Medium Puzzle #39 - 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	2						5	8			Medium Puzzle #39 - November 8, 2005
2	4	9			8		2		1		Original puzzle as published © joe-ks.com
3				7	1			4
4	9						4		8
5	3	7		4	6
6				1	5		3		7
7	1							3
8	6	8		9	4		7		2
9					2		9	5
	A	B	C	D	E	F	G	H	I
1	2						5	8			Step 1: Column G needs #1: #1 MUST go in Cell G5
2	4	9			8		2		1		(#1 in Row 3 @ E1 excludes use of Cell G3, &
3				7	1			4			#1 in Row 7 @ A7 excludes use of Cell G7)
4	9						4		8
5	3	7		4	6		1
6				1	5		3		7
7	1							3
8	6	8		9	4		7		2
9					2		9	5
	A	B	C	D	E	F	G	H	I
1	2						5	8			Step 2: #1 is now in Columns G & I: #1 MUST go in Cell H8...
2	4	9			8		2		1
3				7	1			4			Step 3: #1 is now in Rows 7 & 8: #1 MUST go in Cell F9
4	9						4		8		(#1 in Column D @ D6 excludes use of Cell D9)
5	3	7		4	6		1
6				1	5		3		7
7	1							3
8	6	8		9	4		7	1	2
9					2	1	9	5
	A	B	C	D	E	F	G	H	I
1	2						5	8			Step 4: Block II needs # 8: #8 MUST go in Cell G7
2	4	9			8		2		1		(#8 in Column I @ I4 excludes use of Cells I7 & I9)
3				7	1			4
4	9						4		8		Step 5: #8 is now in Rows 7 & 8: #8 MUST go in Cell D9...
5	3	7		4	6		1
6				1	5		3		7
7	1						8	3
8	6	8		9	4		7	1	2
9				8	2	1	9	5
	A	B	C	D	E	F	G	H	I
1	2					4	5	8			Step 6: #4 is in Rows 2 & 3: #4 MUST go in Cell F1
2	4	9			8		2		1		(#4 in Column D @ D5 excludes use of Cell D1, &
3				7	1			4			#4 in Column E @ E8 excludes use of Cell E1)
4	9						4		8
5	3	7		4	6		1				Step 7: #6 is in Row 8 (@ A8 in Block GG): #6 must go in
6				1	5		3		7		Blocks HH in either D7 or F7… BUT that means that #6
7	1						8	3			in Block II MUST go in Block II, Row 9 - & it MUST be in
8	6	8		9	4		7	1	2		the only cell remaining - in Cell I9)
9				8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2		7			4	5	8			Step 8: Complete Block II: #4 MUST go in Cell I7...
2	4	9			8		2	7	1
3				7	1			4			Step 9: #7 is in Columns G & I: #7 MUST go in Cell H2…
4	9						4		8
5	3	7		4	6		1				Step 10: #7 is now in Rows 2 & 3: #7 MUST go in Cell C1
6				1	5		3		7		(#7 in Column B @ B5 excludes use of Cell B1)
7	1						8	3	4
8	6	8		9	4		7	1	2
9				8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2		7			4	5	8			Step 11: Complete Column G: #6 MUST go in Cell G3...
2	4	9			8		2	7	1
3				7	1		6	4			Step 12: #7 is in Columns B & C: #7 MUST go in Cell A9...
4	9						4		8
5	3	7		4	6		1
6				1	5		3		7
7	1						8	3	4
8	6	8		9	4		7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2		7			4	5	8			Step 13: Block HH needs #3: #3 MUST go in Cell F8
2	4	9			8		2	7	1		(#3 in Row 7 @ H7 excludes use of Cells D7, E7 & F7)
3				7	1		6	4
4	9						4		8		Step 14: #5 is in Columns G & H: #5 MUSt go in Cell I5…
5	3	7		4	6		1		5
6				1	5		3		7
7	1						8	3	4
8	6	8		9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2		7			4	5	8			Step 15: #9 is in Rows 8 & 9: #9 MUST go in Cell C7
2	4	9			8		2	7	1		(#9 in Column B @ B2 excludes use of Cell B9)
3				7	1		6	4
4	9						4		8
5	3	7		4	6		1		5
6				1	5		3		7
7	1		9				8	3	4
8	6	8		9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7			4	5	8			Step 16: #1 is in Rows 2 & 3: #1 MUST go in Cell B1...
2	4	9			8		2	7	1
3				7	1		6	4			Step 17: #1 is now in Columns A & B: #1 MUST go in Cell C4
4	9		1				4		8		(#1 in Row 5 @ G5 excludes use of Cell C5, &
5	3	7		4	6		1		5		#1 in Row 6 @ D6 excludes use of Cell C6)
6				1	5		3		7
7	1		9				8	3	4
8	6	8		9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6		4	5	8			Step 18: Block AA needs #6: #6 MUST go in Cell C2
2	4	9	6		8		2	7	1		(#6 in row 3 @ G3 exludes use of Cells A3, B3 & C3)
3				7	1		6	4
4	9		1				4		8		Step 19: #6 is now in Rows 2 & 3: #6 MUST go in Cell D1
5	3	7		4	6		1		5		(#6 in Column E @ E5 excludes use of Cell E1)
6				1	5		3		7
7	1		9			6	8	3	4		Step 20: #6 in now in Columns D & E: #6 MUST go in Cell F7
8	6	8		9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6		4	5	8			Step 21: Complete Block HH: need #s 5 & 7…
2	4	9	6		8		2	7	1		#5 can't go in Cell E7 (cf #5 in Column E @ E6), so
3				7	1		6	4			#5 MUST go in Cell D7, & therefore #7 MUST go in Cell E7
4	9		1			7	4		8
5	3	7		4	6		1		5		Step 22: #7 is now in Columns D & E: #7 MUST go in Cell F4
6				1	5		3		7		(#7 in Row 5 @ B5 excludes use of Cell F5, &
7	1		9	5	7	6	8	3	4		#7 in Row 6 @ I6 excludes use of Cell F6)
8	6	8		9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6		4	5	8			Step 23: #5 is in Rows 7 & 9: #5 MUST go in Cell C8...
2	4	9	6		8	5	2	7	1
3	5			7	1		6	4			Step 24: #5 is in Rows 5 & 6: #5 MUST go in  Cell B4...
4	9	5	1			7	4		8
5	3	7		4	6		1		5		Step 25: #5 is now in Columns B & C: #5 MUST go in Cell A3
6				1	5		3		7
7	1		9	5	7	6	8	3	4		Step 26: #5 is now in Rows 1 & 3: #5 MUST go in Cell F2
8	6	8	5	9	4	3	7	1	2		(#5 in Column D @ D7 excludes use of Cell D2)
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6		4	5	8			Step 27: Complete Block AA: need #s 3 & 8…
2	4	9	6		8	5	2	7	1		#8 can't go in Cell B3 (cf #8 in Column B @ B8), so
3	5	3	8	7	1		6	4			#8 MUST go in Cell C3, & therefore #3 MUST go in Cell B3
4	9	5	1			7	4		8
5	3	7		4	6	8	1		5		Step 28: Complete Column A: #8 MUST go in Cell A6...
6	8			1	5		3		7
7	1		9	5	7	6	8	3	4		Step 29: #8 is now in Rows 4 & 6: #8 MUST go in Cell F5...
8	6	8	5	9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6		4	5	8	3		Step 30: Complete Row 2: #3 MUST go in Cell D2...
2	4	9	6	3	8	5	2	7	1
3	5	3	8	7	1		6	4			Step 31: #3 is now in Rows 2 & 3: #3 MUST go in Cell I1...
4	9	5	1		3	7	4		8
5	3	7		4	6	8	1		5		Step 32: #3 is now in Columns D & F: #3 MUST go in Cell E4
6	8			1	5		3		7
7	1		9	5	7	6	8	3	4
8	6	8	5	9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6	9	4	5	8	3		Step 33: Complete Row 1: #9 MUST go in Cell E1...
2	4	9	6	3	8	5	2	7	1
3	5	3	8	7	1	2	6	4			Step 34: #9 is now in Columns D & E: #9 MUST go in Cell F6
4	9	5	1	2	3	7	4		8
5	3	7		4	6	8	1		5		Step 35: Complete Block EE: #2 MUST go in Cell D4...
6	8			1	5	9	3		7
7	1		9	5	7	6	8	3	4		Step 36: Complete Block BB: #2 MUST go in Cell F3...
8	6	8	5	9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6	9	4	5	8	3		Step 37: Complete Block CC: #9 MUST go in Cell I3...
2	4	9	6	3	8	5	2	7	1
3	5	3	8	7	1	2	6	4	9		Step 38: Complete Row 4: #6 MUST go in Cell H4...
4	9	5	1	2	3	7	4	6	8
5	3	7		4	6	8	1		5
6	8			1	5	9	3		7
7	1		9	5	7	6	8	3	4
8	6	8	5	9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6	9	4	5	8	3		Step 39: Complete Row 5: need #s 2 & 9…
2	4	9	6	3	8	5	2	7	1		#9 can't go in Cell C5 (cf #9 in Column C @ C7), so
3	5	3	8	7	1	2	6	4	9		#9 MUST go in Cell H5, & therefore #2 MUST go in Cell C5
4	9	5	1	2	3	7	4	6	8
5	3	7	2	4	6	8	1	9	5		Step 40: Complete Column H: #2 MUST go in Cell H6...
6	8			1	5	9	3	2	7
7	1		9	5	7	6	8	3	4
8	6	8	5	9	4	3	7	1	2
9	7			8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6	9	4	5	8	3		Step 41: Complete Block DD: need #s 4 & 6…
2	4	9	6	3	8	5	2	7	1		#6 can't go in Cell C6 (cf #6 in Column C @ C2), so
3	5	3	8	7	1	2	6	4	9		#6 MUST go in Cell B6, & therefore #4 MUST go in Cell C6
4	9	5	1	2	3	7	4	6	8
5	3	7	2	4	6	8	1	9	5		Step 42: Complete Column C: #3 MUST go in Cell C9...
6	8	6	4	1	5	9	3	2	7
7	1		9	5	7	6	8	3	4
8	6	8	5	9	4	3	7	1	2
9	7		3	8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6	9	4	5	8	3		Step 43: Complete Block GG (& Puzzle): need #s 2 & 4…
2	4	9	6	3	8	5	2	7	1		#2 can't go in Cell B9 (cf #2 in Row 9 @ E9), so
3	5	3	8	7	1	2	6	4	9		#2 MUST go in Cell B7, & therefore #4 MUST go in Cell B9.
4	9	5	1	2	3	7	4	6	8
5	3	7	2	4	6	8	1	9	5
6	8	6	4	1	5	9	3	2	7
7	1	2	9	5	7	6	8	3	4
8	6	8	5	9	4	3	7	1	2
9	7	4	3	8	2	1	9	5	6
	A	B	C	D	E	F	G	H	I
1	2	1	7	6	9	4	5	8	3	45	Final Proof:
2	4	9	6	3	8	5	2	7	1	45	- All Rows add up to 45;
3	5	3	8	7	1	2	6	4	9	45
4	9	5	1	2	3	7	4	6	8	45
5	3	7	2	4	6	8	1	9	5	45
6	8	6	4	1	5	9	3	2	7	45
7	1	2	9	5	7	6	8	3	4	45
8	6	8	5	9	4	3	7	1	2	45
9	7	4	3	8	2	1	9	5	6	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