Who Stole What from Whom? (Who Stole What from Whom? Part X)

(N.b. my reasoning differs from that in the solution presented by the author substantially, yet we reach the same conclusion. I am not sure the solution is airtight but it seems pretty solid so I am posting it here anyway.)

“And now, we come to a particularly good puzzle,” I said to the group proudly.
“Three girls—Abigail, Bernice, and Carol—each had a pet; one was a dog, one a cat, and the other a horse, but we are not told which girl owned which pet. One day, our three villains—Mike, Spike, and Slug—each stole a pet from one of the girls, but it was not known who stole what from whom. The case proved extremely baffling, but, fortunately, Inspector Craig of Scotland Yard was visiting the country at the time...”
“Who is Inspector Craig?” asked Barry.
“He is a character from one of my books,” I replied.
“What is the name of this book?” asked Barry.
“You just guessed it!” I said.
“Whatever do you mean?” asked Barry in astonishment.
“I mean just what I said; its name is What Is the Name of This Book?”
“Stop kidding us!” said Barry.
“He’s not kidding!” said Alice. “I’ve read the book, and its title really is What Is the Name of This Book?, and it really does contain a whole chapter of cases from the files of Inspector Craig.”
“Anyway,” I intervened, “Inspector Craig was able to find out the following facts, which were enough to solve the case.

1. The one who stole the horse is a bachelor and is the most dangerous thief of the three.
2. Abigail is younger than the girl who owns the dog.
3. Mike’s brother-in-law, Slug, who stole from the eldest of the three girls, is less dangerous than the one who stole the dog.
4. The man who stole from Abigail is an only child.
5. Mike did not steal from Bernice.

Who stole what from whom?”

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

Slug is revealed to be the brother-in-law of Mike, which means that Mike is married and is therefore not a bachelor and is therefore neither the horse-thief nor the most dangerous of the three. Additionally, Slug has been described as "less dangerous" than one of the other thieves, which leaves only Spike to be the horse-thief.

Since the horse is now (partially) accounted for, it should be pointed out that Slug is compared as "less dangerous" to the one who stole the dog. This leaves only the dog to be stolen by him. And it also means that Mike stole the dog. So far, so good; who stole which pet is already fully accounted for.

Slug (the cat-thief) stole from the eldest of the three girls. Since Abigail is described as younger than the girl who owns the dog these facts mean jointly that she must own the horse.

With the horse now fully accounted for, the fact that Mike (the dog-thief) did not steal from Bernice means that Bernice owns the cat. With only one pet left, Carol must own the dog.

Final answer: Mike stole the dog from Carol; Spike, the horse from Abigail; and Slug, the cat from Bernice.

Who Stole What? (Who Stole from Whom? Part IX)

One day, Mike, Spike, and Slug went to the neighboring town of Middleberg and committed three robberies. One of them stole a rifle, one stole some money, and one stole a book. The three were caught, but it was not known which man stole what. At the trial, they made the following statements:
Mike: Slug stole the book.
Spike: Not so; Slug stole the money.
Slug: Those are both lies. I didn’t steal either!
As it happened, the one who stole the rifle was lying, and the one who stole the book was telling the truth.
Who stole what?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

Mike cannot have stolen the book, because he would have said that he stole the book. Slug cannot have stolen the book for the same reason. Therefore, Spike stole the book, which means that Slug stole the money and Mike stole the rifle.

Who Owns the Goat? (Who Stole from Whom? Part VIII)

The goat belonged to either Farmer White, Farmer Brown, or Farmer Black. Farmer White claimed that the goat was his. Farmer Brown claimed that the goat did belong to Farmer White. Farmer Black either claimed that the goat belonged to him, or he claimed that it belonged to Farmer Brown, but, unfortunately, the court records are confused on this point. At any rate, at least two of the claims were correct.
Who owns the goat?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

If Farmer Brown owned the goat, then Farmer Brown would be lying, as would Farmer White, leaving only one more claim to be possibly true, so Farmer Brown does not own the goat. If Farmer Black owned the goat, then Farmer Brown and Farmer White are still both lying. Therefore Farmer White owns the goat.

Who Stole the Goat? (Who Stole from Whom? Part VII)

One day a goat was stolen. Naturally, Mike, Spike, and Slug were the suspects, and, in fact, one and only one of them was guilty. Each of the three accused one of the others, and Mike was the only one who lied. Was Mike necessarily guilty?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

Consider the two alternatives: first, if Spike stole the goat, then Spike cannot accuse himself, only one of the others, falsely. The same contradiction applies to Slug. Therefore Mike was necessarily guilty.

Which Farmer Owned the Horse? (Who Stole What from Whom? Part VI)

The horse was recovered and was to be given back to the rightful owner, who was either Farmer White, Farmer Brown, or Farmer Black. The three farmers each made two statements:

Farmer White:

1. The horse does not belong to Farmer Brown.
2. It belongs to me.

Farmer Brown:

1. The horse does not belong to Farmer Black.
2. It belongs to Farmer White.

Farmer Black:

1. The horse does not belong to Farmer White.
2. It belongs to me.

As it happened, one of the three made two true statements; one made just one true statement; and one made statements that were both false.
Who owns the horse?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

Assume that Farmer White is making two true statements. Accordingly, Farmer Brown is also making two true statements, which is a contradiction. Conversely, the assumption that Farmer Brown is making two true statements is rendered a contradiction by the statements of Farmer White, who would also be required to make two true statements under this assumption. Therefore, only Farmer Black can be making two true statements.

It has now already been established that Farmer Black is the owner of the horse but to complete the puzzle, it should be pointed out that Farmer Brown is making two false statements and Farmer White is making one true and one false statement.

Who Stole the Horse? (Who Stole What from Whom? Part V)

One day, a horse was stolen. Again, Mike, Spike, and Slug were rounded up for questioning. This time, each one made two statements. None of them made more than one false statement.

Mike:

1. I did not steal the horse.
2. The one who stole the horse is Italian.

Slug:

1. Mike never stole the horse.
2. The one who stole the horse is German.

Spike:

1. I never stole the horse.
2. It was Slug who stole the horse.

Assuming that one of those three men really stole the horse, which one was it?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

Spike cannot have stolen the horse because he would be issuing two false statements. If Mike stole the horse, then his second statement must be true, namely that the one who stole the horse is Italian. But then Slug would be issuing two false statements as was the case with Spike earlier. Accordingly, Slug stole the horse.

Who Owns the Cat? (Who Stole What from Whom? Part IV)

The cat belonged to one of three girls—Annabelle, Betsy, or Cynthia. Annabelle claimed that Betsy doesn't own the cat, and Betsy claimed that Cynthia owns the cat. Now, it so happens that the the owner of the cat always tells the truth and is the only one of the three girls who ever tells the truth.
Who owns the cat?

(Source: King Arthur in Search of His Dog and Other Curious Logic Puzzles by Raymond Smullyan)

Suppose that Annabelle is not the owner. This would imply that her claim that Betsy doesn't own the cat is a falsehood. This would in turn imply that Betsy is the owner of the cat and therefore speaks truth. But if Betsy were the owner of the cat and accordingly a truth-teller, she would not claim that Cynthia owns the cat, which is a contradiction. Therefore Annabelle must be the owner of the cat.

Who Stole the Cat? (Who Stole What from Whom? Part III)

One day a cat was stolen. Mike, Spike, and Slug were again rounded up for questioning. Mike claimed that Spike had stolen it, and Spike claimed that Slug had stolen it. Now, it was not certain that any of the three suspects had stolen it, but later investigation showed that no guilty person told the truth and no innocent person lied. Also, the cat was not stolen by more than one person.
Can it be determined who stole the cat?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

If Mike stole the cat then Spike's accusation is false, which is not allowed, letting him off the hook. The same reasoning applies to the possibility of Slug being the thief: Mike is falsely accusing Spike. It can't be the case that no one stole the cat because in this case, not one but two false accusations are being made. Therefore Spike stole the cat.

Who Owned the Dog? (Who Stole What from Whom? Part II)

The dog was recovered. It belonged to one of three boys—Arthur, Bernard, or Charles. They made the following statements:
Arthur: Bernard doesn't own it.
Bernard: That is true.
Charles: Arthur doesn't own it.
As it happened, the real owner was telling the truth, and at least one of the others was lying.
Which boy owns the dog?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

Charles is excluded from being the owner because that makes the other two statements true. Bernard is also excluded because he would be agreeing with a lie (Arthur's statement). Arthur is the only candidate left.

Who Stole the Dog? (Who Stole What from Whom? Part I)

A certain dog was stolen one day. Three suspects—Mike, Spike, and Slug—were rounded up for questioning. They made the following statements:
Mike: I didn't steal the dog.
Slug: I stole the dog.
Spike: Slug never stole the dog!
As it happened, at most, one of these three statements was true.
Who stole the dog?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

This one actually falls to the first option: if Mike stole the dog, then Spike's statement is the only true statement here.

Apples and Oranges

In front of you are three boxes, the first labelled ‘apples’, the second ‘oranges’ and the third ‘apples and oranges’. One box contains apples, one contains oranges, and the other contains apples and oranges. Each label, however, is on the wrong box. Your job is to correctly reassign the labels. You can’t see (or smell) what’s in any of the boxes. But you are allowed to stick your hand in one of them and remove a single piece of fruit.
Which box do you choose, and once you see that piece of fruit how do you deduce the correct contents of all the boxes?

(Source: Can You Solve My Problems? A Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles by Alex Bellos)

Take a fruit from the box labeled "apples and oranges". That box is to be labeled with the sign bearing the name of that fruit. If the first labeled box contains apples then the other two are currently labeled "apples" and "oranges". The box labeled "apples" contains oranges and the box labeled "oranges" contains apples and oranges. If however the first labeled box contains oranges then the box labeled "apples" contains apples and oranges and the box labeled "oranges" contains "apples and oranges".

St Dunderhead's

St. Dunderhead’s School at Fogwell has a high reputation for hockey – but not so high a reputation for veracity. The First XI played a match at Diddleham recently, after which the girls were allowed to go to a concert. Miss Pry, the mistress in charge, collected the team afterwards; she saw ten girls emerge from the concert hall and one from the cinema next door. When she asked who had been to the cinema, the members of the team replied as follows:

Joan Juggins: ‘It was Joan Twigg.’
Gertie Gass: ‘It was I.’
Bessie Blunt: ‘Gertie Gass is a liar.’
Sally Sharp: ‘Gertie Gass is a liar, and so is Joan Juggins.’
Mary Smith: ‘It was Bessie Blunt.’
Dorothy Smith: ‘It was neither Bessie nor I.’
Kitty Smith: ‘It wasn’t any of us Smith girls.’
Joan Twigg: ‘It was either Bessie Blunt or Sally Sharp.’
Joan Forsyte: ‘Both of the other Joans are telling lies.’
Laura Lamb: ‘Only one of the Smith girls is telling the truth.’
Flora Flummery: ‘No, two of the Smith girls are telling the truth.’

Given that, of these eleven assertions, at least seven are untrue, who went to the cinema?

(Source: Can You Solve My Problems? A Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles by Alex Bellos)

It isn't necessary to go through every possibility. After evaluating the statements for the first two girls I noticed a lot of the statements have to do with the Smith girls, so a lot would hinge on one of them having gone to the cinema. And in fact it was Dorothy. Checking this is trivial, so I will omit a full solution.

Darklands Puzzle #33

The path is blocked by a grim iron door. Carved overhead are the words:
EACH STATUE SPEAKS EITHER ALL TRUTH OR ALL LIES.
PUSH A STATUE TO PASS.
Standing by on the door are two statues: one of a dwarf, the other of a kobold.
The dwarf statue says, "The statue which opens the door always lies."
Which statue should you push? A mistake could (will. ed.) release a trap! You think carefully, then press...
...the dwarf statue.
...the kobold statue.

(Source: Darklands cluebook by MicroProse Software)

If the dwarf is lying then one must press the kobold statue, as the dwarf statue would be telling the truth if pressing it opened the door. If, on the other hand, the dwarf is telling the truth then one must still press the kobold statue, as the dwarf statue would be implicating itself as a liar if pressing it opened the door, which is not possible.

Darklands Puzzle #32

A grim iron door blocks your way. Above the door is carved:
EACH FACE SPEAKS EITHER WHOLLY TRUTH OR ALL LIES.
PRESS ONE OF THE FACES TO OPEN THE DOOR.
Two embossed faces, one gold, one silver, hang near the door. They speak.
Gold: "Press Silver to open the door."
Silver: "Exactly one of us speaks the truth."
The wrong face probably (certainly. ed.) triggers a trap. After careful calculation you press...
...the gold face.
...the silver face.

(Source: Darklands cluebook by MicroProse Software)

If Silver is telling the truth then Gold is lying and one must touch the Gold face. On the other hand if Silver is lying then the only option is that no one is telling the truth, because the alternative of both of them telling the truth would result in a contradiction. In this case Gold is still lying and one must still touch the Gold face.

Darklands Puzzle #30

A door blocks your path. An inscription reads:

Ooo, ooo, aaah? Is this some type of dwarf joke? In any case, five metal knobs are on the door, each bearing a number. Pressing the wrong knob may (will. ed.) spring a trap! You ponder, then press...
...0.
...2.
...4.
...6.
...8.

(Source: Darklands cluebook by MicroProse Software)

The leftmost digit, "A", must be one, as established in the solution to Darklands puzzle #2. The fact that the rightmost column, where "O" is added to itself, results in "H" in this instance, but that the same addition results in "A" in all other instances, indicates that carrying is taking place. The smallest number which, when added to itself, results in a carry operation is five. It is also the correct one. In other words, the decrypted addition is $555 + 555 = 1110$. This means that one must touch the knob labeled zero.

Darklands Puzzle #28

The path is blocked by a dark iron door. Carved over it is an inscription:
PASS WITH THE NEXT NUMBER.
27 64 125 216 343
Embossed on the door are five metal knobs. each bearing a number. Doubtless pressing the wrong number releases a trap! You press...
...512.
...434.
...675.
...0.
...717.

(Source: Darklands cluebook by MicroProse Software)

These numbers are a sequence of cubes. Starting from three and leading up to seven inclusive. The cube of eight is 512 so one must touch the knob labeled as such.

Darklands Puzzle #26

The path is blocked by a heavy iron door. Carved above it is an inscription:
TOUCH THE NEXT TO PASS.
1 1 2 3 5 8 13 21 34 55
On the door are different plates, each with numbers. Which should you touch? The wrong choice could (will. ed.) release a terrible doom trap! You consider carefully, then touch...
...85.
...89.
...99.
...100.
...123.

(Source: Darklands cluebook by MicroProse Software)

The writers at MicroProse have made another small error: this is almost but not quite the Fibonacci sequence. (The Fibonacci sequence starts with zero and one.) One must touch 89.

Darklands Puzzle #25

A door blocks the path. On it are carved the following words:
PRESS THE NEXT NUMBER.
1 2 3 5 7 11 13 17 19 23
Upon the door are five numbered knobs. Clearly, you are supposed to press one of the knobs. But what is next in the sequence? The wrong choice may (will. ed.) release a horrible trap! You cogitate, then press...
...knob 25.
...knob 26.
...knob 27.
...knob 29.
...knob 31.

(Source: Darklands cluebook by MicroProse Software)

Almost all of these are prime numbers! The writers at MicroProse Software must have forgotten that the primes start at two. The next prime number after 23 is 29 so press knob 29.

Darklands Puzzle #23

The path is blocked by a grim iron door. Carved overhead are the words:
EACH SPEAKS EITHER WHOLLY TRUE OR ALL LIES.
TO PASS, TOUCH THE ONE THAT MUST SPEAK TRULY.
Embossed on the door are three metal faces: gold, silver and copper.
Two of the faces speak.
Silver: "At least one of us three is a liar."
Copper: "Press gold to open the door."
Which is the correct choice? A mistake could (will. ed.) release a trap! You think carefully, then touch...
...the gold face.
...the silver face.
...the copper face.

(Source: Darklands cluebook by MicroProse Software)

If Silver is lying then Silver is not lying, because Silver makes for at least one liar. This is a contradiction. Therefore Silver must tell the truth and one should touch the Silver face.

Darklands Puzzle #22

A grim iron door blocks your way. Above the door is carved:
ALL STATEMENTS ARE TRUE.
On the door are embossed four statements:

1. If the silver key does not open the door, neither does the copper key.
2. If the copper key does not open the door, neither does the silver key.
3. If the gold key opens the door, so does exactly one other key.
4. If exactly two keys open the door, one of them is gold.

Four keys hang nearby. You ponder, then choose...
...the gold key.
...the silver key.
...the copper key.
...the lead key.

(Source: Darklands cluebook by MicroProse Software)

Consider first the possibility of statement #3: "if the gold key opens the door, so does exactly one other key". This statement can be connected with statement #4: "if exactly two keys open the door, one of them is gold". The other key must be lead because exactly one other key can join gold. Statements #1 and #2 make it clear that silver and copper must both be able to open the door, or neither of them do. So it is possible that the pair of gold and lead keys can open the door. The preceding discussion should make it clear that no other pairs are possible.

But that possibility is only that: a possibility. There may be others. If one and only one key opens the door, it can only be lead. Silver and copper must be paired. Gold also requires a further key (which was previously established as lead).

The possibility that three keys open the door is also available, in which case these keys must be silver, copper and lead. Gold is excluded per statement #3. Four keys are also impossible according to the same statement.

All told, there are three possibilities. Which of them is true is underdetermined, but fortunately lead is the common factor among all of them, so one should choose the lead key.

Darklands Puzzle #20

A strong, iron door blocks the path. An inscription reads:
ALL FACES LIE OR ALL FACES SPEAK TRUE.
Six brass faces suddenly speak.
One: "The gold key opens the door."
Two: "The silver key opens the door."
Three: "Faces One and Two are not both liars."
Four: "Face One is a liar. Face Two speaks truth."
Five: "Faces Three and Four either both speak truth or both speak lies."
Six: "Face Five is a liar. Dwarfs are tall and willowy."
Three metal keys hang nearby. You ponder, then use...
...the gold key.
...the silver key.
...the copper key.

(Source: Darklands cluebook by MicroProse Software)

This one was badly worded. I thought the criterion was that either all faces are "knights" or all faces are "knaves". In fact, this is a standard "knights and knaves" puzzle.

Anyway, Six is obviously a liar because he described Dwarves as "tall and willowy". This means Five is not a liar, meaning that faces Three and Four either both speak truth or both speak lies. If they both speak lies, then, per Three's statement, Faces One and Two are both liars. But then face Four tells one truth and one lie about faces One and Two, which is not possible. Therefore faces Three and Four are both "knights". Accordingly, the silver key opens the door.

Darklands Puzzle #19

A door blocks the path. An inscription reads:
ALL THE FACES ARE LYING.
THREE FACES ARE NAMED REPIN, GOLIBERT, AND HANSU.
On the wall are six numbered faces, who speak:
One: Press Face Two to open the door.
Two: Press Golibert to open the door.
Three: At least one of Golibert, Hansu and Repin is an odd-numbered face.
Four: Face Six is Repin.
Five: Press an odd-numbered face to open the door.
Six: I am Hansu.
The door may (does. ed.) hide a trap! You think, then press...
...Face One.
...Face Two.
...Face Three.
...Face Four.
...Face Five.
...Face Six.

(Source: Darklands cluebook by MicroProse Software)

Three's statement means that none of Golibert, Hansu and Repin is an odd-numbered face, meaning that all names are to be assigned to even-numbered faces. The statements of Four and Six preclude the possibility that Six is either Repin or Hansu, meaning that Six is Golibert. Five's statement means that one must press an even-numbered face to open the door. One's statement precludes the possibility that Two opens the door and Two's statement precludes the possibility that Golibert (i.e. Six) opens the door. The only face left is Four.

Darklands Puzzle #18

The path is blocked by a heavy door. Carved above it are the words:
ONE HEAD ALWAYS LIES.
ONE HEAD SPEAKS TRUTH.
KRUSAD'S HEAD CAN TELL TRUTH OR LIES.
MULTIPLE ANSWERS ARE POSSIBLE.
PRESS THE HEAD THAT CANNOT BE KRUSAD'S TO OPEN THE DOOR.
Embossed on the door are three metal heads. They speak:
Gold: "I am Aubyn."
Silver: "That is true. Gold is indeed Aubyn."
Copper: "Not so, I am Aubyn."
You press...
...the gold head.
...the silver head.
...the copper head.

(Darklands cluebook by MicroProse Software)

As suggested by the cluebook, if Copper is Aubyn, then gold and silver are either both telling the truth or both lying. But there have to be one "knight" and one "knave" in addition to the more flexible Krusad. Therefore Copper cannot be Krusad.

Darklands Puzzle #14

Your way is blocked by an iron door. Carved above it are the words:
ALL FACES SPEAK TRUTH.
THE FACES ARE NAMED NARM, NENN, AND KROCHT.
THEIR FATHERS ARE HOD, ELT, AND MOT.
TOUCH KROCHT TO OPEN THE DOOR.
On the door are three metal faces: gold, silver, copper. They speak:
Gold: "Narm is not silver. The son of Hod is copper."
Silver: "Nenn is not gold. The son of Elt is Krocht."
Copper: "The son of Mot is silver."
Which is Krocht? The order of names and fathers is clearly irrelevant. You touch...
...the gold face.
...the silver face.
...the copper face.

(Source: Darklands cluebook by MicroProse Software)

The key here is to ignore irrelevant details and focus on the following two statements: "the son of Hod is copper" and "the son of Mot is silver". There is only one metal left for the son of Elt (i.e. Krocht): gold.

Darklands Puzzle #13

The path is blocked by a grim iron door. Carved overhead are the words:
THE FACES SPEAK ONLY TRUTH.
PUSH GYMER'S FACE TO OPEN THE DOOR.
Embossed on the door are four faces, a gold dwarf, a gold kobold, a silver gnome, and a silver ogre. The faces speak.
Gold Dwarf: "Albech is made of gold."
Gold Kobold: "Hoder is made of silver."
Silver Gnome: "The kobold is neither Gymer nor Albech."
Silver Ogre: "I am not Hoder."
Which is Gymer? A false choice may (will. ed.) release a trap! You think carefully, then press...
...the dwarf.
...the kobold.
...the gnome.
...the ogre.

(Source: Darklands cluebook by MicroProse Software)

Four faces and three names. The Gold Kobold tells us that Hoder is made of Silver and the Silver Ogre denies being Hoder. Because no dirty liars are present for a change, this means that the Silver Gnome is Hoder. This leaves only the names Albech and Gymer behind. Because the Gold Kobold is neither Gymer nor Albech, as the Silver Gnome says, then Albech must be the Gold Dwarf, as he has stated that Albech is made of gold. Now only Gymer remains to be assigned. Because it has been established that the Gold Kobold is neither Gymer nor Albech then the Gold Kobold's name is unknown and the only possible candidate is the Silver Ogre.

Darklands Puzzle #12

A grim iron door blocks your way. Above the door is carved:
ALL STATEMENTS ARE TRUE.
NAME TIFSYN'S FOLK TO OPEN THE DOOR.
On the door are embossed six statements:

1. All full-blooded kobolds love to drink rust wine.
2. Tifsyn is Hoondit's child.
3. Hourly, Tifsyn calls out the correct time from the depths of his lair.
4. Tifsyn is either a gnome, dwarf, or kobold.
5. Hoondit hates rust wine.
6. No gnome is ever truthful.

You ponder, then say...
...Tifsyn must be a dwarf.
...Tifsyn must be a gnome.
...Tifsyn must be a kobold.

(Source: Darklands cluebook from MicroProse Software)

Statement #5 means, per statement #1, that Hoondit is not a kobold. Per statement #2, Tifsyn is Hoondit's child, meaning that Tifsyn can only be a gnome or dwarf. Per statement #6, no gnome is ever truthful and accordingly, per statement #3, Tifsyn cannot be a gnome. Tifsyn is a Dwarf.

Darklands Puzzle #11

The path is blocked by an iron door. Above the door is carved:
ONE STATUE ALWAYS LIES, ONE SPEAKS ONLY TRUTH AND THE THIRD SPEAKS BOTH TRUTH AND LIES.
MULTIPLE SOLUTIONS ARE POSSIBLE.
TO OPEN THE DOOR, TOUCH THE ONE THAT CANNOT BE HARDGREP.
The three statues seem to have recently been shuffled around. They speak:
Gold says, "I am Tifsyn. Silver is Hardgrep."
Silver says. "True, gold is Tifsyn. However, I myself am Gymer."
Copper says. "Not so. Gold is Gymer."
You touch...
...the gold statue.
...the silver statue.
...the copper statue.

(Source: Darklands cluebook by MicroProse Software)

The cluebook has the hint "If Gold lies, then Silver cannot be the truth-teller." which was quite useful. If Gold lies then he is not Tifsyn and Silver is the intermediate sort of character (hereafter referred to simply as "the intermediate") who tells one truth and one lie, making him Gymer. This then means that Copper is also a "knave", which is not possible in this case, so this possibility can be disregarded entirely.

On the other hand, if Gold is the intermediate, then either:

• Gold is Tifsyn and Silver is not Hardgrep or
• Gold is not Tifsyn and Silver is Hardgrep

I will not make a further examination of whether Gold even can be the intermediate, like I did in the previous instance of considering whether Gold can be the "knave" because it's already clear that Gold can't be Hardgrep in this instance.

The final possibility that Gold is the "knight" leads to the trivial inference that Gold is not Hardgrep because Silver is. Accordingly, touch the gold statue.

Darklands Puzzle #10

A door blocks the path. An inscription reads:
FACES ALWAYS LIE OR ALWAYS SPEAK TRUTH.
TOUCH ONE KNOB TO OPEN THE DOOR.
On the wall are six numbered faces, who speak:
One: "Gold opens the door."
Two: "Face One speaks truth. Copper cannot open the door."
Three: "Face Four is a liar."
Four: "Face Six is a liar. Face Six and myself are the only two liars."
Five: "Of the odd-numbered faces, exactly two tell the truth."
Six: "Lead cannot open the door."
Four metal keys hang nearby. You ponder, then use...
...the gold key.
...the silver key.
...the copper key.
...the lead key.

(Source: Darklands cluebook by MicroProse Software)

Four must be a liar because "knights" would never call themselves liars. Neither would knaves for that matter, at least not in an unqualified fashion. However the statement is a little more complex than that: "Face Six and myself are the only two liars" really means that there are other liars than Four. (Six is not a liar because Four said Six is a liar.)

If Five is a "knight" then Three and Five are the two "knights" of the odd-numbered faces and the choices are restricted to silver and copper. (One is a "knave" and Six, previously established as a "knight", has said that lead cannot open the door.) If, on the other hand, Five is a "knave", then only one of the odd-numbered faces can be a "knight": "exactly two" is ruled out and "all three" is contradicted by the assumption that Five is a "knave". In this case, Three is the only "knight" and lead and gold are still both ruled out. Whether Five is a "knight" or a "knave", the choices are still limited to silver and copper and One is a "knave".

Having established all of this, Two must also be a "knave", because Two claims that One speaks the truth, meaning that the copper key opens the door.

Darklands Puzzle #9

A door blocks the path. Its inscription reads:
FACES ALWAYS LIE OR ALWAYS SPEAK TRUTH.
TOUCH ONE KNOB TO OPEN THE DOOR.
On the wall are six numbered faces, who speak:
One: "Copper cannot open the door."
Two: "Face One speaks the truth. Face Four speaks truth. Gold cannot open the door."
Three: "All odd-numbered faces speak truth."
Four: "If Face Three lies, silver opens the door."
Five: "Gold opens the door."
Six: "Black is white. Copper opens the door."
Upon the door are four metal knobs. You touch...
...the gold.
...the silver.
...the copper.
...the lead.

(Source: Darklands cluebook by MicroProse Software)

The first clue is a gimme: Six is claiming black is white and is therefore a liar. This means that the copper knob does not open the door. This means that One speaks the truth. In turn, Two must speak the truth, because all faces are perfectly uniform about lying or speaking the truth. Four, who has already been established as a truth-teller, says that, if Three lies, silver opens the door. Five is lying, meaning that Three's claim is a lie. Therefore the silver knob opens the door.

Darklands Puzzle #8

The path is blocked by an iron door. Carved about it are the words:
ONE HEAD INVARIABLY SPEAKS TRUTH.
THE OTHER HEADS ALWAYS LIE.
Embossed on the door are four metal heads. They speak:
Gold: "Yesterday, Hootvin said that the gold knob opened the door."
Silver: "The copper head speaks the truth."
Copper: "I am not Hootvin."
Lead: "Naturally not, for I am Hootvin."
The door has two knobs, gold and silver. One opens the door, the other is probably (is. ed.) a trap. You press...
...the gold knob.
...the silver knob.

(Source: Darklands cluebook by MicroProse Software)

Silver is obviously lying because only one head can speak the truth. This means that Copper is also lying and is therefore Hootvin. Lead is lying because he can't be Hootvin. (Presumably there is only one Hootvin.) This leaves Gold as the sole truth-teller but there is a caveat: Gold is relaying what Hootvin (an inveterate liar) said. This means that the silver knob opens the door.

Darklands Puzzle #6

The path is blocked by a grim iron door. To one side is a golden statue of a dwarf. On the other is a silver statue of a dwarf. Embossed on the door are the words:
ONE STATUE ALWAYS LIES.
ONE STATUE ALWAYS SPEAKS TRUTH.
As you ponder this, they speak.
The gold statue says, "To open the door, touch the statue which speaks truth."
The silver statue says, "To open the door, touch the statue which lies." Which statue is right? The wrong statue may (will. ed.) release a dwarf trap! You think carefully, then...
...touch the gold statue.
...touch the silver statue.

(Source: Darklands cluebook by MicroProse Software)

Assume first that Gold is the "knight" of the pair. This means that one would touch Gold. But this assumption may not be warranted and on the other hand it may be the case that Gold  is the "knave" of the pair. In this case, Gold is really telling the player to touch the statue that doesn't tell the truth (i.e. lies). And, in this case, Silver (i.e. the "knight") is fully willing to back up the tacit statement of the Gold: touch the statue that is a dirty liar (i.e. Gold). In any case, one should touch Gold. And pray that it doesn't start to melt like the one in the Hobbit films.

Dies ist nicht dein Königreich. Dies ist Zwergenland, dies ist Zwergengold. Und wir bekommen unsere Rache!

Darklands Puzzle #5

Here is a dark iron door. Carved in it are:
ONLY ONE KNOB OPENS THE DOOR.
ONLY ONE STATEMENT IS WHOLLY TRUE.
Four knobs are on the door, of gold, silver, copper and lead. Four statements are on the wall nearby:

1. The gold knob opens the door.
2. The lead knob opens the door.
3. Neither the silver knob nor the gold knob open the door.
4. The lead knob does not open the door.

Only one statement is true. But which? Only one knob opens the door. Which?
...gold.
...silver.
...copper.
...Iead.

(Source: Darklands cluebook by MicroProse Software)

The cluebook makes the very helpful suggestion of starting with focusing attention on statements #2 and #4. Only one of them can be true. If statement #2 is true then statement #3 is also, true, which contradicts the stipulations of the puzzle. This means that #4 is the only wholly true statement out of the lot. Because statement #3 is a logical conjunction, one of its operands is permitted to be true while the other is false, making it not wholly true. Statement #1 does not have this luxury and is therefore required to be false. This means that the silver knob opens the door.

Darklands Puzzle #4

(Yes, #4, I didn't say I was doing them all.)

Here is a grim iron door inscribed:
ONLY ONE KNOB OPENS THE DOOR.
EACH METAL'S STATEMENTS ARE EITHER BOTH TRUE OR BOTH FALSE.
One the floor are six statements and three metal knobs, each of a
different metal.
Gold: Tifsyn's only son is Hardgrep.
Gold: The gold knob opens the door.
Silver: The gold knob opens the door.
Silver: The silver knob does not open the door.
Copper: Tifsyn's only son is Gymer.
Copper: The gold statements are both true.
You press...
...gold.
...silver.
...copper.

(Source: Darklands cluebook by MicroProse Software)

Well let's see here: Copper claims that Gold's statements are both true. This mean's that Tifsyn's only son is Hardgrep. But Copper also claims that Tifsyn's only son is Gymer. We have a contradiction! Because what Copper is saying in one instance cannot possibly be true, as stipulated by the puzzle, both of Copper's statements are false. This means that Gold's statements are both also false. Where does that put Silver? Well Gold and Silver both claim the gold knob opens the door. That means that everyone here is a liar. Very sad! The silver knob opens the door.

Darklands Puzzle #2

Your path is blocked by a grim iron door. Embossed onto it is a legend:

Yep, all of these images are going to be equally shitty

Five knobs are labeled "5" to "9" consecutively. The wrong knob may (will. ed.) release a trap. Which numeral does the letter "E" stand for? You select...
...5.
...6.
...7.
...8.
...9.

(Source: Darklands cluebook by MicroProse software)

The key is the value of "F", which is carried over from the addition of the second leftmost column. Does two or any larger value ever carry over? No, it's always one. Working from right to left, "L" is two and "O" is four. "E" needs to add together with "E" so that a one carries over and the remainder is "O" (i.e. 4). The appropriate value is of course seven.

Darklands Puzzle #1

Since I've decided to resurrect my puzzle blog that no one reads, I'm going to be doing puzzles from the 1992 historical fantasy RPG Darklands, set in the Holy Roman Empire of the late 15th century.

Ironic given that when I played the game, Gretchen had the sword and Gunther had the hammer

The puzzles are thrown at the player by Dwarves occupying human-owned mines in order to proceed further in resolving the issues behind the occupation, as the Dwarves of Darklands, in addition to being portrayed as clever, mineral-obsessed and apparently allergic to Christian symbols, are also skilled logicians and mathematicians. (Ha-ha, very funny, laugh it up, MicroProse. I'm sure you got your jollies from stereotypes.) I only ever encountered a fraction of the puzzles I am presenting here while in-game and am taking ones I like from the cluebook. The first of these:

Your way is blocked by dark iron door. Carved above it are the words:
FACES SPEAK EITHER WHOLLY LIES OR WHOLLY TRUTH.
TOUCH A FACE WHICH SPEAKS WHOLLY TRUTH TO OPEN THE DOOR.
On the door are three metal faces: lead, gold, silver. As you ponder, the
lead face speaks, "Pape mimer aleppe."
What could he mean? The gold face translates, "Lead said he always
lies." The silver face cries, "Do not believe Gold! HE is the liar!" Which
face speaks truth? You think, then touch...
...the gold face.
...the silver face.

(Source: Darklands cluebook by MicroProse Software)

So, this is essentially a knights-and-knaves type of puzzle. Perhaps Darklands mines have become a sort of afterlife for the late Raymond Smullyan.

What the lead face is saying is a canard. There is no point in trying to interpret it. What is important is the incoherent assertion of the gold face: if lead is a "knight" then he would never claim to lie, which is equally true if he is a "knave". Neither will ever claim to lie. The gold face is then a "knave". So the silver face is telling the truth.