(1/25) A B C D E F G H I J K L M N P Q R S T U V W X Y Z ?

O tells you that Cell 13 is C.

(2/25) A B D E F G H I J K L M N P Q R S T U V W X Y Z ?

O tells you that Cell 5, 21, and 25 are some combination of S, H, E. C tells you that “SYLPH” is a word in one column. So it must be in the far right column. Whether it starts at Cell 5 or 25, the L is in cell 15.

With O in Cell 1, “SYLPH” cannot go in the far left column. Therefore O tells you that the E goes in Cell 21.

(4/25) A B D F G H I J K M N P Q R S T U V W X Y Z ?

E tells you that you’re looking for “ACNE.” So the A must go in Cell 9 and the N must go in Cell 17.

(6/25) B D F G H I J K M P Q R S T U V W X Y Z ?

The C tells you that the Y is either in Cell 10 or 20. So in order to spell “DRY,” the D would have to be in Cell 8 or 18, both of which are adjacent to the C. C cannot be adjacent to D, according to L, so according to A, you’ll need to spell “MAP” or “PAW.” Since the P has to be in the far right column (C), it must be in Cell 10.

(7/25) B D F G H I J K M Q R S T U V W X Y Z ?

Now you know from C that Cell 5 is H, Cell 20 is Y, and Cell 25 is S.

(10/25) B D F G I J K M Q R T U V W X Z ?

Since you have to spell “FUN” (E), you know that the U is either in Cell 12 or Cell 18. You also have to spell “QUIZ.” H tells you that Z cannot go in the top row, so QUIZ cannot be Cells 16, 12, 8, 4. QUIZ also cannot be Cells 6, 12, 18, 24, according to L, for the Z would be adjacent to the Y. So the only option left for QUIZ is Cells 24, 18, 12, 6.

(14/25) B D F G J K M R T V W X ?

The F obviously must go in Cell 19.

Z tells you that you need to find “GNU,” so the G is in Cell 16.

(16/25) B D J K M R T V W X ?

According to S, K is in either Cell 4 or 8. According to N, the J is in Cell 2, 3, or 4. J and K cannot be adjacent, according to L. All of J’s possibilities are adjacent to Cell 8, so K cannot go in Cell 8; it must go in Cell 4.

(17/25) B D J M R T V W X ?

The J still cannot be adjacent to the K, so it must go in Cell 2, according to N.

(18/25) B D M R T V W X ?

J and N tell you where you will not find T, but T could still not be in the puzzle at all. T cannot go in Cell 3, according to H. It cannot go in Cell 7, according to N. It cannot go in Cell 8, according to A. It cannot go in Cell 11, according to J. And it cannot go in Cells 14, 22, or 23, according to L. So T is the missing letter. Now, where can B go? Not in Cells 3, 7, 8, or 14, according to L. Not in 11 or 23, according to J. So the B must go in Cell 22.

(19/25) D M R V W X

Given the remaining letters and what H tells you, Cell 3 must be either D or M. If Cell 3 is M, then Cell 8 must be W, according to A. D would have to go in Cell 11 or 23, not 7 or 14, according to L. This would mean that 2 of R, V, X would go in Cells 7 and 14. Neither V nor X can be adjacent to W, which is in Cell 8 in this scenario, because of L. Therefore Cell 3 is not M; it is D.

(20/25) M R V W X

Of the remaining letters, only R and W can go in Cell 14. M would be adjacent to L. V would be adjacent to U. X would be adjacent to Y. So D says that if R is in Cell 14, then W is not in Cell 8, which would mean M is in Cell 8, according to A. If R is not in Cell 14, W is in Cell 14, meaning it could not go in Cell 8. So Cell 8 would be M, according to A. Either way, Cell 8 is M.

(21/25) R V W X

In Roman numerals, eleven is XI, six is VI, four is IV, and nine is IX. So it actually doesn’t matter if you find XI and VI or IV and IX; they are the same thing. Bottom line is Cells 7 and 11 are V and X or vice versa. This means 14 and 23 are R and W or vice versa. R cannot go in Cell 23, according to L, so it goes in Cell 14, with W in Cell 23.

(23/25) V X

W tells you that the X is adjacent to O, so Cell 7 is X.

(24/25) V

V is the last letter; it goes in Cell 11.