| Easy Puzzle #18 - One Possible Solution Approach… | ||||||||||||
| NB: There is only one final solution to this Sudoku puzzle… | ||||||||||||
| Rules: Place a number from 1-9 in each empty cell so that each row, each column AND each 3x3 block contains all the numbers from 1-9. | ||||||||||||
| 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 | 6 | 5 | Easy Puzzle #18 - October 18, 2005 | |||||||
| 2 | 9 | 6 | 3 | 1 | 4 | Original puzzle as published on joe-ks.com… | ||||||
| 3 | 8 | 7 | 9 | 3 | ||||||||
| 4 | 2 | 5 | 4 | 9 | ||||||||
| 5 | 7 | 2 | 5 | 1 | 4 | |||||||
| 6 | 1 | 8 | 2 | |||||||||
| 7 | 3 | 8 | 1 | 2 | 6 | |||||||
| 8 | 4 | 6 | 3 | 1 | ||||||||
| 9 | 6 | 2 | 3 | 7 | 9 | 8 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 7 | 6 | 5 | Step 1: #4 is in Rows 1 & 2: #4 MUST go in Cell D3… | |||||||
| 2 | 9 | 6 | 3 | 1 | 4 | |||||||
| 3 | 8 | 4 | 7 | 9 | 3 | |||||||
| 4 | 2 | 5 | 4 | 9 | Step 2: #4 is in Rows 4 & 5: #4 MUST go in Cell A6 | |||||||
| 5 | 7 | 2 | 5 | 1 | 4 | (cf #4 is Column B @ B1 excludes use of Cell B6) | ||||||
| 6 | 4 | 1 | 8 | 2 | ||||||||
| 7 | 3 | 8 | 1 | 2 | 6 | Step 3: #1 is in Rows 7 & 8: #1 MUST go in Cell A9… | ||||||
| 8 | 4 | 6 | 3 | 1 | ||||||||
| 9 | 1 | 6 | 2 | 3 | 7 | 9 | 8 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 7 | 6 | 9 | 5 | Step 4: #1 is in Column A & C: #1 MUST go in Cell B3… | ||||||
| 2 | 9 | 6 | 3 | 1 | 4 | |||||||
| 3 | 1 | 8 | 4 | 7 | 9 | 3 | ||||||
| 4 | 2 | 5 | 4 | 9 | Step 5: #9 is in Column G & I: #9 MUST go in Cell H1 | |||||||
| 5 | 7 | 2 | 5 | 1 | 4 | (cf #9 in Row 3 @ F3 excludes use of Cell H3) | ||||||
| 6 | 4 | 1 | 8 | 2 | ||||||||
| 7 | 3 | 8 | 1 | 2 | 6 | |||||||
| 8 | 4 | 6 | 3 | 1 | ||||||||
| 9 | 1 | 6 | 2 | 3 | 7 | 9 | 8 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 4 | 7 | 6 | 9 | 5 | Step 6: Complete Column I: #7 MUST go in Cell I2… | ||||||
| 2 | 9 | 6 | 3 | 1 | 4 | 7 | ||||||
| 3 | 1 | 8 | 4 | 7 | 9 | 3 | ||||||
| 4 | 2 | 5 | 4 | 9 | Step 7: Complete Column F: #2 MUST go in Cell F8… | |||||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | ||||||
| 6 | 4 | 1 | 8 | 2 | ||||||||
| 7 | 3 | 8 | 1 | 2 | 6 | Step 8: Complete Column C: #9 MUST go in Cell C5… | ||||||
| 8 | 4 | 6 | 2 | 3 | 1 | |||||||
| 9 | 1 | 6 | 2 | 3 | 7 | 9 | 8 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 6 | 9 | 5 | Step 9: Complete Row 9: need #s 4 & 5… | |||||
| 2 | 9 | 6 | 3 | 1 | 4 | 7 | #4 can't go in Cell H9 (cf #4 in Column H @ H2), so | |||||
| 3 | 1 | 8 | 4 | 7 | 9 | 3 | #4 MUST go in Cell E9, & therefore #5 MUST go in Cell H9 | |||||
| 4 | 2 | 5 | 4 | 9 | ||||||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | Step 10: #3 is in Rows 2 & 3: #3 MUST go in Cell A1… | |||||
| 6 | 4 | 1 | 8 | 2 | ||||||||
| 7 | 3 | 8 | 1 | 2 | 6 | |||||||
| 8 | 4 | 6 | 2 | 3 | 1 | |||||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 6 | 8 | 9 | 5 | Step 11: Block CC needs #8: #8 can't go in Cells G3 or G3 | ||||
| 2 | 9 | 6 | 3 | 1 | 4 | 7 | (cf #8 in Row 3 @ D3), so #8 MUST go in Cell G1… | |||||
| 3 | 1 | 8 | 4 | 7 | 9 | 3 | ||||||
| 4 | 2 | 5 | 4 | 9 | ||||||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | ||||||
| 6 | 4 | 1 | 8 | 2 | ||||||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | Step 12: #4 is in Rows 8 & 9: #4 MUST go in Cell G7… | |||||
| 8 | 4 | 6 | 2 | 3 | 1 | |||||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 6 | 8 | 9 | 5 | Step 13: Complete Block II: #7 mUST go in Cell G8… | ||||
| 2 | 9 | 6 | 8 | 3 | 1 | 4 | 7 | |||||
| 3 | 1 | 8 | 4 | 7 | 9 | 3 | ||||||
| 4 | 2 | 5 | 4 | 9 | Step 14: Block BB needs #8: #8 MUST go in Cell E2 | |||||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | (#8 in Row 1 @ G1 excludes Cells D1 & E1, & #8 in | |||||
| 6 | 4 | 1 | 8 | 2 | Column D @ D7 excludes use of Cell D2) | |||||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | ||||||
| 8 | 4 | 6 | 2 | 7 | 3 | 1 | ||||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 15: Complete Row 1: need #s 1 & 2… | ||
| 2 | 9 | 6 | 8 | 3 | 1 | 4 | 7 | #2 can't go in Cell E1 (cf #2 in Column E @ E5), so | ||||
| 3 | 1 | 8 | 4 | 7 | 9 | 3 | #2 MUST go in Cell D1, & therefore #1 MUST go in Cell E1 | |||||
| 4 | 2 | 5 | 4 | 9 | ||||||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | ||||||
| 6 | 4 | 1 | 8 | 2 | ||||||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | ||||||
| 8 | 4 | 6 | 2 | 7 | 3 | 1 | ||||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 16: Complete Row 2: need #s 2 & 5… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | #2 can't go in Cell D2 (cf #2 in Column D @ D1), so | ||
| 3 | 1 | 8 | 4 | 7 | 9 | 3 | #2 MUST go in Cell A2, & therefore #5 MUST go in Cell D2 | |||||
| 4 | 2 | 5 | 4 | 9 | ||||||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | Step 17: #5 is in Rows 4 & 5: #5 MUST go in Cell G6 | |||||
| 6 | 4 | 1 | 8 | 5 | 2 | (cf #5 in Column H9 excludes use of Cell H6) | ||||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | ||||||
| 8 | 4 | 6 | 2 | 7 | 3 | 1 | ||||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 18: Complete Block AA: #5 MUST go in Cell A3… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | |||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 3 | |||||
| 4 | 2 | 5 | 1 | 4 | 9 | Step 19: #1 is in Rows 5 & 6: #1 MUST go in Cell D4 | ||||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | (cf #1 in Column # @ E1 excludes use of Cell E4) | |||||
| 6 | 4 | 1 | 8 | 5 | 2 | |||||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | ||||||
| 8 | 4 | 6 | 2 | 7 | 3 | 1 | ||||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 20: #8 is in Column G & I: #8 MUST go in Cell H4 | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | (cf #8 in Row 6 @ F8 excludes H6) | ||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 3 | |||||
| 4 | 2 | 5 | 1 | 4 | 8 | 9 | ||||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | ||||||
| 6 | 4 | 1 | 8 | 5 | 2 | |||||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | ||||||
| 8 | 4 | 6 | 2 | 7 | 3 | 1 | ||||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 21: Complete Column H: need #s 6 & 7… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | #7 can't go in Cell H3 (cf #7 in Row 3 @ E3), so | ||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 6 | 3 | #7 MUST go in Cell H6, & therefore #6 MUST go in Cell H3 | |||
| 4 | 7 | 2 | 5 | 1 | 4 | 8 | 9 | |||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | Step 22: #7 is now in Rows 5 & 6: #7 MUST go in Cell A4… | |||||
| 6 | 4 | 1 | 8 | 5 | 7 | 2 | ||||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | ||||||
| 8 | 4 | 6 | 2 | 7 | 3 | 1 | ||||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 23: Complete Block CC: #2 MUST go in Cell G3… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | |||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 2 | 6 | 3 | |||
| 4 | 7 | 2 | 5 | 1 | 4 | 8 | 9 | Step 24: Complete Column D: need #s 6 & 9… | ||||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | #6 can't go in Cell D8 (cf #6 in Row 8 @ E6), so | |||||
| 6 | 4 | 1 | 6 | 8 | 5 | 7 | 2 | #6 MUST go in Cell D6, & therefore #9 MUST go in Cell D8 | ||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | ||||||
| 8 | 4 | 9 | 6 | 2 | 7 | 3 | 1 | |||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 25: Complete Row 4: need #3 & 6… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | #6 can't go in Cell E4 (cf #6 in Column E @ E8), so | ||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 2 | 6 | 3 | #6 MUST go in Cell G4, & therefore #3 MUST go in Cell E4 | ||
| 4 | 7 | 2 | 5 | 1 | 3 | 4 | 6 | 8 | 9 | |||
| 5 | 9 | 7 | 2 | 5 | 1 | 4 | ||||||
| 6 | 4 | 1 | 6 | 8 | 5 | 7 | 2 | |||||
| 7 | 3 | 8 | 1 | 4 | 2 | 6 | ||||||
| 8 | 4 | 9 | 6 | 2 | 7 | 3 | 1 | |||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 26: Complete Block FF: #3 MUST go in Cell G5… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | |||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 2 | 6 | 3 | |||
| 4 | 7 | 2 | 5 | 1 | 3 | 4 | 6 | 8 | 9 | Step 27: Complete Column E: need #s 5 & 9… | ||
| 5 | 9 | 7 | 2 | 5 | 3 | 1 | 4 | #5 can't go in Cell E6 (cf #5 in Row 6 @ G6), so | ||||
| 6 | 4 | 1 | 6 | 9 | 8 | 5 | 7 | 2 | #5 MUST go in Cell E7, & therefore #9 MUST go in Cell E6 | |||
| 7 | 3 | 8 | 5 | 1 | 4 | 2 | 6 | |||||
| 8 | 4 | 9 | 6 | 2 | 7 | 3 | 1 | |||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 28: Complete Row 5: need #s 6 & 8… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | #6 can't go in Cell B5 (cf #6 in Column B @ B9), so | ||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 2 | 6 | 3 | #6 MUST go in Cell A5, & therefore #8 MUST go in Cell B5 | ||
| 4 | 7 | 2 | 5 | 1 | 3 | 4 | 6 | 8 | 9 | |||
| 5 | 6 | 8 | 9 | 7 | 2 | 5 | 3 | 1 | 4 | |||
| 6 | 4 | 1 | 6 | 9 | 8 | 5 | 7 | 2 | ||||
| 7 | 3 | 8 | 5 | 1 | 4 | 2 | 6 | |||||
| 8 | 4 | 9 | 6 | 2 | 7 | 3 | 1 | |||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 29: Complete Block DD: #3 MUST go in Cell B6… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | |||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 2 | 6 | 3 | |||
| 4 | 7 | 2 | 5 | 1 | 3 | 4 | 6 | 8 | 9 | |||
| 5 | 6 | 8 | 9 | 7 | 2 | 5 | 3 | 1 | 4 | |||
| 6 | 4 | 3 | 1 | 6 | 9 | 8 | 5 | 7 | 2 | |||
| 7 | 3 | 8 | 5 | 1 | 4 | 2 | 6 | |||||
| 8 | 4 | 9 | 6 | 2 | 7 | 3 | 1 | |||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 30: Complete Column B: need #s 5 & 7… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | #5 can't go in Cell B7 (cf #5 in Row 7 @ E7), so | ||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 2 | 6 | 3 | #5 MUST go in Cell B8, & therefore #7 MUST go in Cell B7 | ||
| 4 | 7 | 2 | 5 | 1 | 3 | 4 | 6 | 8 | 9 | |||
| 5 | 6 | 8 | 9 | 7 | 2 | 5 | 3 | 1 | 4 | |||
| 6 | 4 | 3 | 1 | 6 | 9 | 8 | 5 | 7 | 2 | |||
| 7 | 7 | 3 | 8 | 5 | 1 | 4 | 2 | 6 | ||||
| 8 | 5 | 4 | 9 | 6 | 2 | 7 | 3 | 1 | ||||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | Step 31: Complete Row 7: #9 MUST go in Cell A7… | ||
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | |||
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 2 | 6 | 3 | |||
| 4 | 7 | 2 | 5 | 1 | 3 | 4 | 6 | 8 | 9 | Step 32: Complete Row 8 (& Block GG): | ||
| 5 | 6 | 8 | 9 | 7 | 2 | 5 | 3 | 1 | 4 | #8 MUST go in Cell A8. | ||
| 6 | 4 | 3 | 1 | 6 | 9 | 8 | 5 | 7 | 2 | |||
| 7 | 9 | 7 | 3 | 8 | 5 | 1 | 4 | 2 | 6 | |||
| 8 | 8 | 5 | 4 | 9 | 6 | 2 | 7 | 3 | 1 | |||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 2 | 1 | 6 | 8 | 9 | 5 | 45 | Final Proof: | |
| 2 | 2 | 9 | 6 | 5 | 8 | 3 | 1 | 4 | 7 | 45 | - All Rows add up to 45; | |
| 3 | 5 | 1 | 8 | 4 | 7 | 9 | 2 | 6 | 3 | 45 | ||
| 4 | 7 | 2 | 5 | 1 | 3 | 4 | 6 | 8 | 9 | 45 | ||
| 5 | 6 | 8 | 9 | 7 | 2 | 5 | 3 | 1 | 4 | 45 | ||
| 6 | 4 | 3 | 1 | 6 | 9 | 8 | 5 | 7 | 2 | 45 | ||
| 7 | 9 | 7 | 3 | 8 | 5 | 1 | 4 | 2 | 6 | 45 | ||
| 8 | 8 | 5 | 4 | 9 | 6 | 2 | 7 | 3 | 1 | 45 | ||
| 9 | 1 | 6 | 2 | 3 | 4 | 7 | 9 | 5 | 8 | 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 | ||||||||||
Send your Comments to joe-ks.com