Beginner Logic Puzzle: Harry Potter Walkthrough

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(1/25) 
Dumbledore says that Ron is in C2.

(2/25) 
Dumbledore says that the four Triwizard champions are in corners. So according to Ron, Fleur must be in A5.

(3/25) 
Fleur tells you that Column E has no Gryffindor. This means, according to Dumbledore, that Harry Potter is in A1.

You know from Dumbledore that E5 is a Triwizard champion. According to Fleur, E5 died, so E5 must be Cedric Diggory.

(5/25) 
Dumbledore now tells you that the remaining Triwizard champion, Viktor Krum, goes in E1.

(6/25) 
Viktor Krum tells you that Igor Karkaroff is in D5.

Harry’s wife is Ginny Weasley. She did not die and she is a Gryffindor. This means she cannot be in Column E, according to Ron/Fleur and cannot be in Row 5, according to Fleur. So if she’s adjacent to Cedric, as Harry says, she must be in D4.

(8/25) 
Ginny says that Fred and George are adjacent to her. E3 and E4 are not Gryffindors, according to Fleur. According to Harry and Cedric, James Potter must be adjacent to both Ginny and Dumbledore, meaning either D3 or C4. So the only two places for Fred and George are D3/C4 and C5. Fleur tells you that C5 died, so C5 must be Fred.

(9/25) 
George was either D3 or C4. Now you know from Fred that George is D3.

(10/25) 
According to George, Lord Voldemort must go in B5.

James Potter has to be adjacent to Ginny (Harry) and has to be adjacent to Dumbledore (Cedric), so James goes in C4.

(12/25) 
James Potter tells you everyone who is adjacent to Harry. Two of them are female, and Ron says B1 cannot be female, so B1 must be Vernon Dursley.

(13/25) 
Vernon tells you that Petunia is not adjacent to Dumbledore. James tells you she is adjacent to Harry. So Petunia is in A2, meaning Hermione is in B2.

(15/25) 
Cedric tells you that Dumbledore is adjacent to all four Marauders. At the moment he is adjacent to only one and only three unknown cells. This means that B3, B4, and D2 are the remaining Marauders. Therefore, according to D3, Neville Longbottom is in A3.

Cedric tells you that Dumbledore is adjacent to all four Marauders, meaning Sirius is B3, B4, or D2. So according to Hermione, Sirius must be in D2.

(17/25) 
Fred Weasley tells you that the only Weasley siblings are Percy, Fred, George, Ron, and Ginny. So according to Neville and the fact that B3 and B4 are Marauders, Percy is in A4.

(18/25) 
Percy tells you that D1 and E2 are Ravenclaws. This means, according to Sirius, that Severus Snape is either C1 or E3. Lord Voldemort says that Snape and Draco Malfoy are adjacent to each other. Draco is also not a Ravenclaw, so Snape cannot go in C1; he must go in E3 so that Draco can be adjacent to him in E4.

(20/25) 
Draco tells you that Roger Davies must go in E2.

(21/25) 
Roger Davies tells you that Peter Pettigrew must be in B4.

(22/25) 
According to Cedric, B3 must be Remus Lupin.

(23/25) 
Lupin tells you that Lucius Malfoy is adjacent to a Muggle. D1 is a Ravenclaw, so not Lucius, meaning Lucius must be in C1.

(24/25) 
Snape told you that there is another head of house in the puzzle. The last remaining cell is D1, which Percy says is a Ravenclaw. So D1 must be Filius Flitwick.

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Beginner Logic Puzzle: NBA Teams Walkthrough

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(2/30) 
Memphis Grizzlies tell you that the San Antonio Spurs were better than 56-26, so the San Antonio Spurs were a Winning team.

(3/30) 
San Antonio Spurs tell you that the Los Angeles Clippers and Los Angeles Lakers were both Winning teams.

(5/30) 
San Antonio Spurs tell you that either the Golden State Warriors or Sacramento Kings were a winning team. Therefore, according to the Los Angeles Clippers, the Golden State Warriors were a Winning team.

(6/30) 
Golden State Warriors tell you that the Chicago Bulls and and Houston Rockets were both 45-37, that is, Winning teams.

(8/30) 
Chicago Bulls tell you that the Miami Heat were a Winning team, since every team played 82 games, according to the Los Angeles Lakers.

The Houston Rockets tell you that every division except that one has to have two winning teams and two losing teams. So you know that both the Phoenix Suns and Sacramento Kings are Losing teams.

(11/30) 
Miami Heat tell you that the Atlanta Hawks were a Winning team.

(12/30) 
The Miami Heat tell you that none of the Charlotte Hornets, Orlando Magic, or Washington Wizards were winning teams. The Atlanta Hawks tell you that none of those teams was .500. So all three of them were Losing teams.

According to the Sacramento Kings, the Milwaukee Bucks must have been .500.

(16/30) 
The Detroit Pistons tell you that exactly one team in the division had a worse record than they did. The Milwaukee Bucks tell you that the Indiana Pacers were either 49-33 or 33-49. If they were 33-49, then the Cleveland Cavaliers would also have to be a losing team with fewer than 29 wins in order for the Detroit Pistons clue to be true. But then that division would be one winning team, one .500 team, and three losing teams. But according to the Houston Rockets, it has to have at least two losing teams. So the Indiana Pacers are not a losing team, meaning they lost 33 games, making them a Winning team.

(17/30) 
According to the Houston Rockets, the Cleveland Cavaliers must be a Losing team.

(18/30) 
So far the only team in the middle of the division with the best division record is the Miami Heat. This means, according to the Cleveland Cavaliers, that the New York Knicks and the Oklahoma City Thunder were both Winning teams, since the Houston Rockets require at least two winning teams per division (except their own).

(20/30) 
According to the Orlando Magic, the Minnesota Timberwolves were 28-54, that is, a Losing record.

(21/30) 
The Houston Rockets require at least two winning teams and at least two losing teams in every division except their own. The Los Angeles Clippers tell you that the San Antonio Spurs are not adjacent to any winning team, including Portland and Utah. This means that the Denver Nuggets are a Winning team.

(22/30) 
The Los Angeles Clippers tell you that the San Antonio Spurs are not adjacent to any winning team, including Utah. Denver Nuggets tell you that the Utah Jazz won as many games as two teams from the Atlanta Hawks’ division combined. The only two teams in that division whose win totals do not sum to at least 42 (which would make Utah a winning team) are Charlotte Hornets + Orlando Magic. Their wins total 41, which means that the Utah Jazz were a .500 team.

(23/30) 
According to the Houston Rockets, the Portland Trail Blazers must have been a Losing team.

(24/30) 
The Portland Trail Blazers tell you that the Toronto Raptors won 34 games, which means they lost 48 and are a Losing team.

(25/30) 
The New Orleans Pelicans were not a winning team, according to the Los Angeles Clippers. The New Orleans Pelicans were also not a .500 team, according to the Toronto Raptors + New York Knicks. So the New Orleans Pelicans were a Losing team.

(26/30) 
The New York Knicks tell you there were four .500 teams. Right now you have two. According to the Houston Rockets, the top division cannot have two .500 teams, so you know that one of those remaining two .500 teams is the Dallas Mavericks.

(27/30) 
Now you know that the top division has the last remaining .500 team (New York Knicks), as well as two winning teams and two losing teams (Houston Rockets). This means that the middle record within that division must be the .500 team, so according to the Dallas Mavericks, the Boston Celtics were .500.

(28/30) 
The Boston Celtics tell you that the Brooklyn Nets must have been better than the Chicago Bulls, meaning they were a Winning team.

(29/30) 
According to the Houston Rockets, the Philadelphia 76ers were a Losing team.

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Beginner Logic Puzzle: Cartridge Colors Walkthrough

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(1/25) 
#1 tells you that #9 is cyan.

(2/25) 
#9 tells you that #13 is cyan.

(3/25) 
#1 tells you that no other corner is black. Therefore #13 tells you that #5 is yellow.

(4/25) 
#5 already shares a diagonal with two cyan cartridges: #9 and #13. Therefore #17 and #21 cannot be cyan. So according to #1, #21 is magenta and #25 is cyan.

(6/25) 
#25 tells you that #7 is magenta.

(7/25) 
#7 tells you that #2 cannot be black. Therefore #13 tells you that #2 must be yellow.

(8/25) 
#2 is adjacent to two magenta cartridges, one of them being #7. #6 is not magenta, according to #7. #3 is not magenta, according to #13. So #8 must be magenta.

(9/25) 
#3 cannot be black, according to #7, so according to #13, #3 must be yellow.

(10/25) 
#15 cannot be cyan, according to #9. Therefore, according to #3, #11 must be cyan.

(11/25) 
#11 says it is not adjacent to any black cartridge. #21 says it is adjacent to a black cartridge. Therefore #22 must be black.

(12/25) 
According to #21, #16 and #17 are cyan and yellow or vice versa. So #5 tells you that #16 is cyan and #17 is yellow.

(14/25) 
According to #16, #6 must be yellow.

#4 is either black or yellow, according to #13. So according to #6, it must be black.

(16/25) 
#10 is not black, according to #6. It is not cyan, according to #9. It is not magenta, according to #25. So #10 is yellow.

(17/25) 
#10 tells you that that column still needs a black and a magenta. So according to #7, #15 is magenta and #20 is black.

(19/25) 
Only the middle row and the bottom row have enough unknown cells to have three magenta cartridges. But #20 tells you that the bottom row has at least one additional black cartridge. So according to #15, #12 and #14 are both magenta.

(21/25) 
#12 tells you that #18 is black.

(22/25) 
#18 tells you that the bottom row needs at least one more magenta cartridge. According to #7, #23 cannot be magenta, so #24 must be magenta.

(23/25) 
#20 tells you that #23 must be black.

(24/25) 
#23 tells you that the fourth row cannot have any magenta cartridge. #19 also cannot be black, according to #7. It also cannot be yellow, according to #16, so #19 must be cyan.

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Beginner Logic Puzzle: Numbers Walkthrough

Make sure not to lose sight of the first clue, that every number is adjacent to one or both of its consecutive numbers.
Prime numbers between 1-25 are 2, 3, 5, 7, 11, 13, 17, 19, 23.

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(1/25) 
1 tells you that E2 is 22 and gives you what is henceforth called “the main rule” of the puzzle.

(2/25) 
1 must be adjacent to 2, according to the main rule. 22 tells you that no number in Row 2 is prime, so the 02 must be in B1.

(3/25) 
2 tells you that E5 is 08.

(4/25) 
Since there are five multiples of 5 (5, 10, 15, 20, 25), 8 tells you that every number in Column C is one of them. Since C3 has to be prime (22) and only one multiple of 5 is prime, C3 must be 05.

(5/25) 
5 tells you that 11 is B4, C4, or E4. E4 does not work, according to 22, because 11 is prime. C4 does not work, according to E5. So B4 is 11.

(6/25) 
E1 cannot be a prime number, according to 22, so according to B4, A5 is 17 and E1 is 04.

(8/25) 
Given where 5 is, 4 must be adjacent to 3, according to the main rule. D2 is not prime, according to 22, so D1 must be 03.

(9/25) 
C1 and C2 are both multiples of 5, according to 8, so according to D1, D2 is 16.

Since 16 is adjacent to 3, 17 must be adjacent to 18, according to the main rule. A4 is less than 17, according to 17, so B5 must be 18.

(11/25) 
B2 is not a prime number, according to 22, so B5 tells you that B2 is 06 and B3 is 19.

(13/25) 
18 is not adjacent to 19, so 19 must be adjacent to 20, according to the main rule. So C5 cannot be 20. According to 8, C5 is a multiple of 25 and according to B3, it must be greater than 18, so C5 has to be 25.

(14/25) 
The only remaining single digit numbers are 7 and 9. So according to 25 and 22, E4 is 09 and D5 is 07.

(16/25) 
You know from 8 that 10 is in Column C. Since it cannot be adjacent to 9, it must be adjacent to 11. So 10 goes in C4.

(17/25) 
19 is not adjacent to 18, so it must be adjacent to 20, which also has to be in Column C, according to 8. So C2 is 20.

25 must be adjacent to 24. So D4 is 24.

(19/25) 
According to 3 or 8, C1 must be 15.

(20/25) 
You can do this step earlier, but it’s easier to see now that the only remaining numbers are 12, 13, 14, 21, and 23. According to 17, then, A2, A3, and A4 are 12, 13, and 14 respectively.

(23/25) 
21 and 23 are left. 22 tells you that 21 must go in E3, with 23 in D3.

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Word Search Logic Puzzle 5 Walkthrough

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(1/25) A B C D E F G H I J K L M N O P R S T U V W X Y Z ?
Q tells you that Cell 19 is J.

(2/25) A B C D E F G H I K L M N O P R S T U V W X Y Z ?
Q tells you that LURK is either Cells 5-10-15-20 or Cells 20-15-10-5. According to J, it must be 20-15-10-5.

(6/25) A B C D E F G H I M N O P S T V W X Y Z ?
L tells you that either Cell 14 or 24 is B. It also tells you that that B is adjacent to the I. If Cell 24 is B, then either Cell 18 or 23 would be I. But both of those cells are adjacent to J, and I cannot be adjacent to J, according to J. So B is in Cell 14.

(7/25) A C D E F G H I M N O P S T V W X Y Z ?
The important thing to gather from B is that X cannot go in Cell 12. Since all of Cells 16-18 are adjacent to Cell 12, and one of 16-18 is W, X cannot be in Cell 12 according to J. This means that the “FOX” from K cannot go 4-8-12 or 2-7-12. I cannot be in Cell 13, according to J, so “FIB” must go 2-8-14 or 4-9-14. So since the F is in either Cell 2 or 4 and “FOX” cannot go 4-8-12 or 2-7-12, you know that “FOX” must go 2-3-4 or 4-3-2. Either way, O is in Cell 3.

(8/25) A C D E F G H I M N P S T V W X Y Z ?
You just established that the I is in Cell 8 or 9. So according to O, A and E go in the fourth and fifth rows or vice versa. Since W is in the fourth row according to B, there’s no way to spell “NEW” with E in the bottom row. So it must be the E in the fourth row and the A in the bottom row. Since you only have three unknown cells in the fourth row and you know that two of them are E and W and you have to spell “NEW,” obviously “NEW” goes either 16-17-18 or 18-17-16. Either way E is in Cell 17.

(9/25) A C D F G H I M N P S T V W X Y Z ?
The multiples of 6 are 6, 12, 18, and 24. M cannot go in Cell 24, according to J, because it is adjacent to L. Since you have to spell “NEW” in the fourth row, you know that Cell 18 cannot be M. Since N is going to be either Cell 16 or 18, you know from J that M cannot be in Cell 12. So according to E, M must be in Cell 6.

(10/25) A C D F G H I N P S T V W X Y Z ?
M tells you that you need to find “PAY” and that Y is not in Cell 24. You know from O that A is in the bottom row, so the entire word “PAY” must be in the bottom row. 21-22-23 would work. 22-23-24 would not work, according to M. 23-22-21 would work. 24-23-22 would not work, according to J. So for sure the A is in Cell 22.

(11/25) C D F G H I N P S T V W X Y Z ?
You had established that “FIB” is either 4-9-14 or 2-8-14. I is the 9th letter of the alphabet, so according to A, “FIB” goes 4-9-14.

(13/25) C D G H N P S T V W X Y Z ?
According to K, you need to spell “FOX,” so Cell 2 is X.

(14/25) C D G H N P S T V W Y Z ?
X tells you that Z is the missing letter and that Cell 1 is C or H or S. Since you now for sure need to find every other letter besides Z, you can narrow down D. It is not in Cell 1, according to X. It’s not in the middle column, according to A. It’s not in Cell 11, 12, 16, or 21, according to J (all adjacent to E). I effectively tells you that Cell 24 must be C, G, or H. This means the only place for D is Cell 7.

(15/25) C G H N P S T V W Y
Now use similar logic for the C. A rules out the middle column. J and the location of D rule out Cells 1, 11, and 12. You know that Cells 16 and 18 are N and W or vice versa (B). You know that Cells 21 and 23 are P and Y or vice versa (M). So all that’s left for C is Cell 24.

(16/25) G H N P S T V W Y
You know that Cells 16 and 18 are N and W or vice versa (B). You know that Cells 21 and 23 are P and Y or vice versa (M). You know that Cells 8 and 13 are N or later in the alphabet. This means the only cells for G and H are Cells 1, 11, and 12. G and H cannot be adjacent to each other, according to J, so one of them must go in Cell 1. According to X, it’s H.

(17/25) G N P S T V W Y
You know that Cells 16 and 18 are N and W or vice versa (B). You know that Cells 21 and 23 are P and Y or vice versa (M). This means that Cells 8, 11, 12, and 13 are the only cells for S and T, which cannot be adjacent, according to J. So if Cell 12 is S or T it would certainly be adjacent to the other. So Cell 12 cannot be S or T. It must be G or V. If V, then G would go in Cell 11 and S and T would still be adjacent in Cells 8 and 13. Or S and T would not be adjacent and G would be in the middle column, but it cannot be, according to A. Cell 12 cannot be V either; it must be G.

(18/25) N P S T V W Y
G tells you that you have to spell “YES.” Since you have to spell “PAY” in the bottom row (M), Y is either Cell 21 or 23, which means S is either Cell 11 or 13. T is also either Cell 11 or 13, according to K. So the only place for V is Cell 8.

(19/25) N P S T W Y
V places the T at Cell 13.

(20/25) N P S W Y
Since you have to spell “PET” (K), Cell 21 is P.

(21/25) N S W Y
Since you have to spell “PAY” (M) and “YES” (G), Y goes in Cell 23 and S goes in Cell 11.

(23/25) N W
The middle column has Y, so according to S, Cell 16 is W.

(24/25) W
Since you have to spell “NEW” (B), or since Z is not used (X) Cell 18 is N.

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Trivial Numbers Logic Puzzle Walkthrough

Read the bold print for a hint. Continue reading for the step by step breakdown.

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(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.

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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

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Which U.S. State Logic Puzzle Walkthrough

Remember that no two people are from the same state. Here is a map of the United States that should tell you everything you need to know. Only land borders count, so Ohio and Pennsylvania do not border Canada. Nor does Michigan border Minnesota. Clues to help you with the next step are in bold. Underneath the logic is spelled out.

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(0/25) Are there any letters A, F, K, P, U, that are the first letter in only one state?
The initial clue tells you that the people in the far left column are from states that start with the same letter as their name. There is only one state that starts with F, so Fiona is from Florida. There is only one state that starts with P, so Paula is from Pennsylvania. There is only one state that starts with U, so Usher is from Utah.

(3/25) What could Alice possibly be?
The initial clue tells you that Keith is from Kansas or Kentucky. Neither one has a coastline, so according to Fiona, everyone else adjacent to her is from a state with coastline. This means Alice must be from Alaska or Alabama (not Arizona or Arkansas). But Paula tells you that no one is from a Canada-bordering state except people in the middle column, so Alice is not from Alaska; she must be from Alabama.

(4/25) Does any row have only one male?
There are four W states: Washington, West Virginina, Wisconsin, and Wyoming. None of them borders Canada or has a coastline except Washington, which does both. Rich is the only male in his row, so he must be from a ‘W’ state, according to Alice. He also must be from a state that borders Canada, according to Paula, so Rich is from Washington.

(5/25) What are the options for Keith?
Kentucky borders Ohio, so according to the initial clue and Rich, Keith is from Kansas.

(6/25) Which column has room for the Mexico-bordering states?
Keith tells you that there’s someone from California, Arizona, New Mexico, and Texas, and they are all in the same column. They obviously cannot go in the middle column because no state that borders Mexico also borders Canada.
Bud’s column has three people from coastline states, according to Fiona. So California and Texas could be two of top three and Arizona and New Mexico would be in the bottom two, but that doesn’t work, according to Usher.
The far right column has Jace and Zach. Jace has to be from a ‘W’ state because Greg cannot be (must have coastline) and Hank cannot be (must border Canada). Zach also must be from a ‘W’ state because Walt also must be from a state that borders Canada. The remaining ‘W’ states are West Virginina, Wisconsin, and Wyoming, none of which borders Mexico or Canada or has a coastline.
So it has to be Dave’s column. You know that Nick is from a ‘W’ state because he is the only unknown male in the row. So the rest of Dave’s column are from the four states that border Mexico. Only one of them starts with a vowel, so according to Usher, Iris is from Arizona.

(7/25) Who can be from West Virginia?
You have established that Jace, Nick, and Zach are from the three remaining ‘W’ states. Now you know from Iris that neither Jace nor Nick is from West Virginia. so Zach must be from West Virginia.

(8/25) Do the implications of either of Nick’s options lead to a contradiction?
Nick is from Wisconsin or Wyoming. Zach tells you that Maria is from a bordering state, and that state borders Canada, according to Paula. Olena is also from a state that borders Nick’s home state, and her state must start with a vowel, according to Usher. So if Nick is from Wyoming, then Maria would have to be from Montana or Idaho. Olena would be from Utah or Idaho, but Usher is from Utah, and Idaho borders Canada. So Olena cannot be from a state that borders Wyoming. So Nick must be from Wisconsin.

(9/25) What’s left for Maria? What’s left for Jace? 
According to Alice (and the fact that Greg is from a coastline state and Hank’s home state borders Canada), Jace must be from Wyoming.

Wisconsin borders two states that border Canada: Minnesota and Michigan. But Maria cannot be from Michigan, according to Rich, so she is from Minnesota.

(11/25) Where can there be a male from Delaware?
Jace tells you that some male is from Delaware. Delaware does not border Canada, so it’s not Hank or Walt. Delaware does not border Mexico, so it’s not Dave. Delaware does not start with a vowel, so it’s not Earl. This leaves Bud and Greg. Delaware is an East Coast state, so if Bud is from Delaware, then Vera and Walt are also from East Coast states, according to Nick. Maria tells you that someone is from Alaska and someone is from Hawaii, but neither is adjacent to her. Alaska borders Canada so it’s either Cleo or Walt from Alaska. If Bud is from Delaware and Vera and Walt are from East Coast states, then Cleo has to be from Alaska. She would also have to be adjacent to the person from Hawaii. But Dave is from a state that borders Mexico, Hank is from a state that borders Canada, and Greg is adjacent to Maria. So if Bud is from Delaware, the person from Alaska cannot be adjacent to the person from Hawaii. Bud is not from Delaware. So Greg must be from Delaware.

(12/25) Which individuals must be in two-word states? And what must Dave be?
According to Greg and Iris, Dave is not from Texas. According to Iris, he’s not from New Mexico. So according to Keith, he is from California.

The person from Texas is in Dave’s column, according to Keith. Iris is adjacent to everyone adjacent to Dave and she says she’s not adjacent to anyone from a two-word state, so Dave is definitely not from Texas, according to Greg. this leaves Sylvia and Yuri. You know from Zach that Olena is from a state that borders Wisconsin. Usher says it must start with a vowel, so Illinois or Iowa. Both are one word. Wisconsin and Minnesota are also one word, so whether Sylvia or Yuri is from Texas, Tara and Walt must both be from two-word states. Those two, Zach, and Syliva/Yuri (New Mexico) makes four two-word states. This means Walt is not from Alaska, so according to Maria, Cleo must be.

(14/25) Who’s from Hawaii?
Maria says that the person from Alaska is adjacent to the person from Hawaii, but neither is adjacent to her. So Bud must be from Hawaii.

(15/25) Louisiana?
Louisiana does not border Canada, so according to Jace, Lola is from Louisiana.

(16/25) Where can Tara be from?
South Dakota and South Carolina do not border Mexico or Canada. They do not start with a vowel. This leaves only Quinn, Vera, and Tara for the “South” states. Syliva and Yuri are from New Mexico and Texas or vice versa. Olena is from a vowel state. So if Tara is from either “South” state, no one adjacent to her can be from the other one. So according to Lola, it must be Quinn and Vera from the “South” states. This helps you narrow down Tara. She is from a two-word state, according to Greg. The unused two-word states are New Hampshire, New Jersey, New Mexico, New York, North Carolina, North Dakota, Rhode Island, South Carolina, and South Dakota. Of those New Hampshire, New York, and North Dakota border Canada. Cleo says no one is from North Carolina or New Jersey. New Mexico is Sylvia or Yuri. Quinn and Vera are the “South” states. So the only option for Tara is Rhode Island.

(17/25) Find a state to fit Tara’s pattern.
The bottom four rows all have at least four different vowels. The top row has only A, I, and O. Tara says two home states in the row must have all three of the vowels that are in the row. Right now only California has A, I, and O. So Earl’s home state must also have those three vowels. All you know about Earl is that his home state starts with a vowel (Usher). So that leaves Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, and Oregon. Of those only Idaho and Iowa have A, I, and O. But Idaho borders Canada, so Earl must be from Iowa.

(18/25) What does Wisconsin border?
Zach told you that Olena is from a state that borders Wisconsin. Usher tells you Olena’s home state starts with a vowel, so it is not Michigan but Illinois.

(19/25) South _______ > __________ > Canada. Hmmm…
Quinn and Vera are from the “South” states. So Olena is saying that Walt’s home state borders either South Carolina or South Dakota. Walt is also from a state that borders Canada, according to Paula. No state borders both South Carolina and Canada, but three states border both South Dakota and Canada: Montana, North Dakota, and Minnesota. Minnesota is already used, and we also know from  Greg that Walt must be from a two-word state. So Walt is from North Dakota.

(20/25) Where is the ocean?
Quinn and Vera are from the “South” states. Walt tells you that Quinn lives by the ocean, so she is not from South Dakota but South Carolina. So Vera is from South Dakota.

(22/25) Which of those states can have all its bordering states in the quiz?
Sylvia and Yuri are from Texas and New Mexico or vice versa. Hank is from a state that borders Canada. California borders Oregon, Nevada, and Arizona. Oregon and Nevada are clearly not in the quiz. Arizona also borders Nevada. Texas borders New Mexico, Oklahoma, Arkansas, and Louisiana, two of which are not in the quiz. New Mexico also borders Oklahoma. So Vera must be talking about Nick and Wisconsin. So every state that borders Wisconsin is someone’s home state: Minnesota, Iowa, Illinois, and Michigan. So Hank is from Michigan.

(23/25) Check out Michigan on a map.
“Across the lake” from Michigan could conceivably mean Minnesota or Illinois or Indiana or Ohio or Pennsylvania or New York. Most obviously, it refers to Wisconsin. But in any case, it certainly cannot refer to Washington, North Dakota, Rhode Island, West Virginia, or New Mexico. So the person from Texas is adjacent to the person from Wisconsin. So Sylvia is from Texas.

(24/25) Finish it up.
Keith tells you that Yuri is from New Mexico.

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1-10 Numbers Logic Puzzle (#2) Walkthrough

EXPLANATION OF RULE IN HOW TO PLAY

Each cell that contains a number is adjacent to the number that corresponds to how many numbers are around it.

In the crude diagram below, you see that the 4 is adjacent to 5 cells. Two of them are X’s. If you find out that the other three have to be numbers, then one of them must be the 3.

|X|  |  |

|4|  |  |

|X|  |  |

In the next diagram, suppose you know that all the X’s are already on the grid and that the top row is all prime numbers. What would the next move be?

|X|  |2|  |  |  …

|4|  |7|  |  |  …

|X|  |3|  |5|  …

It would be to put the 6 to the right of the 7 because the 7 is adjacent to six numbers and 6 is not prime so cannot go in the top row. Got it? Remember that this rule is not in play for X’s.

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WALKTHROUGH SECTION BELOW

(1/20)
E4 tells you that A4 is X.

(2/20)
According to E4, C1 cannot be adjacent to more than four numbers. A4 tells you that C1 is not adjacent to the 1, the 2, the 3, or the 4. This means that C1 cannot be adjacent to the number that is the quantity of numbers adjacent to it. So C1 is X.

(3/20)
E2 x D3 = C4. The only numbers that could work are
2 x 3 = 6
3 x 2 = 6
2 x 4 = 8
4 x 2 = 8
2 x 5 = 10
5 x 2 = 10
The last two actually don’t work because they require both multiples of 5, at least one of which is adjacent to C1, according to A4. But the bottom line is 2 is going to be used in either E2 or D3. Now take a look at A1. According to E4 it can be adjacent to up to two numbers, meaning, if it is a number, it will need to be adjacent to the 1 or 2. You just established that the 2 is nowhere near. A4 says that 1 cannot be in Column A. It also says that neither B1 nor B2 is any number under 5. So A1 cannot be adjacent to the 1 or the 2, meaning it cannot be a number; it is X.

(4/20)
Apply similar logic as the previous step to B1. If it is a number, it must be adjacent to the 1, the 2, or the 3. No number adjacent to C1 is less than 5 and the A column has no odd number. And since the 2 is either E2 or D3, B1 cannot be adjacent to the number that is the quantity of numbers adjacent to it. So B1 is X.

(5/20)
B1 tells you that Row 3 is all numbers. E4 tells you that D4 is a number. C1 tells you that C4 is a number. Therefore, according to E4, B4 must be X or else C4 is not adjacent to any X.

(6/20)
You know from B1 that A3 and B3 are numbers. So A3 must be adjacent to the 1, the 2, or the 3.
If A3 is only adjacent to one number, then it is adjacent to the 1 and it would have to be B3, since B3 is definitely a number.
A3 cannot be adjacent to two numbers because then it would be adjacent to the 2, but the 2 is E2 or D3, according to C1.
A3 cannot be adjacent to three numbers because then it would be adjacent to the 3, but A2 cannot be odd (A4) and B2 and B3 cannot be prime (B4).
So A3 is adjacent to just one number, and you know B3 is a number so it must be the 1. A2 and B2, of course, are both X.

(9/20)
Consider B3. You know that A3, C3, and C4 are numbers. C2 could be, so B3 is either adjacent to three numbers or four numbers, meaning it must be adjacent to the 3 or 4. C4 is either 6 or 8, according to C1. C2 is either X or 5 or greater, according to A4. So the number that is the quantity of numbers adjacent to B3 is definitely in C3. So if C3 is 3, C2 would be X. E3, which you know is a number would not be adjacent to the 3, so would have to be adjacent to four numbers and to the 4. So D2 would be a number and the final X would be D1 or E1. But then both C3 and D2 would be numbers that are adjacent to five numbers, so they would both have to be adjacent to the 5. C3 and D2 are both adjacent to C2 and D3. In this scenario C2 is X. D3 has been established as 2 or 3 or 4. So the scenario does not work. C3 cannot be 3, so B3 must be adjacent to four numbers, meaning C3 is 4.

(10/20)
C1 tells you that E2 x D3 = C4. Since 4 is out, it  must be 2 x 3 = 6 or 3 x 2 = 6. So C4 is 6.

E3 is a number (E4) that is adjacent to four unknowns that could be numbers. But E3 is not adjacent to the 4, so it must be adjacent to at least one unknown X. E4 tells you that  D3 and D4 are definitely numbers and C1 tells you that E2 is a number. So the only box adjacent to E3 that could be X is D2.

(12/20)
You have placed nine X’s. You know B3 is adjacent to four numbers, so C2 is a number. C1 and E4 tell you that E2, D3, E3, and D4, are all numbers. So the last remaining X is D1 or E1. If D1 is the final X, then E1 would be adjacent to only one number, but E1 clearly is not adjacent to the 1. So D1 is not the final X; E1 is.

(13/20)
Now every unknown box must be a number since all X’s are placed.

D1 is adjacent to two numbers, so it must be adjacent to the 2. C2 cannot be 2, according to A4, so E2 is 2.

Since D1 and C2 are both numbers, one of them must be 5, according to A4. There’s no way 10 can be the smallest number adjacent to C1 unless it is the only number adjacent to C1. C3 is adjacent to five numbers, so C2 must be 5.

(15/20)
E2 being 2 means, according to C1, that D3 is 3.

(16/20)
A3 is not an odd number, according to A4. 2, 4, and 6 are already placed. D3 tells you that the 10 is either in D1 or E3. So A3 must be 8.

D3 says the 10  is either in D1 or E3. C2 says the 10 is not in D1, so it is in E3.

(18/20)
The 8 is already known, so E3 must be referring to 3+7. So D4 is 7.

(19/20)
The only remaining number is 9. It goes in D1.

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NFL Division Reassignment Logic Puzzle Walkthrough

The most important rule of the game is that every team moved to a different division from the one it is actually in. For example, the Patriots will not be in the AFC East. Throughout the quiz and the walkthrough, the word “former” essentially means “actual.” Also, there is no geographical rhyme or reason to the new divisions. Many of them will make no sense at all. Here is a list of the actual NFL divisions and here are the NFL teams on a map (but note that it has the Rams in St. Louis; they have recently moved back to Los Angeles)

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(1/32)
Minnesota tells you that the remaining corners are Chicago Bears, Detroit Lions, and Green Bay Packers. It also tells you that all ‘B’ nicknames are listed 1st, so the Chicago Bears are NFC-W-1.

(2/32) 
The Arizona Cardinals are a former NFC West team, so according to Chicago they must go in AFC-W-3.

The Cincinnati Bengals must be listed first, according to Minnesota, so according to Chicago, they are in AFC-W-1.

(4/32) 
The Miami Dolphins were formerly in the AFC East, so they cannot go there. According to Cincinnati, this leaves AFC-N-1 and AFC-N-2. But Arizona also tells you that no ‘B’ nickname team will go in the NFC South. Since there are six total ‘B’ nickname teams, you know that besides Minnesota Vikings and NFC-S-1, all the other 1st positions must be ‘B” nickname teams. So the Miami Dolphins cannot go in the first position, but belong in AFC-N-2.

(5/32) 
There are exactly two teams from Ohio: Cincinnati Bengals and Cleveland Browns. According to Miami, they are not adjacent. Both must be listed first according to Minnesota. Cleveland Browns also cannot go in the AFC North, since that is their former division. NFC-S-1 is reserved for a former NFC East team or the San Diego Chargers or the Jacksonville Jaguars. So the only place left for the Cleveland Browns is NFC-N-1.

(6/32) 
You know from Minnesota that NFC-W-4 is either Green Bay Packers or Detroit Lions. According to Cleveland, then, it must be Green Bay Packers, since Detroit is in Eastern Time. This, of course, puts the Detroit Lions in AFC-E-4.

(8/32) 
Detroit tells you that Buffalo Bills are not in the AFC North. They are also not in the NFC South, according to Arizona. So the Buffalo Bills are either AFC-S-1 or NFC-E-1. According to Green Bay, the Buffalo Bills are not adjacent to the Tennessee Titans, whom you know are in the AFC West from Chicago. Both options for the Buffalo Bills are adjacent to AFC-W-2, so the Tennessee Titans cannot go there, but must go in AFC-W-4.

(9/32) 
According to Chicago, the Baltimore Ravens must be in AFC-W-2.

(10/32) 
Cincinnati tells you that the NFC East has at least one of the following: Seattle Seahawks, San Francisco 49ers, Oakland Raiders, Los Angeles Rams, San Diego Chargers. Tennessee rules out the Oakland Raiders and San Francisco 49ers. Green Bay rules out Seattle Seahawks, since they are in 3rd position, according to Chicago and that would put them adjacent to the Tennessee Titans. The San Diego Chargers are in the NFC South, according to Arizona, so the NFC East must have the Los Angeles Rams. Since the Los Angeles Rams are a former NFC West team, they must be listed 3rd, according to Chicago, so the Los Angeles Rams are in NFC-E-3.

(11/32) 
Los Angeles essentially tells you that the Atlanta Falcons are in the AFC North, AFC South, or NFC East. Baltimore tells you that the Dallas Cowboys are in the AFC East and the New York Jets are in the NFC East. This means, according to Detroit, that the New York Giants must be in the NFC North, since the Buffalo Bills must be listed 1st and the Cleveland Browns are already 1st in the NFC North. So all of that means that the two teams mentioned by Arizona are definitely the Philadelphia Eagles and Washington Redskins. Cincinnati tells you that all bird teams are adjacent to at least one other bird team. So if the Atlanta Falcons are in one of the top five divisions and the Philadelphia Eagles are in the NFC South and the Baltimore Ravens and Arizona Cardinals are already placed, which bird team can possibly be adjacent to the Philadelphia Eagles? There’s only one bird team left, the Seattle Seahawks. They must be adjacent to the Philadelphia Eagles, who are somewhere in the NFC South. The Seattle Seahawks were formerly in the NFC West, so they cannot go there. They cannot go in the NFC South because all its teams are known (Arizona). So the Seattle Seahawks must go in the NFC North, and they must be listed 3rd, according to Chicago: NFC-N-3.

(12/32) 
The Jacksonville Jaguars are in the NFC South, according to Arizona. They cannot be adjacent to the Seattle Seahawks, according to Green Bay. So the Jacksonville Jaguars are in NFC-S-1.

(13/32) 
The Buffalo Bills are not in the AFC North, according to Detroit, so they must be in AFC-S-1, according to Jacksonville and Minnesota.

(14/32) 
The New York Giants must be in the NFC North (Detroit + Baltimore), but they cannot be in NFC-N-2, according to Buffalo, so the New York Giants are in NFC-N-4.

(15/32) 
Denver Broncos must be listed 1st, according to Minnesota. Kansas City Chiefs must be listed 2nd, according to Buffalo. So according to the New York Giants, both the Oakland Raiders and San Diego Chargers must be listed 2nd (not 1st because they are not ‘B’ nicknames). So you know that the San Diego Chargers must go in NFC-S-2, according to the Cardinals.

Cleveland tells you that no NFC West team is based in Eastern Time. This rules out many of the remaining teams: Atlanta Falcons, Carolina Panthers, Indianapolis Colts, New England Patriots, New York Jets, Philadelphia Eagles, Pittsburgh Steelers, Washington Redskins. (Some of them are ruled out for other reasons as well.) You also know from Minnesota that the Denver Broncos and Tampa Bay Buccaneers are listed 1st. The New Orleans Saints are in the AFC, according to Jacksonville. The Dallas Cowboys are in the AFC East, according to Baltimore. The Kansas City Chiefs cannot be all the way down in the NFC West, according to Buffalo. The San Francisco 49ers were formerly in the NFC West, so cannot be now. So you ruled out 14 of the remaining 16 teams for the final two spots in the NFC West. That means those spots belong to the Houston Texans and Oakland Raiders, and according to the New York Giants, it’s the Oakland Raiders in NFC-W-2 and the Houston Texans in NFC-W-3.

(18/32) 
The New Jork Jets are in the NFC East, according to Baltimore. According to Oakland and Minnesota, then, they are in NFC-E-2.

(19/32) 
The New York Jets tell you they are not adjacent to the Denver Broncos. This means, according to Minnesota, that the Denver Broncos are in AFC-N-1 and the Tampa Bay Buccaneers are in NFC-E-1.

(21/32) 
Tampa Bay tells you that the Washington Redskins are listed 4th in their division. Therefore you know from Arizona that they go in NFC-S-4 and the Philadelphia Eagles go in NFC-S-3.

(23/32) 
Follow San Diego’s hypothetical. Dallas Cowboys are in the AFC East, according to Baltimore, so if the Indianapolis Colts are in the AFC East, it’s full. Then where would the Pittsburgh Steelers go? Not in the AFC North because that’s their former division. Not in the AFC South, according to Seattle. Not in NFC-E-4, according to the hypothetical itself. That would leave only NFC-N-2 for the Pittsburgh Steelers, but they cannot go there either, according to Miami. So the Indianapolis Colts cannot go in the AFC East. They also cannot go in NFC-N-2, according to the New York Jets, and they cannot go in the AFC South because that’s their former division. Lastly, they cannot be listed 4th, according to Houston. So the hypothetical does not work, meaning the Indianapolis Colts cannot go in the AFC East. And they cannot go anywhere else except AFC-N-3.

(24/32) 
Indianapolis tells you that the Tampa bay Buccaneers, New Orleans Saints, Carolina Panthers, and Atlanta Falcons are in two total divisions. Tampa Bay Buccaneers are already placed in the NFC East. The other three could all go in the AFC South. In that case the New Orleans Saints would be listed second because of what Oakland says. Or one of the three remaining former NFC South teams could go in NFC-E-4. Then the other two would have to go in the same division. two must go in the same division but it would still have to be the AFC South because the AFC East has the Dallas Cowboys, according to Baltimore. You know that the Saints are in the AFC, according to Jacksonville, so they cannot be in NFC-E-4. So whether it’s 3 and 1 or 2 and 2, the New Orleans Saints have to go in the AFC South. And they cannot be adjacent to the Tennessee Titans, according to Oakland. So the New Orleans Saints definitely go in AFC-S-2.

(25/32) 
The Kansas City Chiefs must go in NFC-N-2, according to Buffalo.

(26/32) 
The Dallas Cowboys are in the AFC East, according to Baltimore. The Pittsburgh Steelers cannot be in the AFC North because that is their former division. The Carolina Panthers and Atlanta Falcons are in the AFC South or NFC East. the San Francisco 49ers must be listed 3rd, according to Chicago. This means that the only remaining team that can go in AFC-N-4 is the New England Patriots.

(27/32) 
New England tells you that the Atlanta Falcons and Carolina Panthers cannot both be in the AFC South, since the New Orleans Saints already are. The Dallas Cowboys are in the AFC East, according to Baltimore. The Pittsburgh Steelers cannot be in the AFC South, according to Seattle. So the only remaining team that can go in AFC-S-3 is the San Francisco 49ers.

(28/32) 
The Los Angeles Rams are adjacent to the Baltimore Ravens, Arizona Cardinals, and Seattle Seahawks. So according to San Francisco, NFC-E-4 cannot be the Atlanta Falcons. So according to Indianapolis, AFC-S-4 is the Atlanta Falcons and NFC-E-4 is the Carolina Panthers.

(30/32) 
The Falcons or the Panthers tell you that the Dallas Cowboys are in AFC-E-3 and the Pittsburgh Steelers are in AFC-E-2, adjacent to the Broncos.

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Back to School Logic Puzzle Walkthrough

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(1/20) 
Binder tells you that uniform and book bag were Reused.

(3/20) 
Book bag tells you that crayons, glue, and markers are one of each status. Uniform tells you that markers were not reused. Binder tells you that crayons were not reused, since book bag was. So you know that glue must have been Reused.

(4/20) 
Uniform tells you that it is the only item in its column that was reused. So according to glue, compass and protractor were both Bought.

(6/20) 
Since compass tells you that Joe did not skip the scissors, you know from binder that either notebook or pencils were skipped. This means, according to protractor, that pens were definitely not skipped. Therefore, according to binder, tissue was Skipped.

(7/20) 
According to binder, pens must have been Reused.

(8/20) 
Glue tells you that no math item was skipped. So according to pens, crayons could not have been skipped. So according to binder, crayons were Bought and eraser was Skipped.

(10/20) 
Book bag told you that crayons, glue, and markers were one of each status. This means that markers were Skipped.

(11/20) 
Markers tell you that ruler was not bought new. It also was not skipped, according to glue. So ruler was Reused.

(12/20) 
Pens now tell you that crayons must be the same as calculator, so the calculator was Bought.

(13/20) 
Folders were not reused, according to uniform. So according to binder, folders were Skipped and flash drive was Reused.

(15/20) 
Flash drive tells you that scissors was Bought.

(16/20) 
If scissors were the only bought item in its column, then pencils were skipped. In that case index cards would have to be skipped, according to eraser. Also, notebooks would be reused, according to binder. This would mean loose leaf paper was skipped, according to compass. All cells would be filled in, but flash drive would be false because no item would be bought in the second row. So you know that scissors was not the only bought item in its column. Pencils cannot be bought, according to binder, so index cards were Bought.

(17/20) 
The only column without at least one item of each status is the first column. So, according to index cards, notebooks were Skipped.

(18/20) 
According to binder, pencils were Reused.

(19/20) 
Pencils must be referring to scissors, since all its adjacent cells are filled in. Protractor is not adjacent to any known bought item, so according to pencils, loose leaf paper must be Bought.

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