Medium Puzzle #35 - 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		1						6			Medium Puzzle #35 - November 4, 2005
2	3	6	7				9	4	5		Original puzzle as published © joe-ks.com
3	8		5	7		6	2
4				1	2	5
5					6
6				9	7	8
7	9		2	6		1	8		7
8	6	8	3				5	2	1
9		7						9
	A	B	C	D	E	F	G	H	I
1		1					7	6			Step 1: #7 is in Rows 2 & 3: #7 MUST go in Cell G1…
2	3	6	7				9	4	5
3	8		5	7		6	2				Step 2: Row 8 needs #7: #7 MUST go in Cell F8
4				1	2	5					(#7 is Column D excludes use of Cell D8, &
5					6						#7 in Column E excludes use of Cell E8)
6				9	7	8
7	9		2	6		1	8		7
8	6	8	3			7	5	2	1
9		7						9
	A	B	C	D	E	F	G	H	I
1		1				9	7	6			Step 3: #9 is in Rows 7 & 9: #9 MUST go in Cell E8
2	3	6	7				9	4	5		(#9 in Column D @ D6 excludes use of Cell D8)
3	8	9	5	7		6	2
4				1	2	5					Step 4: #9 is now in Columns D & E: #9 MUST go in Cell F1
5					6						(#9 in Row 2@ G2 excludes use of Cell F2)
6				9	7	8
7	9		2	6		1	8		7		Step 5: #9 is now in Rows 1 & 2: #9 MUST go in Cell B3…
8	6	8	3		9	7	5	2	1
9		7						9
	A	B	C	D	E	F	G	H	I
1	2	1	4			9	7	6			Step 6: Complete Block AA: need #s 2 & 4…
2	3	6	7				9	4	5		#2 can't go in Cell C1 (cf #2 in Column C @ C7), so
3	8	9	5	7	4	6	2				#2 MUST go in Cell A1, & therefore #4 MUST go in Cell C1
4				1	2	5
5					6	4					Step 7: #4 is now in Rows 1 & 2: #4 MUST go in Cell E3…
6				9	7	8
7	9		2	6		1	8		7		Step 8: Complete Row 8: #4 MUST go in Cell D8...
8	6	8	3	4	9	7	5	2	1
9		7						9			Step 9: #4 is now in Columns D & E: #4 MUST go in Cell F5
	A	B	C	D	E	F	G	H	I
1	2	1	4			9	7	6			Step 10: Complete Block EE: #3 MUST go in Cell D5…
2	3	6	7				9	4	5
3	8	9	5	7	4	6	2
4				1	2	5
5				3	6	4
6				9	7	8
7	9		2	6		1	8		7
8	6	8	3	4	9	7	5	2	1
9		7						9
	A	B	C	D	E	F	G	H	I
1	2	1	4			9	7	6			Step 11: Complete Column F: need #s 2 & 3…
2	3	6	7			2	9	4	5		#3 can't go in Cell F2 (cf #3 in Row 2 @ A2), so
3	8	9	5	7	4	6	2				#3 MUST go in Cell F9, & therefore #2 MUST go in Cell F2
4				1	2	5
5				3	6	4					Step 12: #3 is now in Rows 8 & 9: #3 MUST go in Cell H7…
6				9	7	8
7	9		2	6		1	8	3	7
8	6	8	3	4	9	7	5	2	1
9		7				3		9
	A	B	C	D	E	F	G	H	I
1	2	1	4			9	7	6	8		Step 13: Complete Row 7: need #s 4 & 5…
2	3	6	7			2	9	4	5		#4 can't go in Cell E7 (cf #4 in Column E @ E3), so
3	8	9	5	7	4	6	2				#4 MUST go in Cell B7, & therefore #5 MUST go in Cell E7
4				1	2	5
5				3	6	4					Step 14: Block CC needs #8: #8 MUST go in Cell I1
6				9	7	8					(#8 in Row 3 @ A3 excludes use of Cell H3 & I3)
7	9	4	2	6	5	1	8	3	7
8	6	8	3	4	9	7	5	2	1
9		7				3		9
	A	B	C	D	E	F	G	H	I
1	2	1	4			9	7	6	8		Step 15: Complete Block CC: need #s 1 & 3…
2	3	6	7		1	2	9	4	5		#3 can't go in Cell H3 (cf #3 in Column H @ H7), so
3	8	9	5	7	4	6	2	1	3		#3 MUST go in Cell I3, & therefore #1 MUST go in Cell H3
4				1	2	5
5				3	6	4					Step 16: #1 is now in Rows 1 & 3: #1 MUST go in Cell E2
6				9	7	8					(#1 in Column D @ D4 excludes use of Cell D2)
7	9	4	2	6	5	1	8	3	7
8	6	8	3	4	9	7	5	2	1
9		7				3		9
	A	B	C	D	E	F	G	H	I
1	2	1	4			9	7	6	8		Step 17: #8 is in Rows 1 & 3: #8 MUST go in Cell D2…
2	3	6	7	8	1	2	9	4	5
3	8	9	5	7	4	6	2	1	3
4				1	2	5
5				3	6	4
6				9	7	8
7	9	4	2	6	5	1	8	3	7
8	6	8	3	4	9	7	5	2	1
9		7				3		9
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8		Step 18: Complete Block BB: need #s 3 & 5…
2	3	6	7	8	1	2	9	4	5		#3 can't go in Cell D1 (cf #3 in Column D @ D5), so
3	8	9	5	7	4	6	2	1	3		#3 MUST go in Cell E1, & therefore #5 MUST go in Cell D1
4				1	2	5
5				3	6	4					Step 19: Complete Column D: #2 MUST go in Cell D9…
6				9	7	8
7	9	4	2	6	5	1	8	3	7		Step 20: Complete Column E: #8 MUST go in Cell E9…
8	6	8	3	4	9	7	5	2	1
9		7		2	8	3		9
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8		Step 21: Complete Block GG: need #s 1 & 5…
2	3	6	7	8	1	2	9	4	5		#5 can't go in Cell C9 (cf #5 in Column C @ C3), so
3	8	9	5	7	4	6	2	1	3		#5 MUST go in Cell A9, & therefore #1 MUST go in Cell C9
4				1	2	5
5				3	6	4					NB: Can't go any farther with deductive reasoning!
6				9	7	8					Time to look at each remaining cell to see what possible #s
7	9	4	2	6	5	1	8	3	7		they can contain… you'd be surprised at what you find!
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3		9
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8		Shown in red are the possible #s for each remaining cell…
2	3	6	7	8	1	2	9	4	5		NB: Look for cells which can only have one possible #...
3	8	9	5	7	4	6	2	1	3		(i.e. for Cell G4, G4 can't contain #s 1, 2 or 5 - from Row 4,
4	4 7	3	6 8 9	1	2	5	3 4 6	7 8	4 6 9		& G4 can't contain #s 7, 9, 2, 8 or 5 - from Column G:
5	1 7	2 5	8 9	3	6	4	1	5 7 8	2 9		therefore only #s 3, 4 & 6 can go in G4…)
6	1 4	2 3 5	6	9	7	8	1 3 4 6	5	2 4 6
7	9	4	2	6	5	1	8	3	7		OBVIOUS results: #3 in B4; #6 in C6; and #1 in G5…
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3	4 6	9	4 6
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8
2	3	6	7	8	1	2	9	4	5
3	8	9	5	7	4	6	2	1	3
4		3		1	2	5
5				3	6	4	1
6			6	9	7	8
7	9	4	2	6	5	1	8	3	7
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3		9
	A	B	C	D	E	F	G	H	I		Step 22: Column G needs #3: #3 MUST go in Cell G6
1	2	1	4	5	3	9	7	6	8		(#3 in Row 4 @ B4 excludes use of Cell G4, &
2	3	6	7	8	1	2	9	4	5		#3 in Row 9 @ F9 excludes use of Cell G9)
3	8	9	5	7	4	6	2	1	3
4		3		1	2	5					Step 23: #1 is in Rows 4 & 5: #1 MUST go in Cell A6
5				3	6	4	1				(#1 in Column B @ B1 excludes use of Cell B6)
6	1		6	9	7	8	3
7	9	4	2	6	5	1	8	3	7
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3		9
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8		Step 24: Complete Column A: need #s 4 & 7…
2	3	6	7	8	1	2	9	4	5		#4 can't go in Cell A5 (cf #4 in Row 5 @ F5), so
3	8	9	5	7	4	6	2	1	3		#4 MUST go in Cell A4, & therefore #7 MUST go in Cell A5
4	4	3		1	2	5		7
5	7			3	6	4	1				Step 25: #7 is now in Rows 5 & 6: #7 MUST go in Cell H4
6	1		6	9	7	8	3				(#7 in Column G @ G1 excludes use of Cell G4, &
7	9	4	2	6	5	1	8	3	7		#7 in Column I @ I7 excludes use of Cell I4)
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3		9
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8		Step 26: Complete Column G: need #s 4 & 6…
2	3	6	7	8	1	2	9	4	5		#4 can't go in Cell G4 (cf #4 in Row 4 @ A4), so
3	8	9	5	7	4	6	2	1	3		#4 MUST go in Cell G9, & therefore #6 MUST go in Cell G4
4	4	3		1	2	5	6	7
5	7			3	6	4	1				Step 27: #6 is now in Columns G & H: #6 MUST go in Cell I9
6	1		6	9	7	8	3
7	9	4	2	6	5	1	8	3	7
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3	4	9	6
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8		Step 28: Complete Column H: need #s 5 & 8…
2	3	6	7	8	1	2	9	4	5		#8 can't go in Cell H6 (cf #8 in Row 6 @ F6), so
3	8	9	5	7	4	6	2	1	3		#8 MUST go in Cell H5, & therefore #5 MUST go in Cell H6
4	4	3	8	1	2	5	6	7
5	7			3	6	4	1	8			Step 29: #8 is now in Rows 5 & 6: #8 MUST go in Cell C4…
6	1		6	9	7	8	3	5
7	9	4	2	6	5	1	8	3	7
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3	4	9	6
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8		Step 30: Complete Row 6: need #s 2 & 4…
2	3	6	7	8	1	2	9	4	5		#4 can't go in Cell B6 (cf #4 in Row 7 @ B7), so
3	8	9	5	7	4	6	2	1	3		#4 MUST go in Cell I6, & therefore #2 MUST go in Cell B6
4	4	3	8	1	2	5	6	7
5	7			3	6	4	1	8
6	1	2	6	9	7	8	3	5	4
7	9	4	2	6	5	1	8	3	7
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3	4	9	6
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8		Step 31: Complete Block DD: need #s 5 & 9…
2	3	6	7	8	1	2	9	4	5		#9 can't go in Cell B5 (cf #9 in Column B @ B3), so
3	8	9	5	7	4	6	2	1	3		#9 MUST go in Cell C5, & therefore #5 MUST go in Cell B5
4	4	3	8	1	2	5	6	7	9
5	7	5	9	3	6	4	1	8	2		Step 32: Complete Block FF (& Puzzle): need #s 2 & 9…
6	1	2	6	9	7	8	3	5	4		#2 can't go in Cell I4 (cf #2 in Row 4 @ E4), so
7	9	4	2	6	5	1	8	3	7		#2 MUST go in Cell I5, & therefore #9 MUST go in Cell I4
8	6	8	3	4	9	7	5	2	1
9	5	7	1	2	8	3	4	9	6
	A	B	C	D	E	F	G	H	I
1	2	1	4	5	3	9	7	6	8	45	Final Proof:
2	3	6	7	8	1	2	9	4	5	45	- All Rows add up to 45;
3	8	9	5	7	4	6	2	1	3	45
4	4	3	8	1	2	5	6	7	9	45
5	7	5	9	3	6	4	1	8	2	45
6	1	2	6	9	7	8	3	5	4	45
7	9	4	2	6	5	1	8	3	7	45
8	6	8	3	4	9	7	5	2	1	45
9	5	7	1	2	8	3	4	9	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