| Medium Puzzle #53 - 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 | 6 | 7 | 2 | 3 | Medium Puzzle #53 - November 22, 2005 | |||||||
| 2 | 5 | Original puzzle as published © joe-ks.com | ||||||||||
| 3 | 8 | 3 | 9 | 1 | 6 | |||||||
| 4 | 7 | 9 | 1 | 5 | 4 | 6 | ||||||
| 5 | 6 | 1 | 4 | 3 | 5 | 9 | ||||||
| 6 | 5 | 3 | 4 | 9 | 2 | 7 | ||||||
| 7 | 6 | 5 | 2 | 3 | 1 | |||||||
| 8 | 4 | |||||||||||
| 9 | 4 | 7 | 1 | 6 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 6 | 7 | 2 | 3 | Step 1: #6 is in Columns A & C: #6 MUST go in Cell B2 | |||||||
| 2 | 6 | 5 | (#6 in Row 1 @ D1 excludes use of Cell B1, & | |||||||||
| 3 | 8 | 3 | 9 | 1 | 6 | #6 in Row 3 @ G3 excludes use of Cell B3) | ||||||
| 4 | 7 | 9 | 1 | 5 | 4 | 6 | Step 2: #6 is in Columns D & F: #6 MUST go in Cell E6 | |||||
| 5 | 6 | 1 | 4 | 3 | 5 | 9 | (#6 in Row 4 @ H4 excludes use of Cell E4, & | |||||
| 6 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | #6 in Row 5 @ A5 excludes use of Cell E5) | ||||
| 7 | 6 | 5 | 2 | 3 | 1 | Step 3: #6 is in Columns G & H: #6 MUST go in Cell I8 | ||||||
| 8 | 4 | 6 | (#6 in Row 7 @ C7 excludes use of Cell I7, & | |||||||||
| 9 | 4 | 7 | 1 | 6 | #6 in Row 9 @ F9 excludes use of Cell I9) | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 6 | 7 | 2 | 3 | Step 4: #3 is in Rows 1 & 3: #3 MUST go in Cell A2 | |||||||
| 2 | 3 | 6 | 5 | (#3 in Column C @ C6 excludes use of Cell C2) | ||||||||
| 3 | 8 | 3 | 9 | 1 | 6 | |||||||
| 4 | 7 | 9 | 1 | 5 | 4 | 6 | Step 5: #1 is in Rows 4 & 5: #1 MUST go in Cell I6... | |||||
| 5 | 6 | 1 | 4 | 3 | 5 | 9 | ||||||
| 6 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | 1 | Step 6: Complete Block HH: need #s 8 & 9… | |||
| 7 | 6 | 5 | 2 | 3 | 1 | #9 can't go in Cell F8 (cf #9 in Column F @ F6), so | ||||||
| 8 | 9 | 4 | 8 | 6 | #9 MUST go in Cell D8, & therefore #8 MUST go in Cell F8 | |||||||
| 9 | 4 | 7 | 1 | 6 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 6 | 7 | 2 | 3 | Step 7: Complete Block DD: need #s 2 & 8… | |||||||
| 2 | 3 | 6 | 5 | #2 can't go in Cell A6 (cf #2 in Row 6 @ G6), so | ||||||||
| 3 | 8 | 3 | 9 | 1 | 6 | #2 MUST go in Cell A4, & therefore #8 MUST go in Cell A6 | ||||||
| 4 | 2 | 7 | 9 | 1 | 5 | 4 | 6 | 8 | ||||
| 5 | 6 | 1 | 4 | 2 | 3 | 5 | 9 | Step 8: #2 is now in Rows 4 & 6: #2 MUST go in Cell D5 | ||||
| 6 | 8 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | 1 | (#2 in Column E @ E7 excludes use of Cell E5, & | ||
| 7 | 6 | 5 | 2 | 3 | 1 | #2 in Column F @ F1 excludes use of Cell F5) | ||||||
| 8 | 9 | 4 | 8 | 6 | ||||||||
| 9 | 4 | 7 | 1 | 6 | Step 9: Complete Block FF: #8 MUST go in Cell I4… | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 6 | 7 | 2 | 3 | Step 9: Block EE needs #3: #3 MUST go in Cell E4 | |||||||
| 2 | 3 | 6 | 8 | 5 | (#3 in Row 5 @ G5 excludes use of Cells E5 & F5) | |||||||
| 3 | 8 | 3 | 9 | 1 | 6 | |||||||
| 4 | 2 | 7 | 9 | 1 | 3 | 5 | 4 | 6 | 8 | Step 10: Complete Column D: #8 MUST go in Cell D2... | ||
| 5 | 6 | 1 | 4 | 2 | 8 | 7 | 3 | 5 | 9 | |||
| 6 | 8 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | 1 | Step 11: #8 is now in Columns D & F: #8 MUST go in Cell E5... | ||
| 7 | 6 | 5 | 2 | 3 | 1 | |||||||
| 8 | 9 | 4 | 8 | 6 | Step 12: Complete Block EE: #7 MUST go in Cell F5... | |||||||
| 9 | 4 | 7 | 1 | 6 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 6 | 7 | 2 | 3 | Step 13: Complete Block BB: #4 MUST go in Cell F2... | |||||||
| 2 | 3 | 6 | 8 | 5 | 4 | |||||||
| 3 | 8 | 3 | 9 | 1 | 6 | |||||||
| 4 | 2 | 7 | 9 | 1 | 3 | 5 | 4 | 6 | 8 | |||
| 5 | 6 | 1 | 4 | 2 | 8 | 7 | 3 | 5 | 9 | |||
| 6 | 8 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | 1 | |||
| 7 | 6 | 5 | 2 | 3 | 1 | |||||||
| 8 | 9 | 4 | 8 | 6 | ||||||||
| 9 | 4 | 7 | 1 | 6 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 159 | 49 | 15 | 6 | 7 | 2 | 589 | 1489 | 3 | Step 14: Look at all possible #s for vacant cells… | ||
| 2 | 3 | 6 | 127 | 8 | 5 | 4 | 79 | 129 | 27 | |||
| 3 | 57 | 24 | 8 | 3 | 9 | 1 | 6 | 24 | 2457 | TWINNING: Look for "twin" cells: I.e. in Row 3, there are 2 twin | ||
| 4 | 2 | 7 | 9 | 1 | 3 | 5 | 4 | 6 | 8 | cells containing #s 2 & 4 (@ Cells B3 & H3). "Twin Cells" | ||
| 5 | 6 | 1 | 4 | 2 | 8 | 7 | 3 | 5 | 9 | indicate #s that cannot go in any other cell (I.e. #s 2 or 4 | ||
| 6 | 8 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | 1 | can't go in any other cell along Row 3): therefore, Cell I3 | ||
| 7 | 79 | 89 | 6 | 5 | 2 | 3 | 1 | 489 | 47 | can be reduced to available #s 5 & 7 only: that means that #4 | ||
| 8 | 157 | 23 | 1257 | 9 | 4 | 8 | 57 | 23 | 6 | can only go in Block CC in Column H: that means that in Block | ||
| 9 | 4 | 2389 | 25 | 7 | 1 | 6 | 589 | 2389 | 25 | II, #4 can't go in Column H and can only go in Cell I7... | ||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 9 | 6 | 7 | 2 | 3 | Step 15: Look at Row 7: Row 7 needs #7 - #7 MUST go in A7 | ||||||
| 2 | 3 | 6 | 8 | 5 | 4 | (cf #7 in Column B @ B4 excludes use of Cell B7, & | ||||||
| 3 | 8 | 3 | 9 | 1 | 6 | #7 in Column H @ H6 excludes use of Cell H7) | ||||||
| 4 | 2 | 7 | 9 | 1 | 3 | 5 | 4 | 6 | 8 | |||
| 5 | 6 | 1 | 4 | 2 | 8 | 7 | 3 | 5 | 9 | Step 16: Column A needs #9: #9 MUST go in Cell A1 | ||
| 6 | 8 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | 1 | (#9 in Row 3 @ E3 excludes use of Cell A3, & | ||
| 7 | 7 | 6 | 5 | 2 | 3 | 1 | 4 | #9 in Row 8 @ D8 excludes use of Cell A8) | ||||
| 8 | 9 | 4 | 8 | 6 | ||||||||
| 9 | 4 | 7 | 1 | 6 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 9 | 6 | 7 | 2 | 5 | 3 | Step 17: Complete Column A: need #s 1 & 5… | |||||
| 2 | 3 | 6 | 8 | 5 | 4 | #1 can't go in Cell A3 (cf #1 in Row 3 @ F3), so | ||||||
| 3 | 5 | 8 | 3 | 9 | 1 | 6 | #1 MUST go in Cell A8, & therefore #5 MUSt go in Cell A3 | |||||
| 4 | 2 | 7 | 9 | 1 | 3 | 5 | 4 | 6 | 8 | |||
| 5 | 6 | 1 | 4 | 2 | 8 | 7 | 3 | 5 | 9 | Step 18: #5 is now in Rows 2 & 3: #5 MUST go in Cell G1 | ||
| 6 | 8 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | 1 | (#5 in Column H @ H5 excludes use of Cell H1) | ||
| 7 | 7 | 6 | 5 | 2 | 3 | 1 | 4 | |||||
| 8 | 1 | 9 | 4 | 8 | 6 | Step 19: #5 is now in Columns G & H: #5 MUST go in Cell I9... | ||||||
| 9 | 4 | 7 | 1 | 6 | 5 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 9 | 6 | 7 | 2 | 5 | 8 | 3 | Step 20: #8 is in Rows 2 & 3: #8 MUST go in Cell H1... | ||||
| 2 | 3 | 6 | 8 | 5 | 4 | |||||||
| 3 | 5 | 8 | 3 | 9 | 1 | 6 | Step 21: #8 is now in Columns H & I: #8 MUST go in Cell G9 | |||||
| 4 | 2 | 7 | 9 | 1 | 3 | 5 | 4 | 6 | 8 | (#8 in Row 8 @ F8 excludes use of Cell G8) | ||
| 5 | 6 | 1 | 4 | 2 | 8 | 7 | 3 | 5 | 9 | |||
| 6 | 8 | 5 | 3 | 4 | 6 | 9 | 2 | 7 | 1 | Step 22: #8 is now in Rows 8 & 9: #8 MUST go in Cell B7... | ||
| 7 | 7 | 8 | 6 | 5 | 2 | 3 | 1 | 4 | ||||
| 8 | 1 | 9 | 4 | 8 | 6 | |||||||
| 9 | 4 | 7 | 1 | 6 | 8 | 5 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 9 | 4 | 1 | 6 | 7 | 2 | 5 | 8 | 3 | Step 23: Complete Column G: need #s 7 & 9… | ||
| 2 | 3 | 6 | 8 | 5 | 4 | 9 | ||||||