(2/25) A C D E F G H I J K L N O P Q R S T U V W X Y Z ?
M tells you that you’re looking for the word “MEAT” or “TEAM.” It could be Cells 1-2-3-4 or 4-8-12-16 or 4-9-14-19. But B tells you what is in Cells 1, 7, 13, and 19: some combination of J, L, R U. So neither Cell 1 nor Cell 19 can be T. This means that the word must be spelled using Cells 4-8-12-16. So whether it’s “MEAT” or “TEAM,” T goes in cell 16.
(3/25) A C D E F G H I J K L N O P Q R S U V W X Y Z ?
You know from M that E is either in Cell 8 or 12. B tells you that L must be on that main diagonal. So in order to spell “ELF,” the possibilities are Cells 12-7-2 or Cells 12-13-14 or Cells 8-13-18 or Cells 8-7-6. The F of “ELF” will also start “FAD,” whose A must be a part of “TEAM” or “MEAT.” If “ELF” goes Cells 8-7-6, then “FAD” goes Cells 6-12-18. but then you won’t be able to spell “TWO,” and B says you have to. If “ELF” goes Cells 8-13-18, then “FAD” goes Cells 18-12-6. Again, there’d be no way to spell “TWO.” So “ELF” cannot start on Cell 8, so it must start on Cell 12; Cell 12 is E.
(4/25) A C D F G H I J K L N O P Q R S U V W X Y Z ?
M now tells you that Cell 8 is A.
(5/25) C D F G H I J K L N O P Q R S U V W X Y Z ?
A tells you that you’re looking for “SIR.” B tells you that R is in Cell 1, 7, 13, or 19. In Cell 1 “SIR” could be 11-6-1, but then T would be adjacent to S, which does not work, according to E. “SIR” in 3-2-1 does not work because there’d be no way to spell both “ELF” and “FAD” if Cell 2 is I. R in Cell 7 does not work because there’s definitely no way to spell “SIR” that way, since Cells 13 and 19 can only be certain things, according to B. R in Cell 13 works. “SIR” could be 13-18-23 or 5-9-13. 21-17-13 would not work because T and S would be adjacent. 15-14-13 would not work because it would prevent spelling both “FAD” and “ELF.” R in Cell 19 does not work to spell “SIR.” 9-14-19 would prevent spelling both “FAD” and “ELF.” 17-18-19 would place T adjacent to S. So the bottom line is “SIR” can only be spelled with R in Cell 13.
(6/25) C D F G H I J K L N O P Q S U V W X Y Z ?
Now “ELF” must go 12-7-2.
(8/25) C D G H I J K N O P Q S U V W X Y Z ?
So “FAD” must go 2-8-14.
A and E are already in non-prime Cells. Since you have to spell “SIR,” I is in Cell 9 or 18, neither prime. Since you have to spell “TWO,” O is in Cell 6 or 18, neither prime. So according to F, U must be in a prime numbered cell. B tells you that U must go in Cell 1 or 19, so it must go in Cell 19.
(10/25) C G H I J K N O P Q S V W X Y Z ?
According to B, Cell 1 must be J.
(11/25) C G H I K N O P Q S V W X Y Z ?
Since you have to find “TWO,” the only way to find “OF” is with O in cell 6. The only other option for “TWO” is 16-17-18, which would also force I into Cell 9, since you have to spell “SIR.” So for either option of “TWO,” I ends up in Cell 9.
(12/25) C G H K N O P Q S V W X Y Z ?
Since you have to spell “SIR” (A), S goes in Cell 5.
(13/25) C G H K N O P Q V W X Y Z ?
A tells you that V is adjacent to exactly one vowel. That rules out Cells 3, 15, and 18. S rules out Cell 6 for V. Cell 11 cannot be V because it is either W or adjacent to W, since you have to spell “TWO.” Same thing for Cell 17; it is either W or adjacent to W. Cells 20, 23, and 24 are adjacent to U, so cannot be V. Cell 21 is definitely not adjacent to any vowel. If Cell 22 is adjacent to a vowel, Cell 18 is O. That would make Cell 17 W, which would hinder V being in Cell 22. At this point you know V is in the puzzle, but it cannot go anywhere except Cell 10.
(14/25) C G H K N O P Q W X Y Z ?
V tells you that X is adjacent to zero vowels. The only unfilled cells that are adjacent to no vowels are Cells 21 and 22, so one of them must be the X. Both those cells are adjacent to Cell 17, so according to E, Cell 17 cannot be W. This means, according to B, that “TWO” is 16-11-6.
(16/25) C G H K N P Q X Y Z ?
R confirms that G is in the puzzle. It cannot go in Cell 3, because Cell 3 is adjacent to F. G cannot go in Cell 15, according to W. G also cannot go in Cell 17, 18, or 20, according to D. Cell 21 is only adjacent to three consonants, but G is adjacent to more than three, according to R. O rules out Cell 24 as an option for G, so G must go in Cell 22 or 23. Either way, H goes in Cell 20, according to D.
(17/25) C G K N P Q X Y Z ?
You had G narrowed down to Cell 22 or 23. H tells you that it cannot go in Cell 22, so Cell 23 is G.
(18/25) C K N P Q X Y Z ?
Cells 3 and 15 are P and N or vice versa, according to G, but N cannot be adjacent to M, according to E, so Cell 3 is P and Cell 15 is N.
(20/25) C K Q X Y Z ?
C cannot go in Cell 17 or 18, according to D. It cannot go in Cell 22, according to P. It cannot go in Cell 24, according to E. It has not yet been confirmed, but if it is in the puzzle, it must go in Cell 21. That would make Cell 22 X, according to S. Cell 24 is C, X, Y or Z, according to O. So with C in Cell 21 and X in Cell 22, Cell 24 would have to be Y, to avoid X and Y being adjacent. That would leave Cells 17 and 18 for K, Q and Z, but Q cannot go in either, according to E. So K would go in Cell 18 so that Z would not be adjacent to Y; Z would go in Cell 17.
Since only Cell 21 could possibly be C, what happens if it is not C? That would mean you would for sure use K, Q, X, Y, and Z. X is in Cell 21 or 22, according to S. Then Cell 24 would be Y or Z, according to O. Again, E says that Q cannot go in Cell 17 or 18, so it would have to go in Cell 21 or 22, whichever X is not in. This means that Cells 17, 18, and 24 would be K, Y, and Z in some order. But Y and Z cannot be adjacent to each other, according to E, meaning they would have to go in Cells 17 and 24. This would put K in Cell 18. Then, since X would be in Cell 21 or 22, Y could not be in Cell 17, but would have to go in Cell 24, with Z in Cell 17.
Whether or not C is in the puzzle, Cell 17 is Z, Cell 18 is K, and Cell 24 is Y.
(23/25) C Q X?
Z tells you that Q is adjacent to G, so Q goes in Cell 22.
(24/25) C X ?
C and X remain. X is mentioned by V as being in the puzzle, so C is not. X goes in Cell 21.