The answers to the 80 clues can be grouped into 40 pairs where the answers are the same length and share mostly the same letters (7 out of 10, 8 out of 11, 8 or 9 out of 12, 9 out of 13, or 10 out of 14). Each of those pairs can be given a unique binary pattern where 1 = matching and 0 = non-matching:
| 1. SOUNDING BOARD | 36. STANDING GUARD | 1001111100111 |
| 2. BUTTER KNIFE | 26. GUTTERSNIPE | 01111101101 |
| 3. TIGHT SCHEDULE | 31. LIGHTS THE FUSE | 0111110110101 |
| 4. BEACHGRASS | 52. BENCH PRESS | 1101101011 |
| 5. FRIGHT FEST | 25. WEIGHTIEST | 0011110111 |
| 6. RECORD-KEEPING | 77. SECOND HELPING | 0111010101111 |
| 7. UNDERTAKEN | 73. INTERLAKEN | 0101101111 |
| 8. CLEAN SLATE | 65. CHEAPSKATE | 1011010111 |
| 9. AIR STRIKES | 39. PINSTRIPES | 0101111011 |
| 10. GET-TOGETHERS | 44. GOT TO BE THERE | 101110111110 |
| 11. CAMPANELLA | 80. CAMPOBELLO | 1111001110 |
| 12. EXTRA POINT | 59. ENTRAPMENT | 1011110011 |
| 13. JUMPER CABLES | 56. SUPPER TABLES | 010111011111 |
| 14. CARBON COPY | 63. CARSON CITY | 1110111001 |
| 15. SNAKEDANCE | 50. IN ABEYANCE | 0110101111 |
| 16. MIGHTY MIGHTY | 78. EIGHTY-EIGHTH | 011111011110 |
| 17. LOUDSPEAKER | 32. LORD’S PRAYER | 11011101011 |
| 18. BRENDAN FRASER | 22. BREAD AND WATER | 1110111001011 |
| 19. BRINGS TO LIGHT | 24. GOING STRAIGHT | 0011111001111 |
| 20. BARTON FINK | 46. BARTENDING | 1111010110 |
| 21. SILLY WALKS | 60. SALLY WELLS | 1011110101 |
| 23. WEST GERMAN | 33. WEATHER MAP | 1101011110 |
| 27. MONTE CARLO | 57. MONTICELLO | 1111010011 |
| 28. SOLAR HEATING | 38. SPEARHEADING | 100111110111 |
| 29. FROOT LOOPS | 40. FRONT DOORS | 1110101101 |
| 30. ON THE CARPET | 58. IN THE MARKET | 01111011011 |
| 34. SEA CUCUMBER | 55. BEACHCOMBER | 01110101111 |
| 35. BILL OF RIGHTS | 49. PILLOW FIGHTS | 011110011111 |
| 37. WORKING CLASS | 45. LOOKING-GLASS | 010111101111 |
| 41. SCARIFYING | 72. SEALIFTING | 1010110111 |
| 42. LEADHOLDER | 71. LEAFROLLER | 1110011011 |
| 43. CARPENTER ANTS | 48. CURRENT EVENTS | 1010111100111 |
| 47. THE ROAD WARRIOR | 68. THERMAL BARRIER | 11110100111101 |
| 51. HANGING TOUGH | 54. HACKING COUGH | 110011101111 |
| 53. LAND O’LAKES | 70. HAND BRAKES | 0111001111 |
| 61. TIRE TREADS | 76. AIRSTREAMS | 0110111101 |
| 62. MIXED EMOTIONS | 69. TAX EXEMPTIONS | 0011011011111 |
| 64. CONCERT GRAND | 75. CONCORD GRAPE | 111101011100 |
| 66. HANNA-BARBERA | 79. SANTA BARBARA | 011011111011 |
| 67. COLD READING | 74. COLOR-CODING | 11101001111 |
The next step is to find the 40 binary patterns in the grid such that the given rules are all obeyed. Here is one possible solving path, with pairs given in the order they can be uniquely proven in the grid (where letter + number = row/column):
- 19/24
- 62/69
- 16/78
- 18/22
- 43/48
- 1/36
- 5/25
- 17/32
- 30/58
- 6/77
- 51/54
- 66/79
- 3/31
- 2/26
- 37/45
- 35/49
- 42/71
- 13/56
- 10/44 [only way to use B13]
- 27/57 [only way to use 015 vertically]
- 12/59 [only way to use R14]
- 28/38 [only way to use F14 horizontally]
- 14/63 [only way to use L6]
- 23/33 [only way to use Q1]
- 47/68
- 8/65 [only way to use A14]
- 29/40 [only way to use L10]
- 67/74 [only way to use N8]
- 7/73
- 11/80
- 53/70
- 9/39
- 61/76
- 64/75
- 34/55
- 15/50 [only way to use P2]
- 20/46 [only way to use 03]
- 21/60
- 4/53 [to avoid two matches in K7]
- 41/72
Once the grid is filled, look at the common letter in each boldfaced red circle; in order from top to bottom and left to right, they spell THE PURPLE ROSE OF CAIRO, which is the solution to the puzzle.
