Medium Puzzle #37 - 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				4				6			Medium Puzzle #37 - November 6, 2005
2	6		4		3		2		8		Original puzzle as published © joe-ks.com
3	2	3				6			7
4	8		7				4
5	4	9	3	6	5	7	8	1	2
6	5		2				3
7	3	8				4			9
8	9		6		1		7		4
9				2				3
	A	B	C	D	E	F	G	H	I
1				4				6	3		Step 1: #4 is in Columns A & C: #4 MUST go in Cell B9
2	6		4		3		2		8		(#4 in Row 8 @ I9 excludes use of Cell B8)
3	2	3				6			7
4	8		7				4
5	4	9	3	6	5	7	8	1	2		Step 2: #3 is in Columns G & H: #3 MUST go in Cell I1...
6	5		2				3
7	3	8				4			9
8	9		6		1		7		4
9		4		2				3
	A	B	C	D	E	F	G	H	I
1				4				6	3		Step 3: #4 is in Rows 1 & 2: #4 MUST go in Cell H3
2	6		4		3		2		8		(#4 in Column G @ G4 excludes use of Cell G3)
3	2	3				6		4	7
4	8		7				4
5	4	9	3	6	5	7	8	1	2
6	5		2				3
7	3	8				4			9
8	9		6		1		7		4
9		4		2				3
	A	B	C	D	E	F	G	H	I
1				4				6	3		Step 4: #7 is in Column G & I: #7 MUST go in Cell H6
2	6		4		3		2		8		(#7 in Row 4 @ C4 exlcudes use of Cell H4)
3	2	3				6		4	7
4	8		7				4				Step 5: Block GG needs #2: #2 MUST go in Cell B8
5	4	9	3	6	5	7	8	1	2		(#2 in Column C @ C6 excludes use of Cells C7 & C9, &
6	5		2				3	7			#2 in Row 9 @ D9 further exludes use of Cell A9)
7	3	8				4		2	9
8	9	2	6		1		7		4		Step 6: #2 is now in Rows 8 & 9: #2 MUST go in Cell H7
9		4		2				3			(#2 in Column G @ G2 excludes use of Cell G7)
	A	B	C	D	E	F	G	H	I
1				4				6	3		Step 7: #4 is in Columns D & F: #4 MUST go in Cell E6
2	6		4		3		2		8
3	2	3				6		4	7
4	8		7				4				Step 8: #8 is in Columns G & I: #8 MUST go in Cell H8...
5	4	9	3	6	5	7	8	1	2		(#4 in Row 4 @ G4 excludes use of Cell E4)
6	5		2		4		3	7
7	3	8				4		2	9
8	9	2	6		1		7	8	4
9		4		2				3
	A	B	C	D	E	F	G	H	I
1	1			4				6	3		Step 9: Block GG needs #7: #8 MUST go in Cell A9
2	6		4		3		2		8		(#7 in Column C @ C4 excludes use of Cells C7 & C9)
3	2	3				6	1	4	7
4	8		7				4				Step 10: Complete Column A: #1 MUST go in Cell A1...
5	4	9	3	6	5	7	8	1	2
6	5		2		4		3	7			Step 11: Block CC needs #1: #1 MUST go in Cell G3
7	3	8				4		2	9		(#1 from Step 10 @ A1 excludes use of Cell G1, &
8	9	2	6		1		7	8	4		(#1 in Column H @ H5 excludes use of Cell H2)
9	7	4		2				3
	A	B	C	D	E	F	G	H	I
1	1			4			9	6	3		Step 12: Clock FF needs #9: #9 MUST go in Cell H4
2	6		4		3		2		8		(#9 in Column I @ I7 excludes use of Cells I4 & I6)
3	2	3				6	1	4	7
4	8		7				4	9			Step 13: #9 is now in Columns H & I: #9 MUST go in Cell G1
5	4	9	3	6	5	7	8	1	2
6	5		2		4		3	7
7	3	8				4		2	9
8	9	2	6		1		7	8	4
9	7	4		2				3
	A	B	C	D	E	F	G	H	I
1	1			4			9	6	3		Step 14: Complete Block CC: #5 MUST go in Cell H2...
2	6		4		3		2	5	8
3	2	3				6	1	4	7		Step 15: Complete Block FF: need #s 5 & 6…
4	8	6	7				4	9	5		#5 can't go in Cell I6 (cf #5 in Row 6 @ A6), so
5	4	9	3	6	5	7	8	1	2		#5 MUST go in Cell I4, & therefore #6 MUST go in Cell I6
6	5		2		4		3	7	6
7	3	8				4		2	9		Step 16: #6 is now in Rows 5 & 6: #6 MUST go in Cell B4...
8	9	2	6		1		7	8	4
9	7	4		2				3
	A	B	C	D	E	F	G	H	I
1	1			4			9	6	3		Step 17: Complete Block DD: #1 MUST go in Cell B6...
2	6		4		3		2	5	8
3	2	3				6	1	4	7		Step 18: #1 is in Columns G & H: #1 MUST go in Cell I9...
4	8	6	7				4	9	5
5	4	9	3	6	5	7	8	1	2		Step 19: #1 is now in Rows 8 & 9: #1 MUST go in Cell C7...
6	5	1	2		4		3	7	6
7	3	8	1			4		2	9		Step 20: Complete Block GG; #5 MUST go in Cell C9...
8	9	2	6		1		7	8	4
9	7	4	5	2				3	1
	A	B	C	D	E	F	G	H	I
1	1			4			9	6	3		Step 21: Complete Block II: Need #s 5 & 6…
2	6		4		3		2	5	8		#5 can't go in Cell G9 (cf #5 from Step 20 in Row 9 @ C9)
3	2	3				6	1	4	7		so #5 MUST go in Cell G7, & therefore #6 MUST go in G9
4	8	6	7				4	9	5
5	4	9	3	6	5	7	8	1	2		Step 22: #6 is now in Rows 8 & 9: #6 MUST go in Cell E7
6	5	1	2		4		3	7	6		(#6 in Column D @ D5 excludes use of Cell D7)
7	3	8	1	7	6	4	5	2	9
8	9	2	6		1		7	8	4		Step 23: #7 is in Rows 8 & 9: #7 MUST go in Cell D7...
9	7	4	5	2			6	3	1
	A	B	C	D	E	F	G	H	I
1	1	5		4			9	6	3		Step 24: Complete Block B: need #s 5 & 7…
2	6	7	4		3		2	5	8		#5 can't go in Cell B2 (cf #5 in Row 2 @ H2), so
3	2	3		5		6	1	4	7		#5 MUST go in Cell B1, & therefore #7 MUST go in Cell B2
4	8	6	7				4	9	5
5	4	9	3	6	5	7	8	1	2		Step 25: #5 is now in Rows 1 & 2: #5 MUST go in Cell D3
6	5	1	2		4		3	7	6		(#5 in Column E @ E5 exlcudes use of Cell E3)
7	3	8	1	7	6	4	5	2	9
8	9	2	6		1	5	7	8	4		Step 26: #5 is now in Columns D & E: #5 MUST go in Cell F8
9	7	4	5	2			6	3	1		(#5 in Row 9 @ C9 excludes use of Cell F9)
	A	B	C	D	E	F	G	H	I
1	1	5	8	4			9	6	3		Step 27: Complete Block AA: need #s 8 & 9…
2	6	7	4		3		2	5	8		#9 can't go in Cell C1 ( cf #9 in Row 1 @ G1), so
3	2	3	9	5	8	6	1	4	7		#9 MUST go in Cell C3, & therefore #8 MUST go in Cell C1
4	8	6	7				4	9	5
5	4	9	3	6	5	7	8	1	2		Step 28: #8 is now in Rows 1 & 2: #8 MUST go in Cell E3…
6	5	1	2		4		3	7	6
7	3	8	1	7	6	4	5	2	9		Step 29: Complete Row 8: #3 MUST go in Cell D8…
8	9	2	6	3	1	5	7	8	4
9	7	4	5	2			6	3	1
	A	B	C	D	E	F	G	H	I
1	1	5	8	4			9	6	3		Step 30: Complete Block HH: need #s 8 & 9…
2	6	7	4		3		2	5	8		#8 can't go in Cell E9 (cf #8 in Column E @ E3), so
3	2	3	9	5	8	6	1	4	7		#8 MUST go in Cell F9, 7 therefore #9 MUST go in Cell E9
4	8	6	7				4	9	5
5	4	9	3	6	5	7	8	1	2
6	5	1	2		4		3	7	6
7	3	8	1	7	6	4	5	2	9
8	9	2	6	3	1	5	7	8	4
9	7	4	5	2	9	8	6	3	1
	A	B	C	D	E	F	G	H	I
1	1	5	8	4			9	6	3		Step 31: Complete Row 6: need #s 8 & 9…
2	6	7	4	9	3		2	5	8		#8 can't go in Cell F6 (cf #8 in Column F @ F9), so
3	2	3	9	5	8	6	1	4	7		#8 MUST go in Cell D6, & therefore #9 MUST go in Cell F6
4	8	6	7	1			4	9	5
5	4	9	3	6	5	7	8	1	2		Step 32: Complete Column D: need #s 1 & 9…
6	5	1	2	8	4	9	3	7	6		#9 can't go in Cell D4 (cf #9 in Row 4 @ H4), so
7	3	8	1	7	6	4	5	2	9		#9 MUST go in Cell D2, & therefore #1 MUST go in Cell D4
8	9	2	6	3	1	5	7	8	4
9	7	4	5	2	9	8	6	3	1
	A	B	C	D	E	F	G	H	I
1	1	5	8	4	7		9	6	3		Step 33: Complete Row 4: need #s 2 & 3…
2	6	7	4	9	3		2	5	8		#3 can't go in Cell E4 (cf #3 in Column E @ E2), so
3	2	3	9	5	8	6	1	4	7		#3 MUST go in Cell F4, & therefore #2 MUST go in Cell E4
4	8	6	7	1	2	3	4	9	5
5	4	9	3	6	5	7	8	1	2		Step 34: Complete Column E: #7 MUST go in Cell E1...
6	5	1	2	8	4	9	3	7	6
7	3	8	1	7	6	4	5	2	9
8	9	2	6	3	1	5	7	8	4
9	7	4	5	2	9	8	6	3	1
	A	B	C	D	E	F	G	H	I
1	1	5	8	4	7	2	9	6	3		Step 35: Complete Block BB (& Puzzle): need #s 1 & 2…
2	6	7	4	9	3	1	2	5	8		#2 can't go in Cell F2 (cf #2 in Row 2 @ G2), so
3	2	3	9	5	8	6	1	4	7		#2 MUST go in Cell F1, & therefore #1 MUST go in Cell F2.
4	8	6	7	1	2	3	4	9	5
5	4	9	3	6	5	7	8	1	2
6	5	1	2	8	4	9	3	7	6
7	3	8	1	7	6	4	5	2	9
8	9	2	6	3	1	5	7	8	4
9	7	4	5	2	9	8	6	3	1
	A	B	C	D	E	F	G	H	I
1	1	5	8	4	7	2	9	6	3	45	Final Proof:
2	6	7	4	9	3	1	2	5	8	45	- All Rows add up to 45;
3	2	3	9	5	8	6	1	4	7	45
4	8	6	7	1	2	3	4	9	5	45
5	4	9	3	6	5	7	8	1	2	45
6	5	1	2	8	4	9	3	7	6	45
7	3	8	1	7	6	4	5	2	9	45
8	9	2	6	3	1	5	7	8	4	45
9	7	4	5	2	9	8	6	3	1	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