Read the bold print for a hint. Continue reading for the step by step breakdown.
(5/25) Which book answer matches the only column rule you know?
70 and 66 give you all the remaining book answers. 4 tells you that one column is only odd prime numbers. That must be the first column, since all the others already have a composite number. So the first column is all odd prime numbers and the remaining numbers in the middle row are 2 (Tale of Two Cities), 50 (50 Shades of Grey), 7 (books in the original HP series), and 9 (members of the Fellowship of the Ring). Since one of those has to go in the first column and the first column is only odd prime numbers, 7 goes in Cell C.
(6/25) Which column must be only multiples of 10?
The column that contains only multiples of 10 must be the second column, so 50 (50 Shades of Grey) goes in Cell H.
(7/25) A place for a U.S. history answer that doesn’t fit any known rules?
The number of years served in the longest American presidency is 12. 12 is neither a multiple of 10 nor an odd prime number. 7 also says that one column is only two-digit palindromes, which must be the middle column. Therefore, since 12 is a U.S. history answer, the only place for it is Cell T.
(8/25) What can Cell I be?
Lionel Messi wears #10, so 10 must be in the top row somewhere. At this point it could be Cell F, P, or U. 15 says that it is the only multiple of 15 that is an answer. This means 30 is not in the quiz. Every answer in the fourth row is between 1-31, since they are all dates, according to 23. Every answer in the second column is a multiple of 10. So Cell I is either 10, 20, or 30, but you’ve now established it is neither 10 nor 30, so it is 20.
(9/25) Is it a two-digit palindrome? Is it an odd prime?
Halloween is on the 31st and the second earliest Father’s Day is the 16th. Neither is a palindrome, so neither goes in the middle column. 16 is not an odd prime number but 31 is, so 31 goes in Cell D and 16 goes in Cell X.
(11/25) Where can the number of stripes go?
The number of stripes on the U.S. flag is 13, so 16 tells you that 13 is the only prime number in its row. You know from 4 that Cell E is definitely an odd prime number, so it must be 13.
(12/25) Where can 11 go?
12 says it is adjacent to 11 or 13, so it must be 11. 16 tells you that 11 cannot be in the bottom row, since 13 is, so 11 goes in Cell N.
(13/25) Which remaining book answer is a multiple of 3?
The two remaining book answers are 2 (Tale of Two Cities) and 9 (members of the Fellowship of the Ring). 9 is a multiple of 3, so 9 goes in Cell R and 2 goes in Cell W.
(15/25) How can guitar and Beethoven not be adjacent?
The number of strings on a standard guitar is 6. Beethoven’s famous symphony in C minor is the 5th. So 5 and 6 are music answers but not adjacent. Cell L has to be a two-digit palindrome. This means 5 or 6 must be in B or else they would be adjacent to each other in Cells Q and V. Since the first column is all odd prime numbers, Cell B is 5.
(16/25) You now have all the rules. Which one fits guitar strings? And what of Messi?
5 gives you the final column’s rule, which must be applied to the last column. Now you know that 6 does go in Cell Q, since 6 is not a power of 2 but is a multiple of 3.
Now that you know all the rules, you know that Lionel Messi’s number, 10, only fits one of them, so Cell F is 10.
(18/25) Narrow down Cell K.
6 tells you that three sports answers are in the 20s. No power of 2 is in the 20s. This means that both Cell K and P must be in the 20s. So Cell K must be 22.
(19/25) Which rule fits?
The date of the vernal equinox has almost always been March 20 lately. 20 is already on the board, so according to 22, Either Cell J or Cell O is 100, since there are 100 U.S. senators. Obviously, 100 is not a two-digit palindrome, so Cell J is 100.
(20/25) Multiple of 3 or power of 2?
There are 32 NFL teams. 32 is not a multiple of 3 but is a power of 2 (2^5). So Cell U is 32.
(21/25) This one’s easy enough.
32 tells you that Cell O must be 77.
(22/25) Use several different clues to narrow down Cell P.
77 tells you that 21 (among many others) is not an answer. This is important because you know from 6 that Cell P is in the 20s. You also know from 11 that Cell P is a multiple of 3, so it is either 21, 24, or 27. Now you know it’s not 21. Also, 10 tells you that 24 is not an answer either, so Cell P is 27.
(23/25) So what can be the last music answer?
27 tells you that 99 is not a music answer. You know that Cell L is a two-digit palindrome. You also know from 32 that it is greater than 77. So Cell L must be 88.
(24/25) Which one gives you a power of two when multiplied by or divided by 11?
Cell V must be a power of 2. So 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc. You also need one of the music answers to be 11x another music answer. None of the revealed music answers multiplied by 11 gives you a power of 2. So the question is which of the revealed music answers divided by 11 gives you a power of 2. 88 / 11 = 8, which is a power of 2, so Cell V is 8.
Here is what I had in mind for the unexplained numbers:
23: the number Michael Jordan wore most of his career
22: the number of players on a football field at a time
27: the number of times the Yankees have won the World Series
88: the number of keys on a standard piano
8: the 1/_th value of a quaver
66: the number of books in the Bible (Protestant Canon)
11: Armistice/Veterans Day
15: the Ides of March
4: the date in July the Declaration of Independence was signed