| Challenging Puzzle #45 - 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 | 8 | 7 | Challenging Puzzle #45 - November 14, 2005 | |||||||||
| 2 | 7 | 3 | 2 | Original puzzle as published © joe-ks.com | ||||||||
| 3 | 9 | 2 | 7 | 4 | ||||||||
| 4 | 1 | 4 | 9 | 7 | ||||||||
| 5 | 3 | 6 | ||||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 3 | 1 | 9 | 4 | ||||||||
| 8 | 4 | 3 | 5 | 6 | 8 | |||||||
| 9 | 9 | 6 | ||||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 7 | Step 1: #3 is in Columns A & B: #3 MUST go in Cell C1... | ||||||||
| 2 | 7 | 3 | 2 | |||||||||
| 3 | 9 | 2 | 7 | 3 | 4 | Step 2: #3 is now in Rows 1 & 2: #3 MUST go in Cell H3... | ||||||
| 4 | 1 | 4 | 3 | 9 | 7 | |||||||
| 5 | 3 | 6 | Step 3: #3 is now in Columns H & I: #3 MUST go in Cell G9... | |||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 3 | 1 | 9 | 4 | Step 4: #3 is in Rows 5 & 6: #3 MUST go in Cell F4 | |||||||
| 8 | 4 | 3 | 5 | 6 | 8 | |||||||
| 9 | 9 | 6 | 3 | |||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | Step 4: #2 is in Rows 2 & 3: #2 MUST go in Cell E1... | |||||||
| 2 | 7 | 3 | 2 | |||||||||
| 3 | 9 | 2 | 7 | 3 | 4 | Step 5: #4 is in Rows 7 & 8: #4 MUST go in Cell E9... | ||||||
| 4 | 1 | 4 | 3 | 9 | 7 | |||||||
| 5 | 3 | 6 | Step 6: Block HH needs #1: #1 MUST go in Cell E8 | |||||||||
| 6 | 7 | 2 | 5 | 3 | (#1 in Row 7 @ C7 excludes use of Cells D7, E7 & F7) | |||||||
| 7 | 3 | 1 | 9 | 4 | ||||||||
| 8 | 4 | 3 | 1 | 5 | 6 | 8 | ||||||
| 9 | 9 | 4 | 6 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | Step 7: Look @ Cell F3: only #1 can go in F3... | |||||||
| 2 | 7 | 3 | 2 | |||||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | ||||||
| 4 | 1 | 4 | 3 | 9 | 7 | |||||||
| 5 | 3 | 6 | ||||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 3 | 1 | 9 | 4 | ||||||||
| 8 | 4 | 3 | 1 | 5 | 6 | 8 | ||||||
| 9 | 9 | 4 | 6 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | Step 8: Look @ Cell G4: only #8 can go in G4... | |||||||
| 2 | 7 | 3 | 2 | |||||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | ||||||
| 4 | 1 | 4 | 3 | 8 | 9 | 7 | ||||||
| 5 | 3 | 6 | ||||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 3 | 1 | 9 | 4 | ||||||||
| 8 | 4 | 3 | 1 | 5 | 6 | 8 | ||||||
| 9 | 9 | 4 | 6 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | Step 9: Look @ Cell A8: only #2 can go in A8... | |||||||
| 2 | 7 | 3 | 2 | |||||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | ||||||
| 4 | 1 | 4 | 3 | 8 | 9 | 7 | ||||||
| 5 | 3 | 6 | ||||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 3 | 1 | 9 | 4 | ||||||||
| 8 | 2 | 4 | 3 | 1 | 5 | 6 | 8 | |||||
| 9 | 9 | 4 | 6 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | Step 10: Look @ Cell H8: only #7 can go in H8... | |||||||
| 2 | 7 | 3 | 2 | |||||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | ||||||
| 4 | 1 | 4 | 3 | 8 | 9 | 7 | ||||||
| 5 | 3 | 6 | ||||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 3 | 1 | 9 | 4 | ||||||||
| 8 | 2 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | ||||
| 9 | 9 | 4 | 6 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | Step 11: Complete Row 8: #9 MUST go in Cell B8... | |||||||
| 2 | 7 | 3 | 2 | |||||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | ||||||
| 4 | 1 | 4 | 3 | 8 | 9 | 7 | ||||||
| 5 | 3 | 6 | ||||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 3 | 1 | 9 | 4 | ||||||||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 456 | 156 | 3 | 8 | 2 | 7 | 15 | 16 | 159 | Look at all possibilites for vacant cells… | ||
| 2 | 4568 | 1568 | 7 | 456 | 3 | 49 | 2 | 168 | 159 | Step 12: in Block BB, #9 is unique to Block: #9 MUST go in F2 | ||
| 3 | 9 | 568 | 2 | 56 | 56 | 1 | 7 | 3 | 4 | Step 13: in Block CC, #8 is unique to Block: #8 MUST go in H2 | ||
| 4 | 1 | 4 | 56 | 256 | 56 | 3 | 8 | 9 | 7 | Step 14: in Block DD, #6 is unique to Block: #6 MUST go in C4 | ||
| 5 | 3 | 58 | 589 | 12457 | 5789 | 2489 | 14 | 12 | 6 | Step 15: in Block FF, #2 is unique to Block: #2 MUST go in H5 | ||
| 6 | 7 | 2 | 689 | 146 | 689 | 489 | 14 | 5 | 3 | |||
| 7 | 568 | 3 | 1 | 27 | 78 | 28 | 9 | 4 | 25 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 58 | 578 | 58 | 9 | 4 | 6 | 3 | 12 | 125 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | ||||||||
| 2 | 7 | 3 | 9 | 2 | 8 | |||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | ||||||
| 4 | 1 | 4 | 6 | 3 | 8 | 9 | 7 | |||||
| 5 | 3 | 2 | 6 | |||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 3 | 1 | 9 | 4 | ||||||||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | 9 | Step 16: #9 is in Rows 2 & 3: #9 MUST go in Cell I1 | ||||||
| 2 | 7 | 3 | 9 | 2 | 8 | (#9 in Column G @ G7 excludes use of Cell G1, & | ||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | #9 in Column H @ H4 excludes use of Cell H1) | |||||
| 4 | 1 | 4 | 6 | 3 | 8 | 9 | 7 | |||||
| 5 | 3 | 2 | 6 | Step 17: #6 is in Rows 8 & 9: #6 MUST go in Cell A7... | ||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 6 | 3 | 1 | 9 | 4 | |||||||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | 6 | 9 | Step 18: Complete Column H: need #s 1 & 6… | |||||
| 2 | 7 | 3 | 9 | 2 | 8 | #6 can't go in Cell H9 (cf #6 in Row 9 @ F9), so | ||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | #6 MUST go in Cell H1, & therefore #1 MUST go in Cell H9 | |||||
| 4 | 1 | 4 | 6 | 3 | 8 | 9 | 7 | |||||
| 5 | 3 | 2 | 6 | |||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 6 | 3 | 1 | 9 | 4 | |||||||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | 6 | 9 | Step 19: Look @ Cell E4: only #5 can go in E4... | |||||
| 2 | 7 | 3 | 9 | 2 | 8 | |||||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | Step 20: Complete Row 4: #2 MUST go in Cell D4... | |||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 2 | 6 | Step 21: #2 is now in Columns D & E: #2 MUST go in Cell F7... | ||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 6 | 3 | 1 | 2 | 9 | 4 | Step 22: #2 is now in Rows 7 & 8: #2 MUST go in Cell I9... | |||||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | 1 | 2 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 23: Complete Column I: need #s 1 & 5… | ||||
| 2 | 7 | 3 | 9 | 2 | 8 | 1 | #1 can't go in Cell I7 (cf #1 in Row 7 @ C7), so | |||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | #1 MUST go in Cell I2, & therefore #5 MUST go in Cell I7 | |||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 2 | 6 | Step 24: #5 is now in Columns H & I: #5 MUST go in Cell G1... | ||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 6 | 3 | 1 | 2 | 9 | 4 | 5 | |||||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | 1 | 2 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 25: Complete Row 7: need #s 7 & 8… | ||||
| 2 | 7 | 3 | 9 | 2 | 8 | 1 | #8 can't go in Cell D7 (cf #8 in Column D @ D1), so | |||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | #8 MUST go in Cell E7, & therefore #7 MUST go in Cell D7 | |||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 2 | 6 | |||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | 1 | 2 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 26: #1 is in Columns A & C: #1 MUST go in Cell B1 | |||
| 2 | 7 | 3 | 9 | 2 | 8 | 1 | (#1 in Row 2 @ I2 excludes use of Cell B2, & | |||||
| 3 | 9 | 2 | 1 | 7 | 3 | 4 | #1 in Row 3 @ F3 excludes use of Cell B3) | |||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 2 | 6 | |||||||||
| 6 | 7 | 2 | 5 | 3 | ||||||||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | 1 | 2 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 27: Look @ Cell E3: only #6 can go in Cell E3… | ||
| 2 | 7 | 3 | 9 | 2 | 8 | 1 | ||||||
| 3 | 9 | 2 | 6 | 1 | 7 | 3 | 4 | Step 28: #6 is now in Columns E & F: #6 MUST go in Cell D6 | ||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | (cf #6 in Row 5 @ I5 excludes use of Cell D5) | ||
| 5 | 3 | 2 | 6 | |||||||||
| 6 | 7 | 2 | 6 | 5 | 3 | Step 29: Complete Row 1: #4 MUST go in Cell A1… | ||||||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 9 | 4 | 6 | 3 | 1 | 2 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 30: Complete Column A: need #s 5 & 8… | ||
| 2 | 5 | 7 | 3 | 9 | 2 | 8 | 1 | #8 can't go in Cell A2 (cf #8 in Row 2 @ H2), so | ||||
| 3 | 9 | 2 | 6 | 1 | 7 | 3 | 4 | #8 MUST go in Cell A9, & therefore #5 MUST go in Cell A2 | ||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 2 | 6 | |||||||||
| 6 | 7 | 2 | 6 | 5 | 3 | |||||||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 8 | 9 | 4 | 6 | 3 | 1 | 2 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 31: Complete Row 9: need #s 5 & 7… | ||
| 2 | 5 | 7 | 3 | 9 | 2 | 8 | 1 | #7 can't go in Cell C9 (cf #7 in Column C @ C2), so | ||||
| 3 | 9 | 2 | 6 | 1 | 7 | 3 | 4 | #7 MUST go in Cell B9, & therefore #5 MUST go in Cell C9 | ||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 7 | 2 | 6 | Step 32: Complete Column E: need #s 7 & 9… | |||||||
| 6 | 7 | 2 | 6 | 9 | 5 | 3 | #7 can't go in Cell E6 (cf #7 in Row 6 @ A6), so | |||||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | #7 MUST go in Cell E5, & therefore #9 MUST go in Cell E6 | ||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 8 | 7 | 5 | 9 | 4 | 6 | 3 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 33: Complete Column C: need #s 8 & 9… | ||
| 2 | 5 | 7 | 3 | 9 | 2 | 8 | 1 | #9 can't go in Cell C6 (cf #9 in Row 6 @ E6), so | ||||
| 3 | 9 | 2 | 6 | 1 | 7 | 3 | 4 | #9 MUST go in Cell C5, & therefore #8 MUST go in Cell C6 | ||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 9 | 7 | 2 | 6 | |||||||
| 6 | 7 | 2 | 8 | 6 | 9 | 5 | 3 | |||||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 8 | 7 | 5 | 9 | 4 | 6 | 3 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 34: Complete Column F: need #s 4 & 8… | ||
| 2 | 5 | 7 | 3 | 9 | 2 | 8 | 1 | #8 can't go in Cell F6 (cf #8 in Row 6 @ C6), so | ||||
| 3 | 9 | 2 | 6 | 1 | 7 | 3 | 4 | #8 MUST go in Cell F5, & therefore #4 MUST go in Cell F6 | ||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 9 | 7 | 8 | 4 | 2 | 6 | Step 35: Complete Row 6: #1 MUST go in Cell G6... | ||||
| 6 | 7 | 2 | 8 | 6 | 9 | 4 | 1 | 5 | 3 | |||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | Step 36: Complete Column G: #4 MUST go in Cell G5... | ||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 8 | 7 | 5 | 9 | 4 | 6 | 3 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 37: Complete Row 5: need #s 1 & 5… | ||
| 2 | 5 | 7 | 3 | 9 | 2 | 8 | 1 | #1 can't go in Cell B5 (cf #1 in Column B @ B1), so | ||||
| 3 | 9 | 2 | 6 | 1 | 7 | 3 | 4 | #1 MUST go in Cell D5, & therefore #5 MUST go in Cell B5 | ||||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 5 | 9 | 1 | 7 | 8 | 4 | 2 | 6 | |||
| 6 | 7 | 2 | 8 | 6 | 9 | 4 | 1 | 5 | 3 | |||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 8 | 7 | 5 | 9 | 4 | 6 | 3 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 38: Complete Row 3: need #s 5 & 8… | ||
| 2 | 5 | 7 | 3 | 9 | 2 | 8 | 1 | #5 can't go in Cell B3 (cf #5 in Column B @ B5), so | ||||
| 3 | 9 | 8 | 2 | 5 | 6 | 1 | 7 | 3 | 4 | #5 MUST go in Cell D3, & therefore #8 MUST go in Cell B3 | ||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 5 | 9 | 1 | 7 | 8 | 4 | 2 | 6 | |||
| 6 | 7 | 2 | 8 | 6 | 9 | 4 | 1 | 5 | 3 | |||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 8 | 7 | 5 | 9 | 4 | 6 | 3 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | Step 39: Complete Row 2 (& Puzzle): need #s 4 & 6… | ||
| 2 | 5 | 6 | 7 | 4 | 3 | 9 | 2 | 8 | 1 | #4 can't go in Cell B2 (cf #4 in Column B @ B4), so | ||
| 3 | 9 | 8 | 2 | 5 | 6 | 1 | 7 | 3 | 4 | #4 MUST go in Cell D2, & therefore #6 MUST go in Cell B2 | ||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | |||
| 5 | 3 | 5 | 9 | 1 | 7 | 8 | 4 | 2 | 6 | |||
| 6 | 7 | 2 | 8 | 6 | 9 | 4 | 1 | 5 | 3 | |||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | |||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | |||
| 9 | 8 | 7 | 5 | 9 | 4 | 6 | 3 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 1 | 3 | 8 | 2 | 7 | 5 | 6 | 9 | 45 | Final Proof: | |
| 2 | 5 | 6 | 7 | 4 | 3 | 9 | 2 | 8 | 1 | 45 | - All Rows add up to 45; | |
| 3 | 9 | 8 | 2 | 5 | 6 | 1 | 7 | 3 | 4 | 45 | ||
| 4 | 1 | 4 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | 45 | ||
| 5 | 3 | 5 | 9 | 1 | 7 | 8 | 4 | 2 | 6 | 45 | ||
| 6 | 7 | 2 | 8 | 6 | 9 | 4 | 1 | 5 | 3 | 45 | ||
| 7 | 6 | 3 | 1 | 7 | 8 | 2 | 9 | 4 | 5 | 45 | ||
| 8 | 2 | 9 | 4 | 3 | 1 | 5 | 6 | 7 | 8 | 45 | ||
| 9 | 8 | 7 | 5 | 9 | 4 | 6 | 3 | 1 | 2 | 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 | ||||||||||
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