Challenging Puzzle #44 - 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		4					Challenging Puzzle #44 - November 13, 2005
2				3	9	1					Original puzzle as published © joe-ks.com
3		2	3	6		5	7
4	9	1	6				5	8
5	8								9
6		7	2					3	4
7		8	7		1		9	4
8	3		9	7		8	2		6
9				9		6
	A	B	C	D	E	F	G	H	I
1				2		4					Step 1: #3 is in Columns A & C: #3 MUST go in Cell B5...
2				3	9	1	4
3		2	3	6		5	7				Step 2: #9 is in Columns D & E: #9 MUST go in Cell F6
4	9	1	6				5	8			(#9 in Row 4 @ A4 excludes use of Cell F4, &
5	8	3							9		#9 in Row 5 @ I5 excludes use of Cell F5)
6		7	2			9		3	4
7		8	7		1		9	4			Step 3: #4 is in Column H & I: #4 MUST go in Cell G2
8	3		9	7		8	2		6		(#4 in Row 1 @ F1 excludes use of Cell G1)
9				9		6
	A	B	C	D	E	F	G	H	I
1		9		2		4					Step 4: Complete Block DD: need #s 4 & 5…
2				3	9	1	4				#4 can't go in Cell A6 (cf #4 in Row 6 @ I6), so
3		2	3	6		5	7	9			#4 MUST go in Cell C5, & therefore #5 MUST go in Cell A6
4	9	1	6				5	8
5	8	3	4						9		Step 5: #9 is in Columns A & C: #9 MUST go in Cell B1
6	5	7	2			9		3	4		(#9 in Row 2 @ E2 exludes use of Cell B2)
7		8	7		1		9	4
8	3		9	7		8	2		6		Step 6: #9 is now in Rows 1 & 2: #9 MUST go in Cell H3
9				9		6					(#9 in Column I @ I5 excludes use of Cell I3)
	A	B	C	D	E	F	G	H	I
1		9		2	7	4					Step 7: Complete Block BB: need #s 7 & 8…
2				3	9	1	4				#7 can't go in Cell E3 (cf #7 in Row 3 @ G3), so
3		2	3	6	8	5	7	9			#7 MUST go in Cell E1, & therefore #8 MUST go in Cell E3
4	9	1	6				5	8
5	8	3	4						9		Step 8: #8 is now in Columns E & F: #8 MUST go in Cell D6
6	5	7	2	8		9		3	4		(#8 in Row 4 @ H4 excludes use of Cell D4, &
7	6	8	7		1		9	4			(#8 in Row 5 @ A5 excludes use of Cell D5)
8	3		9	7		8	2		6
9				9		6					Step 9: #6 is in Rows 8 & 9: #6 MUST go in Cell A7…
	A	B	C	D	E	F	G	H	I
1		9		2	7	4					Step 10: #7 is in Columns B & C: #7 MUST go in Cell A2
2	7			3	9	1	4				(#7 in Row 1 @ E1 excludes use of Cell A1, &
3		2	3	6	8	5	7	9			(#7 in Row 3 @ G3 excludes use of Cell A3)
4	9	1	6				5	8
5	8	3	4						9
6	5	7	2	8		9		3	4
7	6	8	7		1		9	4
8	3		9	7		8	2		6
9				9		6
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4					Step 11: What possible #s can go in A1? Look at all present #s in Row 1,
2	7			3	9	1	4				Column A AND Blcok AA: #1 is the only # that can go in A1…
3		2	3	6	8	5	7	9
4	9	1	6				5	8			Step 12: #1 is now in Columns A & B: #1 MUST go in Cell C9…
5	8	3	4						9
6	5	7	2	8		9		3	4		Step 13: #1 is now in Rows 7 & 9: #1 MUST go in Cell H8…
7	6	8	7		1		9	4
8	3		9	7		8	2	1	6
9			1	9		6
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4					Step 14: Complete Column A: need #s 2 & 4…
2	7			3	9	1	4				#2 can't go in Cell A3 (cf #2 in Row 3 @ B3), so
3	4	2	3	6	8	5	7	9	1		#2 MUST go in Cell A9, & therefore #4 MUST go in Cell A3
4	9	1	6				5	8
5	8	3	4						9		Step 15: Complete Row 3: #1 MUST go in Cell I3…
6	5	7	2	8		9		3	4
7	6	8	7		1		9	4
8	3		9	7		8	2	1	6
9	2		1	9		6
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4					Step 16: Complete Row 6: need #s 1 & 6…
2	7			3	9	1	4				#1 can't go in Cell E6 (cf #1 in Column E @ E7), so
3	4	2	3	6	8	5	7	9	1		#1 MUST go in Cell G6, & therefore #6 MUST go in Cell E6
4	9	1	6				5	8
5	8	3	4				?		9		Step 17: Look at Cell G5: only one # can go in there… ???
6	5	7	2	8	6	9	1	3	4		Hint: Look at all #s in Row 5, Column G AND Block FF…
7	6	8	7		1		9	4
8	3		9	7		8	2	1	6		… #6 MUST go in Cell G5...
9	2		1	9		6
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4					Step 18: Only one # can go in Cell D4: look at all present #s in
2	7			3	9	1	4				Row 4, Column D AND Block EE…
3	4	2	3	6	8	5	7	9	1
4	9	1	6	?			5	8			Step 19: Only one # can go in Cell D7: look at all present #s in
5	8	3	4				6		9		Row 7, Column D AND Block HH…
6	5	7	2	8	6	9	1	3	4
7	6	8	7	?	1		9	4
8	3		9	7		8	2	1	6		==> #4 MUST go in D4;   #5 MUST go in D7…
9	2		1	9		6
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4					Step 20: Complete Column D: #1 MUST go in Cell D5…
2	7			3	9	1	4
3	4	2	3	6	8	5	7	9	1
4	9	1	6	4			5	8
5	8	3	4	1			6		9
6	5	7	2	8	6	9	1	3	4
7	6	8	7	5	1		9	4
8	3		9	7		8	2	1	6
9	2		1	9		6
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4					Step 21: Only one # can go in Cell I7: look at all present #s in
2	7			3	9	1	4				Row 7, Column I AND Block II…
3	4	2	3	6	8	5	7	9	1
4	9	1	6	4			5	8			Step 22: Only one # can go in Cell E8: look at all present #s in
5	8	3	4	1			6		9		Row 8, Column E AND Block HH…
6	5	7	2	8	6	9	1	3	4
7	6	8	7	5	1		9	4	?		==> #3 MUST go in I7;   #4 MUST go in E8…
8	3		9	7	?	8	2	1	6
9	2		1	9		6
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4					Step 23: #3 is now in Rows 7 & 8: #3 MUST go in Cell E9…
2	7			3	9	1	4
3	4	2	3	6	8	5	7	9	1		Step 24: #4 is now in Rows 7 & 8: #4 MUST go in Cell B9…
4	9	1	6	4		3	5	8
5	8	3	4	1			6		9		Step 25: #3 is now in Columns D & E: #3 MUST go in Cell F4...
6	5	7	2	8	6	9	1	3	4		(#3 in Row 5 @ B5 excludes use of Cell F5)
7	6	8	7	5	1		9	4	3
8	3	5	9	7	4	8	2	1	6		Step 26: Complete Block GG: #5 MUST go in Cell B8…
9	2	4	1	9	3	6
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4	3				Step 27: Complete Column G: need #s 3 & 8…
2	7	6		3	9	1	4				#3 can't go in Cell G9 (cf #3 in Row 9 @ E9), so
3	4	2	3	6	8	5	7	9	1		#3 MUST go in Cell G1, & therefore #8 MUST go in Cell G9
4	9	1	6	4		3	5	8
5	8	3	4	1			6		9		Step 28: Complete Row 7: #2 MUST go in Cell F7...
6	5	7	2	8	6	9	1	3	4
7	6	8	7	5	1	2	9	4	3		Step 29: Complete Column B: #6 MUST go in Cell B2...
8	3	5	9	7	4	8	2	1	6
9	2	4	1	9	3	6	8
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4	3				Step 30: Complete Row 4: need #s 2 & 7…
2	7	6		3	9	1	4				#7 can't go in Cell E4 (cf #7 in Column E @ E1), so
3	4	2	3	6	8	5	7	9	1		#7 MUST go in Cell I4, & therefore #2 MUST go in Cell E4
4	9	1	6	4	2	3	5	8	7
5	8	3	4	1			6		9		Step 31: Complete Row 9: need #s 5 & 7…
6	5	7	2	8	6	9	1	3	4		#7 can't go in Cell I9 (cf #7 from Step 30 @ I4), so
7	6	8	7	5	1	2	9	4	3		#7 MUST go in Cell H9, & therefore #5 MUST go in Cell I9
8	3	5	9	7	4	8	2	1	6
9	2	4	1	9	3	6	8	7	5
	A	B	C	D	E	F	G	H	I
1	1	9		2	7	4	3		8		Step 32: Complete Column I: need #s 2 & 8…
2	7	6		3	9	1	4		2		#2 can't go in Cell I1 (cf #2 in Row 1 @ D1), so
3	4	2	3	6	8	5	7	9	1		#2 MUST go in Cell I2, & therefore #8 MUST go in Cell I1
4	9	1	6	4	2	3	5	8	7
5	8	3	4	1	5	7	6	2	9		Step 33: Complete Column E:  #5 MUST go in Cell E5...
6	5	7	2	8	6	9	1	3	4
7	6	8	7	5	1	2	9	4	3		Step 34: Completet Column F: #7 MUST go in Cell F5...
8	3	5	9	7	4	8	2	1	6
9	2	4	1	9	3	6	8	7	5		Step 35: Completet Row 5: #2 MUST go in Cell H5…
	A	B	C	D	E	F	G	H	I
1	1	9	5	2	7	4	3		8		Step 36: Complete Block AA: need #s 5 & 8…
2	7	6	8	3	9	1	4		2		#8 can't go in Cell C1 (cf #8 in Row 1 @ I1), so
3	4	2	3	6	8	5	7	9	1		#8 MUST go in Cell C2, & therefore #5 MUST go in Cell C1
4	9	1	6	4	2	3	5	8	7
5	8	3	4	1	5	7	6	2	9
6	5	7	2	8	6	9	1	3	4
7	6	8	7	5	1	2	9	4	3
8	3	5	9	7	4	8	2	1	6
9	2	4	1	9	3	6	8	7	5
	A	B	C	D	E	F	G	H	I
1	1	9	5	2	7	4	3	6	8		Step 37: Complete Block CC( & Puzzle): need #s 5 & 6…
2	7	6	8	3	9	1	4	5	2		#5 can't go in Cell H1 (cf #5 in Row 1 @ C1), so
3	4	2	3	6	8	5	7	9	1		#5 MUST go in Cell H2, & therefore #6 MUST go in Cell H1.
4	9	1	6	4	2	3	5	8	7
5	8	3	4	1	5	7	6	2	9
6	5	7	2	8	6	9	1	3	4
7	6	8	7	5	1	2	9	4	3
8	3	5	9	7	4	8	2	1	6
9	2	4	1	9	3	6	8	7	5
	A	B	C	D	E	F	G	H	I
1	1	9	5	2	7	4	3	6	8	45	Final Proof:
2	7	6	8	3	9	1	4	5	2	45	- All Rows add up to 45;
3	4	2	3	6	8	5	7	9	1	45
4	9	1	6	4	2	3	5	8	7	45
5	8	3	4	1	5	7	6	2	9	45
6	5	7	2	8	6	9	1	3	4	45
7	6	8	7	5	1	2	9	4	3	45
8	3	5	9	7	4	8	2	1	6	45
9	2	4	1	9	3	6	8	7	5	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