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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Favorite Ninja Turtle Logic Puzzle Walkthrough

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(1/25) 
Moira tells you that Grant, Iggy, and Stan all like Raphael.

(4/25) 
Iggy’s clue is important. He effectively tells you that the center column has exactly one fan of each turtle and every other column has one fan of three of the turtles, plus two fans of one turtle. There’s a 2-Leo column, a 2-Raph column, a 2-Don column, and a 2-Mike column. Since Grant and Iggy both like Raphael, that is the 2-Raph column. So Quinn’s column cannot have two Raphael fans, meaning, according to Grant, that Quinn must like Donatello.

(5/25) 
Since there are four corners and each has a different favorite (Stan) of the four Turtles, then according to Quinn, Yves must like Donatello.

(6/25) 
Yves tells you that her column is the 2-Leo column. Therefore it cannot have a second Donatello fan, so according to Grant, Val must like Raphael.

(7/25) 
Val tells you that Ned and Omar like Leonardo and Raphael or vice versa. Since that middle column has Moira, who cannot decide, Liv and Karl must like Michelangelo and Donatello or vice versa, according to Iggy. So then, according to Grant, it is Liv who likes Donatello and Karl who likes Michelangelo.

Since the far right is the 2-Leo column (Yves) and Val likes Raphael, you know that Uriah must not like Raphael. This means, according to Stan, that either Atlas or Erin likes Raphael. Since the second column is already the 2-Raph column, the first column cannot have a second fan of Raphael. So Brody must like Donatello, according to Grant.

(10/25) 
Brody tells you that Stan is adjacent to at least one male Michelangelo fan and at least one female Michelangelo fan. Neither Ned nor Omar likes Michelangelo, according to Val, so Brody’s Michelangelo-supporting brother who is adjacent to Stan must be Wade or Xeno. Since Yves says that two of that column like Leonardo, then whichever one of Wade/Xeno is not Brody’s brother must like Leonardo and Uriah must also like Leonardo.

(11/25) 
Time to work through Atlas’ options. According to Stan, Atlas likes either Raphael or Michelangelo, and Erin likes the other one. Brody says if Atlas likes Raphael, then Wade likes Leonardo. If Atlas likes Michelangelo, then of course Erin likes Raphael. Since Omar likes either Raphael or Leonardo (Val), Jacki and Tessa would both have to like Michelangelo, according to Yves. And as Uriah says, if Jacki and Tessa have the same favorite, that is also Xeno’s favorite. And if Xeno likes Michelangelo, then according to Yves, Wade would like Leonardo. Bottom line is Atlas only has two options and both lead to Wade liking Leonardo.

(12/25) 
The far right column still needs a fan of Michelangelo, according to Iggy, so Xeno likes Michelangelo.

Wade tells you that neither Val nor Honor likes Michelangelo or Donatello. Honor also cannot like Raphael, since according to Iggy, no column can have more than two fans of the same turtle. So Honor likes Leonardo.

(14/25) 
Honor tells you she is only adjacent to one Leonardo fan. Neither Atlas nor Erin is a Leonardo fan, according to Stan, so according to Iggy, Clive or Diana has to be. So since Honor is only adjacent to one Leonardo fan, Ned cannot be one. So according to Iggy or Val, Ned must like Raphael.

(15/25) 
According to Iggy, Omar must like Leonardo.

(16/25) 
Xeno reveals to you that Paul’s column is the 2-Don column because the far left column has more males than females. So Paul’s column can only have one fan of the other three turtles. According to Brody, Stan is adjacent to at least one female Michelangelo fan, so either Rayne or Tessa (or both). So Paul cannot be a fan of Michelangelo. Stan likes Raphael, so there cannot be another Raphael fan in the column either. Omar tells you that Paul does not like Donatello. This means Paul must like Leonardo.

(17/25) 
Stan tells you that Atlas and Erin like Raphael and Michelangelo or vice versa. Xeno reveals that Paul’s column is the 2-Don column so the far left column must be the 2-Mike column. So then Clive and Diana must like Michelangelo and Leonardo or vice versa. According to Paul, if Clive does not like Michelangelo, then Jacki doesn’t. Because of what Yves says, this would mean Erin must like Michelangelo. Now let’s say Clive does like Michelangelo. This would mean Diana likes Leonardo. That would mean, according to Ned, that Fay and Tessa must have the same favorite. If Fay and Tessa both like Michelangelo, then Jacki would need to be the Donatello fan of her column and Erin would like Michelangelo according to Yves. If Fay and Tessa both like Donatello, then the bottom row would still need two Michelangelo fans, according to Yves. Whether or not Clive likes Michelangelo, Erin ends up liking Michelangelo.

(18/25) 
According to Stan, Atlas must like Raphael.

(19/25) 
Let’s say Jacki and Rayne do not like the same turtle. If Jacki likes Michelangelo, then Rayne would like Donatello. Then Fay would like Donatello and Tessa would like Michelangelo. Jacki liking Donatello and Rayne liking Michelangelo would not work because Tessa would have to like Michelangelo and Donatello simultaneously (Xeno+Yves). So if Jacki and Rayne do not like the same turtle, neither do Fay and Tessa. According to Ned, that would mean Diana likes Michelangelo or Raphael. It would be Michelangelo since she is in the 2-Mike column. Now if Jacki and Rayne do like the same turtle, Atlas says at least one row is symmetric. For Clive’s row to be symmetric, you’d have to put two Leonardo fans in the 2-Don column, so that doesn’t work. Clearly the only other option is Diana’s row. So Diana would like Michelangelo. Again, either way, whether Jacki and Rayne like the same turtle or not, Diana likes Michelangelo.

(20/25) 
According to Iggy, Clive must like Leonardo.

(21/25) 
Now, according to Paul, Jacki does not like Michelangelo. Someone in her column needs to, so Fay likes Michelangelo. Also, Yves says at least two in the bottom row like Michelangelo, so Tessa also likes Michelangelo.

(23/25) 
Jacki’s column needs a Donatello fan, according to Iggy. Rayne’s column needs a second Donatello fan, according to Xeno. So Jacki and Rayne both like Donatello.

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Word Search Logic Puzzle 4 Walkthrough

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(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.

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Lying Politicians Logic Puzzle Walkthrough

Everyone is either always lying or always telling the truth. If you figure out that one of someone’s statements is a lie, so must the other. If you figure out that one of someone’s statements is true, so must the other. The only two options for each politician are (E)lected and (N)ot elected. One person was elected and 24 were not.

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(2/25) 
Since Aaron is clearly adjacent to Ace, Aaron must be telling the truth. Therefore Ace was not elected and is a liar.

(3/25) 
You know Ace is lying, so nobody whose name ends in E was elected: Allie, Moe, and Sadie.

(6/25) 
If Sadie is telling the truth, then so are Allie and Moe, but Allie says that Sadie and Moe are lying. So there’s no way Sadie is telling the truth. This means that Allie and Moe are not both telling the truth; at least one is a liar. If Moe is lying, that means Allie is telling the truth about Moe and Sadie being liars. If Moe is telling the truth, then Allie is lying about Moe being a liar. So the bottom line is Sadie is definitely lying, and either Moe or Allie is lying. Since one of Moe or Allie must be telling the truth and both are adjacent to Colby, you now know that Tracy is a liar. This means that all the three-letter names are not elected: Ash, Tad, and Ted.

(9/25) 
Since Ace is lying, you know that the bottom row does not have at least two liars. That means it has one or zero. We already know Tracy is a liar, so everyone else in the bottom row is telling the truth. This means, according to Ted, that Andy is indeed not elected and is telling the truth.

(10/25) 
We know Andy is telling the truth. This means that the following were not elected: Clint, Cyndi, and Melly.

(13/25) 
You know that Tad is telling the truth (Ace). Since Andy is telling the truth, Colby and Cyndi must both be liars in order for Ash to be adjacent to at least two liars. So since Cyndi is a liar, then any liar who is adjacent to exactly three liars was not elected. Melly says that Mason is telling the truth. If that were true, then Sadie could not be adjacent to at least two liars, since you know that Tad and Talia are telling the truth. This means Melly is a liar; therefore Mason is also a liar and Cecil is telling the truth. Since Cecil is telling the truth, Candy must be a liar so that Aaron can be adjacent to two liars (Ace and Candy). Not only is Candy a liar, but she is also adjacent to exactly three liars (Ace, Mason, and Melly), so according to liar Cyndi, she did not get elected.

(14/25) 
Candy is a liar, so there cannot be even one column of all liars. Right now you have a confirmed liar in every column except the middle and far right. (Skyla has to be a liar so that Tracy can be adjacent to at least two liars, since Theo is telling the truth.) In the far right column Cyndi, Stacy, and Tracy are liars. Stacy has to be so that Tracy can be adjacent to at least two liars. The thing to see now is that Ash and Moe could both be liars (except now Candy says no), they could both be telling the truth, or one could be lying. If both are telling the truth, then a liar who’s not in the bottom row got elected. If Moe is honest and Ash is lying, then a truthteller who’s not in the bottom row got elected. But if Ash is honest and Moe is lying, then a liar in the bottom row got elected. This cannot be, since you know that Talia and Theo are telling the truth. So since every column has to have at least one truthteller, Moe must be telling the truth. Ash could also be, or he could be lying. Since Moe is telling the truth, Theo and Talia did not get elected.

(16/25) 
Talia is telling the truth, so Mindy was not elected.

Tracy and Skyla have been established as liars. Moe and Theo have been established as honest. Theo now tells you that Missy is a liar. This means Stacy is adjacent to exactly three liars, and since she herself is a liar (so Tracy can be adjacent to at least two), she must not have been elected, according to Cyndi.

(18/25) 
Stacy is a liar, so neither Mason nor Missy was elected.

(20/25) 
Mason is established as a liar (Melly had to be lying) so there is not even one column with only one liar; they all must have two or more. Right now the only column without two or more confirmed liars is the middle column. You do know now that Allie is a liar, since Moe was telling the truth, so the middle column needs at least one more liar. Mindy and Clint are obviously either both lying or both telling the truth. If they are both telling the truth, then Sean must be the second liar in the column. But if that’s the case, Ash would be half honest, half true, because Sean would be elected (Clint telling truth), but liars would not outnumber truthtellers in every column (middle column would have three truthtellers). So Sean cannot be the only other liar besides Allie in the middle column. And since Clint and Mindy have to be the same, both of them must be liars. Since Clint says Sean was elected, you know that Sean was not elected.

Now that there are at least three liars in the middle column, you know that Ash is telling the truth because liars outnumber truthtellers in every column (Candy+Mason+Sadie, Ace+Melly+Scott (so that Tad can be adjacent to at least two liars), Allie+Clint+Mindy, Colby+Missy+Skyla, Cyndi+Stacy+Tracy). Since Cecil is telling the truth (Melly), you know he was not elected.

(22/25) 
Since Cecil is telling the truth, Skyla was not elected.

(23/25) 
Skyla is a liar, so she tells you that Colby was not elected.

(24/25) 
So Scott was elected.

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Word Search Logic Puzzle 3 Walkthrough

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(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.

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