Medium Puzzle #17 - One Possible Solution Approach…
	NB:  There is only one final solution to this Sudoku puzzle…
	Rules: Place a number from 1-9 in each empty cell so that each row, each column AND each 3x3 block contains all the numbers from 1-9.
	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		2	6						Medium Puzzle #17 - October 17, 2005
2	5	2		9	4	1	8	6			Original puzzle as published on joe-ks.com…
3
4		5		1	7
5		8	6		3	9	1		2
6	7	9		6	8		4	3
7			4	8		3		9
8		6	8		2				4
9		3			9			2
	A	B	C	D	E	F	G	H	I
1		4		2	6						Step 1: #5 is in Columns A & B: #5 MUST go in Cell C9…
2	5	2		9	4	1	8	6
3							2
4		5		1	7						Step 2: #1 is in Columns D & F: #1 MUST go in Cell E7…
5		8	6		3	9	1		2
6	7	9		6	8		4	3
7			4	8	1	3		9			Step 3: #2 is in Columns H & I: #2 MUST go in Cell G3…
8		6	8		2				4		(cf #2 in Row 1 @ E1 excludes use of Cell H1)
9		3	5		9			2
	A	B	C	D	E	F	G	H	I
1		4		2	6						Step 4: #4 is in Rows 1 & 2: #4 MUST go in Cell H3…
2	5	2		9	4	1	8	6			(cf #4 in Column I @ I8 excludes use of Cell I3)
3							2	4
4		5		1	7						Step 5: #1 is in Rows 4 & 5: #1 MUST go in Cell C6…
5		8	6		3	9	1		2
6	7	9	1	6	8		4	3
7			4	8	1	3		9			Step 6: #9 is in Rows 7 & 9: #9 MUST go in Cell A8…
8	9	6	8		2				4
9		3	5		9			2
	A	B	C	D	E	F	G	H	I
1		4		2	6						Step 7: Complete Column B: need #s 1 & 7…
2	5	2		9	4	1	8	6			#1 can't go in Cell B7 (cf #1 in Row 7 @ E7), so
3		1		3			2	4			#1 MUST go in Cell B3, & therefore #7 MUST go in Cell B7
4		5		1	7
5		8	6		3	9	1		2		Step 8: #3 is in Columns E & F: #3 MUST go in Cell D3…
6	7	9	1	6	8		4	3
7		7	4	8	1	3		9
8	9	6	8		2				4
9		3	5		9			2
	A	B	C	D	E	F	G	H	I
1		4		2	6						Step 9: Complete Row 6: need #s 2 & 5…
2	5	2		9	4	1	8	6			#2 can't go in Cell I6 (cf #2 in Column I @ I5), so
3		1		3	5		2	4			#2 MUST go in Cell F6, & therefore #5 MUST go in Cell I6
4		5		1	7
5		8	6		3	9	1		2		Step 10: Complete Column E: #5 MUST go in Cell E3…
6	7	9	1	6	8	2	4	3	5
7		7	4	8	1	3		9
8	9	6	8		2				4
9		3	5		9			2
	A	B	C	D	E	F	G	H	I
1		4		2	6						Step 11: Block HH needs #6: #6 MUST go in Cell F9…
2	5	2		9	4	1	8	6			(#6 in Row 8 @ B8 excludes Cells D8 & F8, &
3		1		3	5		2	4			#6 in Column D @ D6 excludes Cell D9)
4		5		1	7
5		8	6		3	9	1	7	2		Step 12: Block FF needs #7: #7 MUST go in Cell H5
6	7	9	1	6	8	2	4	3	5		(#7 in Row 4 @ E4 excludes Cells G4, H4 & I4)
7		7	4	8	1	3		9
8	9	6	8		2				4
9		3	5		9	6		2
	A	B	C	D	E	F	G	H	I
1		4		2	6						Step 13: #6 is in Columns B & C: #6 MUST go in Cell A3…
2	5	2		9	4	1	8	6			(cf #6 in Row 1 @ E1 excludes use of Cell A1)
3	6	1		3	5		2	4
4		5		1	7						Step 14: Block HH needs #4: #4 MUST go in Cell D9…
5		8	6		3	9	1	7	2		(#4 in Row 8 @ I8 excludes use of Cells D8 & F8)
6	7	9	1	6	8	2	4	3	5
7		7	4	8	1	3		9
8	9	6	8		2				4
9		3	5	4	9	6		2
	A	B	C	D	E	F	G	H	I
1		4		2	6						Step 15: Complete Row 5: need #s 4 & 5…
2	5	2		9	4	1	8	6			#5 can't go in Cell A5 (cf #5 in Column A @ A2), so
3	6	1		3	5		2	4			#5 MUST go in Cell D5, & therefore #4 MUST go in Cell A5
4		5		1	7
5	4	8	6	5	3	9	1	7	2		Step 16: Now Complete Column D: #7 MUST go in Cell D8…
6	7	9	1	6	8	2	4	3	5
7		7	4	8	1	3		9
8	9	6	8	7	2				4
9		3	5	4	9	6		2
	A	B	C	D	E	F	G	H	I
1		4		2	6						Step 17: Complete Block EE: #4 MUST go in Cell F4…
2	5	2		9	4	1	8	6
3	6	1		3	5		2	4
4		5		1	7	4					Step 18: Complete Block GG: need #s 1 & 2…
5	4	8	6	5	3	9	1	7	2		#1 can't go in Cell A7 (cf #1 in Row 7 @ E7), so
6	7	9	1	6	8	2	4	3	5		#1 MUST go in Cell A9, & therefore #2 MUST go in Cell A7
7	2	7	4	8	1	3		9
8	9	6	8	7	2				4
9	1	3	5	4	9	6		2
	A	B	C	D	E	F	G	H	I
1		4		2	6			5			Step 19: Complete Block HH: #5 MUST go in Cell F8…
2	5	2		9	4	1	8	6
3	6	1		3	5		2	4			Step 20: #5 now in Rows 8 & 9: #5 MUST go in Cell G7
4		5		1	7	4					(#5 in Column I @ I6 excludes Cell I7).
5	4	8	6	5	3	9	1	7	2
6	7	9	1	6	8	2	4	3	5		Step 21: #5 now in Columns G & I: #5 MUST go in Cell H1…
7	2	7	4	8	1	3	5	9
8	9	6	8	7	2	5			4
9	1	3	5	4	9	6		2
	A	B	C	D	E	F	G	H	I
1		4		2	6			5			Step 22: Complete Column H: need #s 1 & 8…
2	5	2		9	4	1	8	6			#1 can't go in Cell H4 (cf #1 in Row 4 @ D4), so
3	6	1		3	5		2	4			#1 MUST go in Cell H8, & therefore #8 MUST go in Cell H4
4		5		1	7	4		8
5	4	8	6	5	3	9	1	7	2
6	7	9	1	6	8	2	4	3	5
7	2	7	4	8	1	3	5	9
8	9	6	8	7	2	5		1	4
9	1	3	5	4	9	6		2
	A	B	C	D	E	F	G	H	I
1		4		2	6			5	1		Step 23: Complete Row 7: #6 MUST go in Cell I7…
2	5	2		9	4	1	8	6
3	6	1		3	5		2	4			Step 24: #1 is in Rows 2 & 3: #1 MUST go in Cell I1…
4		5		1	7	4		8			(cf #1 in Column G @ G5 excludes Cell G1)
5	4	8	6	5	3	9	1	7	2
6	7	9	1	6	8	2	4	3	5
7	2	7	4	8	1	3	5	9	6
8	9	6	8	7	2	5		1	4
9	1	3	5	4	9	6		2
	A	B	C	D	E	F	G	H	I
1		4		2	6			5	1		Step 25: Block II needs #3: #3 can't go in Cells G9 or I9
2	5	2		9	4	1	8	6			(cf #3 in Row 9 @ B9), so #3 MUST go in Cell G8…
3	6	1		3	5		2	4
4	3	5	2	1	7	4		8			Step 26: Complete Block DD: need #s 2 & 3…
5	4	8	6	5	3	9	1	7	2		#2 can't go in Cell A4 (cf #2 in Column A @ A6), so
6	7	9	1	6	8	2	4	3	5		#2 MUST go in Cell C4, & therefore #3 MUST go in Cell A4
7	2	7	4	8	1	3	5	9	6
8	9	6	8	7	2	5	3	1	4
9	1	3	5	4	9	6		2
	A	B	C	D	E	F	G	H	I
1	8	4		2	6			5	1		Step 27: Complete Column A: #8 MUST go in Cell A1…
2	5	2		9	4	1	8	6
3	6	1		3	5		2	4			Step 28: Complete Row 4: need #s 6 & 9…
4	3	5	2	1	7	4	6	8	9		#6 can't go in Cell I4 (cf #6 in Column I @ I7), so
5	4	8	6	5	3	9	1	7	2		#6 MUST go in Cell G4, & therefore #9 MUST go in Cell I4
6	7	9	1	6	8	2	4	3	5
7	2	7	4	8	1	3	5	9	6
8	9	6	8	7	2	5	3	1	4
9	1	3	5	4	9	6		2
	A	B	C	D	E	F	G	H	I
1	8	4		2	6			5	1		Step 29: Complete Block II: need #s 7 & 8…
2	5	2		9	4	1	8	6			#8 can't go in Cell G9 (cf #8 in Column G @ G2), so
3	6	1		3	5		2	4			#8 MUST go in Cell I9, & therefore #7 MUST go in Cell G9
4	3	5	2	1	7	4	6	8	9
5	4	8	6	5	3	9	1	7	2
6	7	9	1	6	8	2	4	3	5
7	2	7	4	8	1	3	5	9	6
8	9	6	8	7	2	5	3	1	4
9	1	3	5	4	9	6	7	2	8
	A	B	C	D	E	F	G	H	I
1	8	4		2	6	7	9	5	1		Step 30: Complete Column F: need #s 7 & 8…
2	5	2		9	4	1	8	6			#8 can't go in Cell F1 (#8 in Row 1 @ A1), so
3	6	1		3	5	8	2	4			#8 MUST go in Cell F3, & therefore #7 MUST go in Cell F1
4	3	5	2	1	7	4	6	8	9
5	4	8	6	5	3	9	1	7	2		Step 31: Complete Column G: #9 MUST go in Cell G1…
6	7	9	1	6	8	2	4	3	5
7	2	7	4	8	1	3	5	9	6
8	9	6	8	7	2	5	3	1	4
9	1	3	5	4	9	6	7	2	8
	A	B	C	D	E	F	G	H	I
1	8	4		2	6	7	9	5	1		Step 32: Complete Column I: need #s 3 & 7…
2	5	2		9	4	1	8	6	3		#3 can't go in Cell I3 (cf #3 in Row 3 @ D3), so
3	6	1		3	5	8	2	4	7		#3 MUST go in Cell I2, & therefore #7 MUST go in Cell I3
4	3	5	2	1	7	4	6	8	9
5	4	8	6	5	3	9	1	7	2
6	7	9	1	6	8	2	4	3	5
7	2	7	4	8	1	3	5	9	6
8	9	6	8	7	2	5	3	1	4
9	1	3	5	4	9	6	7	2	8
	A	B	C	D	E	F	G	H	I
1	8	4	3	2	6	7	9	5	1		Step 33: Complete Row 1: #3 MUST go in Cell C1…
2	5	2	7	9	4	1	8	6	3
3	6	1	9	3	5	8	2	4	7		Step 34: Complete Row 2: #7 MUST go in Cell C2…
4	3	5	2	1	7	4	6	8	9
5	4	8	6	5	3	9	1	7	2		Step 35: Complete Row 3 (& Block AA):
6	7	9	1	6	8	2	4	3	5		#9 MUST go in Cell C3.
7	2	7	4	8	1	3	5	9	6
8	9	6	8	7	2	5	3	1	4
9	1	3	5	4	9	6	7	2	8
	A	B	C	D	E	F	G	H	I
1	8	4	3	2	6	7	9	5	1	45	Final Proof:
2	5	2	7	9	4	1	8	6	3	45	- All Rows add up to 45;
3	6	1	9	3	5	8	2	4	7	45
4	3	5	2	1	7	4	6	8	9	45
5	4	8	6	5	3	9	1	7	2	45
6	7	9	1	6	8	2	4	3	5	45
7	2	7	4	8	1	3	5	9	6	45
8	9	6	8	7	2	5	3	1	4	45
9	1	3	5	4	9	6	7	2	8	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