(2/25) B C D E F G H I J K L M N O P Q R T U V W X Y Z ?
S tells you that Cell 23 is H.

(3/25) B C D E F G I J K L M N O P Q R T U V W X Y Z ?
A tells you that I and X are adjacent to A. H tells you that I cannot be in Cells 17, 19, 22, or 24, leaving only 12, 13, and 14. If “AIR” were spelled in 18-13-8, then R would be adjacent to S. This cannot be, according to H. Also, if “AIR” were spelled in 18-14-10, R would again be adjacent to S. So “AIR” must be spelled in 18-12-6.

(5/25) B C D E F G J K L M N O P Q T U V W X Y Z ?
S tells you that three of the other columns have exactly one vowel, and the other has two. R tells you that E is in the far right column. I tells you that “BUCK” is a word, and there’s now way to arrange “BUCK” so that the U is in the far left column. So, since the far left column needs at least one vowel, but doesn’t have A or I and cannot have E or U, it must have O. I also tells you that “OVAL” is a word. A is already in Cell 18. The only way to arrange “OVAL” with O in the far left column is 16-17-18-19.

(8/25) B C D E F G J K M N P Q T U W X Y Z ?
A told you that “AXE” is a word. R told you that E is in the far right column, so “AXE” must go 18-14-10.

(10/25) B C D F G J K M N P T U W Y Z
E tells you that D is either in Cell 8 or Cell 24 (Cell 16 is already filled). I told you that “BUCK” is a word, and at this point you realize that it has to be entirely in the top row. This means that C is in Cell 2 or 3 or 4. All of those cells are adjacent to Cell 8, meaning, according to H, that Cell 8 cannot be D. Therefore, according to E, D is in Cell 24.

(11/25) B C F G J K M N P U W Y Z
The remaining cells that share a diagonal with L are 1, 7, 13, 15, and 25. Cells 13 and 15 are both adjacent to S, so neither can be T, according to H. If T is in Cell 1, then the rest of that row would have to spell “BUCK,” so “JEN” would be impossible, and so would “TIM,” but O demands one of these. So T is not in Cell 1 either. Finally, S told you that Cell 4 cannot be U, so the “BUCK” in the top row must start with Cell 1 or 2 or 4. All of these options place U in Cell 2 or 3, both of which are adjacent to Cell 7, meaning Cell 7 cannot be T, according to H. Therefore, T must go in Cell 25.

(12/25) B C F G J K M N P U W Y Z
X told you that Q is the missing letter. Given the placement of V and X, the remaining options for W are limited, according to H. It must be in the top row or in Cell 7. Since “BUCK” has to go in the top row, W up there would bar the possibility of spelling “JEN.” And with T in Cell 25, you know from O that you will need to spell “JEN.” Therefore W cannot go in the top row, but goes in Cell 7.

(13/25) B C F G J K M N P U Y Z
You know that the top row contains “BUCK” and either N or J. You now know from W that Y and Z are not in the middle row. This means, according to L, that Y is in Cell 21 or 22. Z cannot be adjacent to Y, according to H, so Z must be in Cell 8 or 20, but T tells you that Cell 8 is in the first half of the alphabet. So Z is in Cell 20.

(14/25) B C F G J K M N P U Y
You know that the top row contains “BUCK” and either N or J. You know from O that Cell 15 is N or J. You know from X that Q is the missing letter. You know from H that P cannot go in Cells 11, 21, or 22. You know from T that Cell 8 cannot be P. The only cell that can be P is Cell 13.

(15/25) B C F G J K M N U Y
P says Cell 22 is not F. It is also not G, according to H. Since J will be either Cell 5 or 15, M has to be Cell 11 or 21, so not Cell 22. All that’s left for Cell 22 is Y.

(16/25) B C F G J K M N U
Even without knowing whether it’s “BUCK” or “KCUB,” you can figure out which column Y is referring to.
Far left column: Cell 1 could be B or K. Cell 11 and 21 could be F, G, M.
Middle column: Cell 3 could be C or U. Cell 8 could be F, G, M.
Fourth column: No chance with the four you already know.
Far right column: Cell 5 and 15 are J and N or vice versa.
It can only be the second column, meaning Cell 2 must be U.

(17/25) B C F G J K M N
Now you finally know, according to I, that “BUCK” is 1-2-3-4.

(20/25) F G J M N
K cannot be adjacent to J, according to H. Therefore, according to O, Cell 5 is N and Cell 15 is J.

(22/25) F G M
According to P, M must be in Cell 11.

(23/25) F G
M tells you that you will not spell “GO.” Therefore, G cannot go in Cell 21, but goes in Cell 8.

(24/25) F
The remaining goes in Cell 21.