Medium Puzzle #49 - 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				7				2		Medium Puzzle #49 - November 18, 2005
2		3			9			4			Original puzzle as published © joe-ks.com
3			6		8		3
4	1			5	2	7			9
5	8	7	9	1	6	3	4	2	5
6	5			8	4	9			3
7			4		1		8
8		2			3			7
9	6				5				1
	A	B	C	D	E	F	G	H	I
1	4			3	7				2		Step 1: #3 is in Rows 2 & 3: #3 MUST go in Cell D1
2		3			9			4			(#3 in Column F @ F5 excludes use of Cell F1)
3			6		8		3
4	1			5	2	7		8	9		Step 2: #8 is in Rows 5 & 6: #8 MUST go in Cell H4
5	8	7	9	1	6	3	4	2	5		(#8 in Column G @ G7 excludes use of Cell G4)
6	5			8	4	9			3
7			4		1		8				Step 3: #1 is in Rows 7 & 9: #1 MUST go in Cell C8
8		2	1		3			7			(#1 in Column A @ A4 excludes use of Cell A8)
9	6				5				1
	A	B	C	D	E	F	G	H	I
1	4			3	7				2		Step 4: #4 is in Columns A & C: #4 MUST go in Cell B4
2		3			9			4			(#4 in Row 6 @ E6 excludes use of Cell B6)
3			6		8		3
4	1	4		5	2	7		8	9		Step 5: #2 is in Columns H & I: #2 MUST go in Cell G9
5	8	7	9	1	6	3	4	2	5		(#2 in Row 8 @ B8 excludes use of Cell G8)
6	5			8	4	9			3
7			4		1		8
8		2	1		3			7
9	6				5		2		1
	A	B	C	D	E	F	G	H	I
1	4			3	7				2		Step 6: #6 is in Columns A & C: #6 MUST go in Cell B6...
2		3			9			4
3			6		8		3				Step 7: #6 is now in Rows 5 & 6: #6 MUST go in Cell G4...
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5		Step 8: Complete Row 4: #3 MUST go in Cell C4...
6	5	6		8	4	9			3
7			4		1		8
8		2	1		3			7
9	6				5		2		1
	A	B	C	D	E	F	G	H	I
1	4			3	7				2		Step 9: Complete Block DD: #2 MUST go in Cell C6...
2		3			9			4
3			6		8		3				Step 10: Complete Block FF: need #s 1 & 7…
4	1	4	3	5	2	7	6	8	9		#7 can't go in Cell H6 (cf #7 in Column H @ H8), so
5	8	7	9	1	6	3	4	2	5		#7 MUST go in Cell G6, & therefore #1 MUST go in Cell H6
6	5	6	2	8	4	9	7	1	3
7			4		1		8
8		2	1		3			7
9	6				5		2		1
	A	B	C	D	E	F	G	H	I
1	4			3	7				2		Step 11: #4 is in Columns G& H: #4 MUST go in Cell I8
2		3			9			4			(#4 in Row 7 @ C7 excludes use of Cell I7)
3			6		8		3
4	1	4	3	5	2	7	6	8	9		Step 12: #3 is in Columns B & C: #3 MUST go in Cell A7
5	8	7	9	1	6	3	4	2	5		(#3 in Row 8 @ E8 excludes use of Cell A8)
6	5	6	2	8	4	9	7	1	3
7	3		4		1		8				Step 13: #3 is now in Rows 7 & 8: #3 MUST go in Cell H9...
8		2	1		3			7	4
9	6				5		2	3	1
	A	B	C	D	E	F	G	H	I
1	4			3	7				2		Step 14: #8 is in Columns G & H: #8 MUST go in Cell I2
2		3			9			4	8		(#8 in Row 3 @ E3 excludes use of Cell I3)
3			6		8		3
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5
6	5	6	2	8	4	9	7	1	3
7	3		4		1		8
8		2	1		3			7	4
9	6				5		2	3	1
	A	B	C	D	E	F	G	H	I
1	4			3	7				2		Step 15: Complete Column I: need #s 6 & 7…
2		3			9			4	8		#6 can't go in Cell I3 (cf #6 in Row 3 @ C3), so
3			6		8		3		7		#6 MUST go in Cell I7, & therefore #7 MUST go in Cell I3
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5
6	5	6	2	8	4	9	7	1	3
7	3		4		1		8		6
8		2	1		3			7	4
9	6				5		2	3	1
	A	B	C	D	E	F	G	H	I
1	4		58	3	7				2		Look at all # possibilities for each vacant cell…
2		3			9			4	8		i.e. the only #s that can go in Cell C1 are:
3			6		8		3		7		Look at all #s presently in Row 1 (4,3,7,2), Block AA (4,3,6) &
4	1	4	3	5	2	7	6	8	9		Column C (6,3,9,2,4,1)
5	8	7	9	1	6	3	4	2	5		Only #s 5 & 8 can go in Cell C1… (see red #s in C1)
6	5	6	2	8	4	9	7	1	3
7	3		4		1		8		6
8		2	1		3			7	4
9	6				5		2	3	1
	A	B	C	D	E	F	G	H	I
1	4	1589	58	3	7	156	159	569	2		Step 16: Here are all the possible #s for each remaining cell…
2	27	3	57	26	9	1256	15	4	8		Look for the "unique" #s:
3	29	159	6	24	8	1245	3	59	7		Cell H1:  #6 is unique to all remaining Block CC #s
4	1	4	3	5	2	7	6	8	9		#6 MUST go in Cell H1...
5	8	7	9	1	6	3	4	2	5		Block GG: #9 MUSTgo in Cell A8; #5 MUST go in Cell B7, &
6	5	6	2	8	4	9	7	1	3		#8 MUST go in Cell B9...
7	3	59	4	279	1	2	8	59	6		Block HH: #2 MUST go in Cell F7...
8	9	2	1	69	3	68	59	7	4
9	6	89	78	479	5	48	2	3	1
	A	B	C	D	E	F	G	H	I
1	4			3	7			6	2		… after Step 16…
2		3			9			4	8
3			6		8		3		7
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5
6	5	6	2	8	4	9	7	1	3
7	3	5	4		1	2	8		6
8	9	2	1		3			7	4
9	6	8			5		2	3	1
	A	B	C	D	E	F	G	H	I
1	4			3	7			6	2		Step 17: Complete Column A: need #s 2 & 7…
2	7	3		2	9			4	8		#7 can't go in Cell A3 (cf #7 in Row 3 @ I3), so
3	2		6		8		3		7		#7 MUST go in Cell A2, & therefore #2 MUST go in Cell A3
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5		Step 18: #2 is now in Rows 1 & 3: #2 MUST go in Cell D2
6	5	6	2	8	4	9	7	1	3		(#3 in Column F @ F7 excludes use of Cell F2)
7	3	5	4		1	2	8		6
8	9	2	1		3			7	4
9	6	8			5		2	3	1
	A	B	C	D	E	F	G	H	I
1	4			3	7			6	2		Step 19: Complete Column H: need #s 5 & 9…
2	7	3		2	9			4	8		#5 can't go in Cell H7 (cf #5 in Row 7 @ B7), so
3	2		6		8		3	5	7		#5 MUST go in Cell H3, & therefore #9 MUST go in Cell H7
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5		Step 20: Complete Row 7: #7 MUST go in Cell D7...
6	5	6	2	8	4	9	7	1	3
7	3	5	4	7	1	2	8	9	6		Step 21: #7 is now in Rows 7 & 8: #7 MUST go in Cell C9...
8	9	2	1		3			7	4
9	6	8	7		5		2	3	1
	A	B	C	D	E	F	G	H	I
1	4			3	7			6	2		Step 22: Complete Row 9: need #s 4 & 9…
2	7	3		2	9			4	8		#9 can't go in Cell F9 (cf #9 in Column F @ F6), so
3	2		6	4	8		3	5	7		#9 MUST go in Cell D9, & therefore #4 MUST go in Cell F9
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5		Step 23: #4 is now in Columns E & F: #4 MUST go in Cell D3...
6	5	6	2	8	4	9	7	1	3
7	3	5	4	7	1	2	8	9	6
8	9	2	1		3			7	4
9	6	8	7	9	5	4	2	3	1
	A	B	C	D	E	F	G	H	I
1	4			3	7			6	2		Step 24: Complete Column D: #6 MUST go in Cell D8...
2	7	3		2	9	6		4	8
3	2		6	4	8		3	5	7		Step 25: #6 is now in Columns D & E: #6 MUST go in Cell F2
4	1	4	3	5	2	7	6	8	9		(#6 in Row 1 @ H1 excludes use of Cell F1, &
5	8	7	9	1	6	3	4	2	5		#6 in Row 3 @ C3 excludes use of Cell F3)
6	5	6	2	8	4	9	7	1	3
7	3	5	4	7	1	2	8	9	6
8	9	2	1	6	3			7	4
9	6	8	7	9	5	4	2	3	1
	A	B	C	D	E	F	G	H	I
1	4		8	3	7		9	6	2		Step 26: Complete Column C: need #s 5 & 8…
2	7	3	5	2	9	6	1	4	8		#8 can't go in Cell C2 (cf #8 in Row 2 @ I2), so
3	2		6	4	8		3	5	7		#8 MUST go in Cell C1, & therefore #5 MUST go in Cell C2
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5		Step 27: Complete Row 2: #1 MUST go in Cell G2...
6	5	6	2	8	4	9	7	1	3
7	3	5	4	7	1	2	8	9	6		Step 28: Complete Block CC: #9 MUST go in Cell G1...
8	9	2	1	6	3		5	7	4
9	6	8	7	9	5	4	2	3	1		Step 29: Complete Column G: #5 MUST go in Cell G8...
	A	B	C	D	E	F	G	H	I
1	4		8	3	7		9	6	2		Step 30: Complete Row 8: #8 MUST go in Cell F8...
2	7	3	5	2	9	6	1	4	8
3	2		6	4	8		3	5	7
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5
6	5	6	2	8	4	9	7	1	3
7	3	5	4	7	1	2	8	9	6
8	9	2	1	6	3	8	5	7	4
9	6	8	7	9	5	4	2	3	1
	A	B	C	D	E	F	G	H	I
1	4	1	8	3	7		9	6	2		Step 31: Complete Block AA: need #s 1 & 9…
2	7	3	5	2	9	6	1	4	8		#9 can't go in Cell B1 (cf #9 in Row 1 @ G1), so
3	2	9	6	4	8		3	5	7		#9 MUST go in Cell B3, & therefore #1 MUST go in Cell B1
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5
6	5	6	2	8	4	9	7	1	3
7	3	5	4	7	1	2	8	9	6
8	9	2	1	6	3	8	5	7	4
9	6	8	7	9	5	4	2	3	1
	A	B	C	D	E	F	G	H	I
1	4	1	8	3	7	5	9	6	2		Step 32: Complete Block BB (& Puzzle): need #s 1 & 5…
2	7	3	5	2	9	6	1	4	8		#5 can't go in Cell F3 (cf #5 in Row 3 @ H3), so
3	2	9	6	4	8	1	3	5	7		#5 MUST go in Cell F1, & therefore #1 MUST go in Cell F3
4	1	4	3	5	2	7	6	8	9
5	8	7	9	1	6	3	4	2	5
6	5	6	2	8	4	9	7	1	3
7	3	5	4	7	1	2	8	9	6
8	9	2	1	6	3	8	5	7	4
9	6	8	7	9	5	4	2	3	1
	A	B	C	D	E	F	G	H	I
1	4	1	8	3	7	5	9	6	2	45	Final Proof:
2	7	3	5	2	9	6	1	4	8	45	- All Rows add up to 45;
3	2	9	6	4	8	1	3	5	7	45
4	1	4	3	5	2	7	6	8	9	45
5	8	7	9	1	6	3	4	2	5	45
6	5	6	2	8	4	9	7	1	3	45
7	3	5	4	7	1	2	8	9	6	45
8	9	2	1	6	3	8	5	7	4	45
9	6	8	7	9	5	4	2	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