8	7	6			9	2	3	5		Step 29: #9 is now in Columns D & E: #9 MUST go in Cell F5...
6	9	3	2	5	7	8	1	4	6
7	7	4	9		6			5	2
8	1	8	3	4	2	5	9	6	7
9	2	6	5	7	9			1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7		1		5	8	9		Step 30: Complete Block EE: need #s 1 & 4…
2	4	5	1	9	8	2	6	7	3		#4 can't go in Cell D5 (cf #4 in Column D @ D8), so
3	3	9	8	6	5	7	4	2	1		#4 MUST go in Cell E5, & therefore #1 MUST go in Cell D5
4	5	1	4	2	3	6	7	9	8
5	8	7	6	1	4	9	2	3	5		Step 31: Complete Column E: #1 MUST go in Cell E1...
6	9	3	2	5	7	8	1	4	6
7	7	4	9		6	1		5	2		Step 32: #1 is now in Column D & E: #1 MUST go in Cell F7
8	1	8	3	4	2	5	9	6	7		(#1 in Row 9 @ H9 excludes use of Cell F9)
9	2	6	5	7	9			1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7	3	1	4	5	8	9		Step 33: Complete Block BB: need #s 3 & 4…
2	4	5	1	9	8	2	6	7	3		#4 can't go in Cell D1 (cf #4 in Column D @ D8), so
3	3	9	8	6	5	7	4	2	1		#4 MUST go in Cell F1, & therefore #3 MUST go in Cell D1
4	5	1	4	2	3	6	7	9	8
5	8	7	6	1	4	9	2	3	5
6	9	3	2	5	7	8	1	4	6
7	7	4	9		6	1		5	2
8	1	8	3	4	2	5	9	6	7
9	2	6	5	7	9			1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7	3	1	4	5	8	9		Step 34: Complete Block HH: need #s 3 & 8…
2	4	5	1	9	8	2	6	7	3		#8 can't go in Cell F9 (cf #8 in Column F @ F6), so
3	3	9	8	6	5	7	4	2	1		#8 MUST go in Cell D7, & therefore #3 MUST go in Cell F9
4	5	1	4	2	3	6	7	9	8
5	8	7	6	1	4	9	2	3	5
6	9	3	2	5	7	8	1	4	6
7	7	4	9	8	6	1		5	2
8	1	8	3	4	2	5	9	6	7
9	2	6	5	7	9	3		1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7	3	1	4	5	8	9		Step 35: Complete Block II (& Puzzle): need #s 3 & 8…
2	4	5	1	9	8	2	6	7	3		#3 can't go in Cell G9 (cf #3 in Row 9 @ F9), so
3	3	9	8	6	5	7	4	2	1		#3 MUSt go in Cell G7, & therefore #8 MUST go in Cell G9.
4	5	1	4	2	3	6	7	9	8
5	8	7	6	1	4	9	2	3	5
6	9	3	2	5	7	8	1	4	6
7	7	4	9	8	6	1	3	5	2
8	1	8	3	4	2	5	9	6	7
9	2	6	5	7	9	3	8	1	4
	A	B	C	D	E	F	G	H	I
1	6	2	7	3	1	4	5	8	9	45	Final Proof:
2	4	5	1	9	8	2	6	7	3	45	- All Rows add up to 45;
3	3	9	8	6	5	7	4	2	1	45
4	5	1	4	2	3	6	7	9	8	45
5	8	7	6	1	4	9	2	3	5	45
6	9	3	2	5	7	8	1	4	6	45
7	7	4	9	8	6	1	3	5	2	45
8	1	8	3	4	2	5	9	6	7	45
9	2	6	5	7	9	3	8	1	4	45
	45	45	45	45	45	45	45	45	45		- All Columns add up to 45;
	45			45			45				- All 3x3 Blocks add up to 45…
	45			45			45
	45			45			45