1. Your spaceship lands in the middle of three villages, and you must decide which village to head to (not all passengers on you spaceship need go to the same village).
2. Each village is home to a tribe, with each tribe having different tendancies (in terms of Honesty and Hostility; see chart at the top).
3. Tribes are identified by their (primary, secondary) colors (as per chart at the top).
4. As you flew in, your spotted the roof (secondary) colors of the three villages: Yellow, Black, and Black. However, as your spaceship spun out of control for a crash landing, when you actually land and look out your window, you don't know which village corresponded to which roof color.
5. The villages are now so far from your landed spacecraft that you are unable to identify their primary (or secondary) colors.
6. The crash landing rendered your spacecraft almost completely useless. Only the broadcast PA communication works, which can broadcast a single message to each of the three villages simultaneously. Based on the primitive communication of the alien lifeform, which is akin to Morse code, it will take about 5 minutes to broadcast any communication to the 3 surrounding villages.
7. Similarly, it will take about 5 minutes for the response from each village to reach your spaceship (you will be able to distinguish which response is coming from which village).
8. You estimate it is about 30 minutes until sundown, at which point the Trollocs will start hunting any human that is not already in a village.
9. You estimate it will take 10 minutes for your passengers to travel from your landing site to any village.
10. Thus, you have time to broadcast one (YES/NO) question to the villages (5min), await the response (5min), and then broadcast a second question (5min) and await the result (5min).
    At that point, you'll have to choose villages for each passenger, so that they have the requisite 10min to reach that village before the Trollocs come out to hunt.

Observations:

• In order to know where to send each passenger (man, woman, child), you need to consider the Hostilities of each Charin tribe type. In particular, solving the riddle requires you to exactly identify the tribe type of each of the three surrounding villages.
• You saw two Black-roofed villages. These are either Aes Sedai or Foresaken (or one of each).
• You saw one Yellow-roofed village, which is either Myrddraal, Aelfinn, or Eelfinn.
• As a result, the following 12 scenarios enumerates all possible scenarios, where 'H' denotes Honest (Aes Sedai), 'D' denotes Dishonest (Foresaken), 'R' denotes Random (Myrddraal), 'Y' denotes YES (Aelfinn), 'N' denotes NO (Eelfinn), and τ denotes an arbitrary translation (rotational shift) of the three villages:
• τ(RHH)
• τ(RHD)
• τ(RDH)
• τ(RDD)
• τ(HHH)   ←  (from τ(NHH), since (per the "Exceptions" of the Tribal Chart) Eelfinn ('N') act like Aes Sedai ('H') when surrounded by two Aes Sedai villages.)
• τ(DDD)   ←  (from τ(YDD), since (per the "Exceptions" of the Tribal Chart) Aelfinn ('Y') act like Foresaken ('D') when surrounded by two Foresaken villages.)
• τ(YYY)   ←  (from τ(YHH), since (per the "Exceptions" of the Tribal Chart) two adjacent Aes Sedai ('H') villages will each act like Aelfinn ('Y') when there is a nearby Aelfinn village.)
• τ(NNN)   ←  (from τ(NDD), since (per the "Exceptions" of the Tribal Chart) two adjacent Foresaken ('D') villages will each act like Eelfinn ('N') when there is a nearby Eelfinn village.)
• τ(YHD)
• τ(YDH)
• τ(NHD)
• τ(NDH)
• Before attempting to identify specific questions, it may be useful to think about the universe of possible Responses, independent of what the actual question(s) are. Namely, regardless of the first question, there are just 8 possible universes of responses (based on receiving a "Yes" vs. "No" response from each of the 3 villages).
• Namely, for each possible "configuration" (assignment of the 3 villages to a Charin tribe type), one (or more) of the 8 possible Responses to your first question must include that configuration as a possibility. In particular, we can construct an "Assignment Table", that distributes/assigns all possible configurations to one of the 8 possible Responses:

  Q1 Response	Configurations
  YYY	???
  YYN	???
  YNY	???
  NYY	???
  YNN	???
  NYN	???
  NNY	???
  NNN	???

• Before thinking about the actual concrete questions you will ask, it may be useful to think about how the Responses may (in an ideal world) partition the possible configurations amongst them, in such a way that the configurations are balanced (in terms of how many configurations are assigned to each of the eight possible Responses), logically sound (see next bullet), and suitably diverse (i.e. the set of configurations that correspond to any single Response type -- e.g. YNY ("Yes", "No", "Yes") -- are suitably distinct from one another so that they can be easily separated/distinguished by the second question).
• In terms of the "logically sound" criteria: Consider any single possible configuration in which the Yellow roof building you saw is a Myrddraal ('R') village; for example one such possibile configuration is: (R, H, H), in which the Northern village is Myrddraal ('R'), and the Southwestern and Southeastern villages are both Aes Sedai ('H'). Suppose, as per the previous hint, you assign row 'YNY' for this Configuration in the Assignment Table. Then, regardless of what your first question actually is, notice that 'NNY' is necessarily also a possible response for this (R, H, H) Configuration. This is because Myrddraal respond to questions Randomly, which means (regardless of the question) they can respond with either 'Yes' or 'No'.
• In particular, this means that as you fill in the Assignment Table, any Configuration that has an 'R' in it must actually appear in (at least) two rows of the table: once for whichever row you choose to put it in, and a second time in the row that has the same response pattern but has flip-flopped the Myrddraal response in terms of 'Y' vs. 'N'.

Succinct Answer:

Q1: Is 1+1 = 2?
Q2a (If the Q1 response contains an ODD number of Y's (Yes) responses): Is the following sum odd?:

1. Add 1 if your village is Aes Sedai ('H'), the village clockwise from you is Foresaken ('D'), and the village counter-clockwise from you is Myrddraal ('R')
2. Add 1 if the village clockwise from you is Aelfinn ('Y') and the village counter-clockwise from you is Aes Sedai ('H').
3. Add 1 if none of the three villages is Foresaken ('D')

Q2b (If the Q1 response contains an EVEN number of Y's (Yes) responses): Is the following sum odd?:

1. Add 1 if your village is Foresaken ('D'), the village clockwise from you is Aes Sedai ('H'), and the village counter-clockwise from you is Myrddraal ('R')
2. Add 1 if the village clockwise from you is Eelfinn ('N') and the village counter-clockwise from you is Foresaken ('D').
3. Add 1 if none of the three villages is Aes Sedai ('H')

Explanation: There are many possible solutions, the above simply highlights one possible solution. Before explaining why the above works, we first explain the reasoning behind the riddle.

As per the Hint, the first thing to deterimine is all possible associations of village to tribal type. For the remainder of the exposition below, we use the terminology Configuration to refer to any specific association of village to tribe type. Furthermore, we express any possible Configuration as simply three concatenated letters, with the first letter specifying the tribal type of the Northern village, the second letter specifying the tribal type of the Southeastern village, and the third letter specifying the tribal type of the Southwestern village.

From the information that there was exactly one Yellow roof and exactly two Black roofs, but you don't know which is which due to the uncontrolled spin of your crash landing, the list of all possible Configurations is:

• RHH, HRH, HHR
• RHD, DRH, HDR
• RDH, HRD, DHR
• RDD, DRD, DDR
• YHD, DYH, HDY
• YDH, HYD, DHY
• YYY   ←  (from τ(YHH), since (per the "Exceptions" of the Tribal Chart) two adjacent Aes Sedai ('H') villages will each act like Aelfinn ('Y') when there is a nearby Aelfinn village.)
• DDD   ←  (from τ(YDD), since (per the "Exceptions" of the Tribal Chart) Aelfinn ('Y') act like Foresaken ('D') when surrounded by two Foresaken villages.)
• HHH   ←  (from τ(NHH), since (per the "Exceptions" of the Tribal Chart) Eelfinn ('N') act like Aes Sedai ('H') when surrounded by two Aes Sedai villages.)
• NNN   ←  (from τ(NDD), since (per the "Exceptions" of the Tribal Chart) two adjacent Foresaken ('D') villages will each act like Eelfinn ('N') when there is a nearby Eelfinn village.)
• NHD, DNH, HDN
• NDH, HND, DHN

A solution to the riddle requires exactly identifying which of these 28 Configurations you are in.

Namely, you will assign passengers to go to villages as follows:

Configuration Category	Actual Configurations	Destination Villages Men Women Children
σ(YYY)	YYY	Y (Aelfinn)	Y (Aelfinn)	Y (Aelfinn)
σ(NNN)	NNN	N (Eelfinn)	N (Eelfinn)	N (Eelfinn)
σ(HHH)	HHH	- (Trollocs)	H (Aes Sedai)	H (Aes Sedai)
σ(DDD)	DDD	- (Trollocs)	- (Trollocs)	D (Foresaken)
σ(RHH)	RHH, HRH, HHR	R (Myrddraal)	H (Aes Sedai)	H (Aes Sedai)
σ(RDD)	RDD,DRD,DDR	R (Myrddraal)	- (Trollocs)	D (Foresaken)
σ(YHD)	YHD,DYH,HDY,YDH,HYD,DHY	Y (Aelfinn)	Y or H (Aelfinn or Aes Sedai)	Y, H, or D (Aelfinn, Aes Sedai, or Foresaken)
σ(NHD)	NHD,DNH,HDN, NDH,HND,DHN	N (Eelfinn)	N or H (Eelfinn or Aes Sedai)	N, H, or D (Eelfinn, Aes Sedai, or Foresaken)
σ(RHD)	RHD,DRH,HDR,RDH,HRD,DHR	R (Myrddraal)	H (Aes Sedai)	H or D (Aes Sedai, or Foresaken)

The next step is to observe that, regardless of the first question that you broadcast to the three villages, and regardless of the association of each village to tribal type, there are only 8 possible responses (arbitrarilly order the responses as the first response is from the village to the North, the second is from the village to the Southeast, and the third is from the village to the Southwest):

1. YYY
2. YYN
3. YNY
4. NYY
5. YNN
6. NYN
7. NNY
8. NNN

Observation 1: Regardless of your first question, you must partition the 40 possible Configurations (28 distinct Configurations, with 12 of these (the ones with 'R' present) appearing twice) into the 8 possible responses. Namely, you must distribute/assign the 40 Configurations to one of the 8 possible rows of the following "Assignment Table:"

Q1 Response	Configurations
YYY	???
YYN	???
YNY	???
NYY	???
YNN	???
NYN	???
NNY	???
NNN	???

Before attempting to assign the 40 Configurations into the 8 response rows of the above table, it will be useful to make an additional observation on a required property that any 'valid' assignment must satisfy. This requirement comes from considering the necessary outcome of your second question: namely, that you can necessarily associate each village to precisely one tribe after your second question. In particular, suppose that after your first question (and based on the assignment of each of the 40 Configurations to the 8 possible response rows), that it remains a possibility that Myrddraal ('R') is one of the three villages. This means that when you direct your second question to this village, the response you get from them could be 'Yes' or 'No'. We can now think about partitioning the remaining possible Configurations (after your first question rules out some of them) into the 8 possible responses of your second question. For example, if RHH is one of the possible Configurations after your first question, and you want to (say) assign the response 'NYY' to your second question to this Configuration, then you must also assign 'YYY' to it. Essentially what this means is that each Configuration that has an 'R' in it must be assigned to two different response rows for the Assignment Table of the second question. Since the second question must uniquely identify each village with the Charin tribe living there, this means that the Assignment Table based on your first question must satisfy:

Observation 2: For any possible Response to your first question (e.g. 'YYY' is one of the 8 possible responses), you must assign some subset of the (28 possible) Configurations to this Response (on average, 5 Configurations must be assigned to each of the 8 possible responses).
If 'r' counts the number of Configurations assigned to this Response that include 'R' (Myrddraal) and 's' counts the number of Configurations assigned to this Response that do not include 'R', then:

2r + s ≤ 8

Actually, Observation 2 can be made stronger by applying a counting argument. Namely, across the 8 total Response rows, we must assign 24 Configurations that have an 'R' and another 16 that do not. Then applying the inequality of Observation 2 simultaneously to all 8 rows would imply: 2*R + S ≤ 64. Indeed, this shows that none of the rows can exhibit the inequality, and all must actually be equality:

Observation 2': If 'r' counts the number of Configurations assigned to any Response row in the Assignment Table that include 'R' (Myrddraal), and 's' counts the number of Configurations that do not include 'R', then:

2r + s = 8

For example, Observation 2' says that there can't be a row in your Assignment Table that has 5 (or more) Configurations with 'R'. Similarly, if a row has 4 Configurations with 'R' (so r = 4), then it must be s = 0 (so there are no other Configurations on this row). Similarly, if a row has 3 Configurations with 'R' (so r = 3), then it must be s = 2 (so there are exactly two other Configurations that don't include 'R' on this row). When combining these facts with the fact that 24 Configurations involving 'R' (12 distinct Configurations that have 'R' in them, with each one needing to appear twice in the Assignment Table) and 16 not involving 'R' must be assigned, this limits the number of ways the Assignment Table can be constructed (even disregarding for the moment an actual question that would generate such a table).

With these observations in hand, there are many possible ways to create a valid Assignment Table that partitions the 40 Configurations into the 8 responses (subject to the constraint that whenever/wherever a Configuration with 'R' appears in one of the rows, then this Configuration must also appear in the other row that has flip-flopped Y/N in the position that 'R' is in). Perhaps one of the most natural ways to do this is:

Q1 Response	Configurations
YYY	YYY, HHH, RHH, HRH, HHR
YYN	YHD, HYD, RHD, HRD, HHR
YNY	YDH, HDY, RDH, HRH, HDR
NYY	DHY, DYH, RHH, DRH, DHR
YNN	HND, HDN, RDD, HRD, HDR
NYN	NHD, DHN, RHD, DRD, DHR
NNY	NDH, DNH, RDH, DRH, DDR
NNN	NNN, DDD, RDD, DRD, DDR

Conceptually, the above table is created by associating a 'Y' in the response with one of: {Y, R, H}; and associating an 'N' in the response with one of: {N, R, D} (and then applying certain rules based on the riddle setup; namely that exactly one of {R, Y, N} must appear in each Configuration; and also the four Configurations that come from the "Exceptions" in the Charin Tribal Chart (at the top of the page): τ(YHH)  →  YYY; τ(YDD)  →  DDD; τ(NHH)  →  HHH; τ(NDD)  →  NNN).

With the above partitioning, it is easy to verify that the following question will indeed create the above Assignment Table:

Q1: "Is 1+1=2?"

Next, depending on which response (row) you receive from your first question, you must determine a second question that will allow you to narrow down the remaining possible Configurations down the unique (one) Configuration that you are in. Again, there are numerous possible solutions, and your second question can depend on which (of the 8 possible) Response you get to your first question.

The table below is one possible solution for what to ask for Q2 (based on the Response you got to your Q1):

Q1 Response	Configurations	Q2
YYY	YYY, HHH, RHH, HRH, HHR	Add 1 if 'H' is clockwise and 'R' is counter-clockwise Is sum odd?
YYN	YHD, HYD, RHD, HRD, HHR	Add 1 if you are 'D' and 'H' is clockwise and 'R' is counter-clockwise Add 1 if 'Y' is clockwise and 'H' is counter-clockwise Add 1 if 'D' is not present Is sum odd?
YNY	YDH, HDY, RDH, HRH, HDR	Same as 'YYN' (above) row
NYY	DHY, DYH, RHH, DRH, DHR	Same as 'YYN' (two above) row
YNN	HND, HDN, RDD, HRD, HDR	Add 1 if you are 'H' and 'D' is clockwise and 'R' is counter-clockwise Add 1 if 'N' is clockwise and 'D' is counter-clockwise Add 1 if 'H' is not present Is sum odd?
NYN	NHD, DHN, RHD, DRD, DHR	Same as 'YNN' (above) row
NNY	NDH, DNH, RDH, DRH, DDR	Same as 'YNN' (two above) row
NNN	NNN, DDD, RDD, DRD, DDR	Add 1 if 'D' is clockwise and 'R' is counter-clockwise Is sum odd?

It is left to the reader to verify that the above Q2's for each Response row indeed partition each of the 5 possible Configurations into distinct Q2 response rows.

Note that the Q2a and Q2b at the top (in the "Succinct Answer") matches the Q2 column above.

Note that the separation of Q2 into Q2a and Q2b could be avoided so that there is a single Q2. While this is not strictly necessary to solve the riddle, it may be more satisfying to some readers (albeit less explicitly clear) to do so. Namely, notice Q2a and Q2b are exactly the same if you swap every occurrence of 'H' and 'D' and swap every occurrence of 'Y' with 'N'. Thus, you could use the parity of the number of "YES" responses to Q1 as an indicator function on whether or not to perform these swaps in each step of the computation of the sum.

1. Your spaceship lands in the middle of three villages, and you must decide which village to head to (not all passengers on you spaceship need go to the same village).
2. Each village is home to a tribe, with each tribe having different tendancies (in terms of Honesty and Hostility; see chart at the top).
3. Tribes are identified by their (primary, secondary) colors (as per chart at the top).
4. As you flew in, your spotted the roof (secondary) colors of the three villages: Yellow, Black, and Black. However, as your spaceship spun out of control for a crash landing, when you actually land and look out your window, you don't know which village corresponded to which roof color.
5. The villages are now so far from your landed spacecraft that you are unable to identify their primary (or secondary) colors.
6. The crash landing rendered your spacecraft almost completely useless. Only the broadcast PA communication works, which can broadcast a single message to each of the three villages simultaneously. Based on the primitive communication of the alien lifeform, which is akin to Morse code, it will take about 5 minutes to broadcast any communication to the 3 surrounding villages.
7. Similarly, it will take about 5 minutes for the response from each village to reach your spaceship (you will be able to distinguish which response is coming from which village).
8. You estimate it is about 30 minutes until sundown, at which point the Trollocs will start hunting any human that is not already in a village.
9. You estimate it will take 20 minutes for the children on board to reach any of the three villages, and 10 minutes for your adult passengers.
10. Thus, you have time to broadcast one (YES/NO) question to the villages (5min) and await the response (5min), at which point in time you'll need to choose a destination village for the children to start walking to (in order for them to have time to reach it by sundown, when the countryside will be crawling with hungry Trollocs). You'll then have time to broadcast a second (YES/NO) question to the villages (5min) and await the response (5min) before you need to decide which village to send the adult (male and female) passengers.

Observations:

The Medium variant of this riddle is very similar to the Easy variant; if you haven't solved the Easy variant yet, it may be worth visiting the Hints and Solution to that one first. These first set of Hints are the same as the Easy Variant:

• In order to know where to send each passenger (man, woman, child), you need to consider the Hostilities of each Charin tribe type. In particular, solving the riddle requires you to exactly identify the tribe type of each of the three surrounding villages.
• You saw two Black-roofed villages. These are either Aes Sedai or Foresaken (or one of each).
• You saw one Yellow-roofed village, which is either Myrddraal, Aelfinn, or Eelfinn.
• As a result, the following 12 scenarios enumerates all possible scenarios, where 'H' denotes Honest (Aes Sedai), 'D' denotes Dishonest (Foresaken), 'R' denotes Random (Myrddraal), 'Y' denotes YES (Aelfinn), 'N' denotes NO (Eelfinn), and τ denotes an arbitrary translation (rotational shift) of the three villages:
• τ(RHH)
• τ(RHD)
• τ(RDH)
• τ(RDD)
• τ(HHH)   ←  (from τ(NHH), since (per the "Exceptions" of the Tribal Chart) Eelfinn ('N') act like Aes Sedai ('H') when surrounded by two Aes Sedai villages.)
• τ(DDD)   ←  (from τ(YDD), since (per the "Exceptions" of the Tribal Chart) Aelfinn ('Y') act like Foresaken ('D') when surrounded by two Foresaken villages.)
• τ(YYY)   ←  (from τ(YHH), since (per the "Exceptions" of the Tribal Chart) two adjacent Aes Sedai ('H') villages will each act like Aelfinn ('Y') when there is a nearby Aelfinn village.)
• τ(NNN)   ←  (from τ(NDD), since (per the "Exceptions" of the Tribal Chart) two adjacent Foresaken ('D') villages will each act like Eelfinn ('N') when there is a nearby Eelfinn village.)
• τ(YHD)
• τ(YDH)
• τ(NHD)
• τ(NDH)
• Before attempting to identify specific questions, it may be useful to think about the universe of possible Responses, independent of what the actual question(s) are. Namely, regardless of the first question, there are just 8 possible universes of responses (based on receiving a "Yes" vs. "No" response from each of the 3 villages).
• Namely, for each possible "configuration" (assignment of the 3 villages to a Charin tribe type), one (or more) of the 8 possible Responses to your first question must include that configuration as a possibility. In particular, we can construct an "Assignment Table", that distributes/assigns all possible configurations to one of the 8 possible Responses:

  Q1 Response	Configurations
  YYY	???
  YYN	???
  YNY	???
  NYY	???
  YNN	???
  NYN	???
  NNY	???
  NNN	???

• Before thinking about the actual concrete questions you will ask, it may be useful to think about how the Responses may (in an ideal world) partition the possible configurations amongst them, in such a way that the configurations are balanced (in terms of how many configurations are assigned to each of the eight possible Responses), logically sound (see next bullet), and suitably diverse (i.e. the set of configurations that correspond to any single Response type -- e.g. YNY ("Yes", "No", "Yes") -- are suitably distinct from one another so that they can be easily separated/distinguished by the second question).
• In terms of the "logically sound" criteria: Consider any single possible configuration in which the Yellow roof building you saw is a Myrddraal ('R') village; for example one such possibile configuration is: (R, H, H), in which the Northern village is Myrddraal ('R'), and the Southwestern and Southeastern villages are both Aes Sedai ('H'). Suppose, as per the previous hint, you assign row 'YNY' for this Configuration in the Assignment Table. Then, regardless of what your first question actually is, notice that 'NNY' is necessarily also a possible response for this (R, H, H) Configuration. This is because Myrddraal respond to questions Randomly, which means (regardless of the question) they can respond with either 'Yes' or 'No'.
• In particular, this means that as you fill in the Assignment Table, any Configuration that has an 'R' in it must actually appear in (at least) two rows of the table: once for whichever row you choose to put it in, and a second time in the row that has the same response pattern but has flip-flopped the Myrddraal response in terms of 'Y' vs. 'N'.

• The three tribes that are violent towards Children are the Myrddraal, Aelfinn, and Eelfinn, with the latter two only dangerous if the Children are sent their without adult male supervision. Since you saw a Yellow roof as you approached your landing site, you know one of the three villages must be one of those three tribe types. Therefore, your first question/response must seek to identify which of the three villages had the Yellow roof.
• However, because the presence of adult males can protect Children from the Aelfinn and Eelfinn, it is less vital that you identify these (if you happen to send your children to an Aelfinn or Eelfinn village, then you'll be able to send adult males to catch up with them -- and thus ensure their safety -- before they reach the village).
• Thus, if you are limited in how much information you can deduce from just one question/response, it is more important to identify villages that are/aren't Myrddraal ('R'), as opposed to the broader question of identifying which of the three villages has the Yellow-roofed buildings.
• If attempting to use the Assigment Table approach (from above hint) to solve this riddle, what this concretely means is that (amongst the 8 possible Reponse rows) there cannot be a Row that has a set of corresponding Configurations that include an 'R' in all three positions. Namely, as you think about how to distribute all the Configurations with an 'R' in them amongst the 8 possible response rows, you need to cluster them so that, in each row, there is at least one village position (North, Southwest, or Southeast) that never has Myrddraal ('R') assigned to it.

Succinct Answer:

Q1: Are any of the following three statements true?:

1. Your clockwise neighbor village has the same Charin tribe type as you, AND your counter-clockwise neighbor is a Myrddraal ('R') village;  OR
2. The Charin tribal types of your two surrounding villages are Aes Sedai ('H') and Eelfinn ('N') (in either order);  OR
3. The Charin tribal types of your two surrounding villages are Foresaken ('D') and Aelfinn ('Y') (in either order).

Then, if the responses to your first question was 'YYY' or 'NNN', then send your Children to any of the three villages (e.g., Northern). Otherwise, the responses from two of the villages will be one thing (e.g., 'Y'), and the response from the third will be the opposite (e.g., 'N'). Send your children to the village that responded differently than the other two.

Then, to determine where to send the adults, ask your second question as follows:

Q2a (If the Q1 response was 'YYY'):
    Are the three villages, in clockwise order (i.e. up to rotational shift), equal to 'HYD' (Aes Sedai, Aelfinn, Foresaken)?
Q2b (If the Q1 response was 'NNN'):
    Are the three villages, in clockwise order (i.e. up to rotational shift), equal to 'HND' (Aes Sedai, Eelfinn, Foresaken)?
Q2c (If the Q1 response had two 'Yes' responses and one 'No' response):
    Are the three villages, in clockwise order (i.e. up to rotational shift), equal to 'HDR' (Aes Sedai, Foresaken, Myrddraal)?
Q2d (If the Q1 response had one 'Yes' response and two 'No' responses):
    Are the three villages, in clockwise order (i.e. up to rotational shift), equal to 'HRD' (Aes Sedai, Myrddraal, Foresaken)?

Explanation:
TL;DR The exposition below is identical to the Easy Variant, up until the text in the red box below "Solution for Medium Variant"; so if you've already read the Easy Variant solution, you can skip over the exposition below and scroll down to this red box.

There are many possible solutions, the above simply highlights one possible solution. Before explaining why the above works, we first explain the reasoning behind the riddle.

As per the Hint, the first thing to deterimine is all possible associations of village to tribal type. For the remainder of the exposition below, we use the terminology Configuration to refer to any specific association of village to tribe type. Furthermore, we express any possible Configuration as simply three concatenated letters, with the first letter specifying the tribal type of the Northern village, the second letter specifying the tribal type of the Southeastern village, and the third letter specifying the tribal type of the Southwestern village.

From the information that there was exactly one Yellow roof and exactly two Black roofs, but you don't know which is which due to the uncontrolled spin of your crash landing, the list of all possible Configurations is:

• RHH, HRH, HHR
• RHD, DRH, HDR
• RDH, HRD, DHR
• RDD, DRD, DDR
• YHD, DYH, HDY
• YDH, HYD, DHY
• YYY   ←  (from τ(YHH), since (per the "Exceptions" of the Tribal Chart) two adjacent Aes Sedai ('H') villages will each act like Aelfinn ('Y') when there is a nearby Aelfinn village.)
• DDD   ←  (from τ(YDD), since (per the "Exceptions" of the Tribal Chart) Aelfinn ('Y') act like Foresaken ('D') when surrounded by two Foresaken villages.)
• HHH   ←  (from τ(NHH), since (per the "Exceptions" of the Tribal Chart) Eelfinn ('N') act like Aes Sedai ('H') when surrounded by two Aes Sedai villages.)
• NNN   ←  (from τ(NDD), since (per the "Exceptions" of the Tribal Chart) two adjacent Foresaken ('D') villages will each act like Eelfinn ('N') when there is a nearby Eelfinn village.)
• NHD, DNH, HDN
• NDH, HND, DHN

A solution to the riddle requires exactly identifying which of these 28 Configurations you are in.

Namely, you will assign passengers to go to villages as follows:

Configuration Category	Actual Configurations	Destination Villages Men Women Children
σ(YYY)	YYY	Y (Aelfinn)	Y (Aelfinn)	Y (Aelfinn)
σ(NNN)	NNN	N (Eelfinn)	N (Eelfinn)	N (Eelfinn)
σ(HHH)	HHH	- (Trollocs)	H (Aes Sedai)	H (Aes Sedai)
σ(DDD)	DDD	- (Trollocs)	- (Trollocs)	D (Foresaken)
σ(RHH)	RHH, HRH, HHR	R (Myrddraal)	H (Aes Sedai)	H (Aes Sedai)
σ(RDD)	RDD,DRD,DDR	R (Myrddraal)	- (Trollocs)	D (Foresaken)
σ(YHD)	YHD,DYH,HDY,YDH,HYD,DHY	Y (Aelfinn)	Y or H (Aelfinn or Aes Sedai)	Y, H, or D (Aelfinn, Aes Sedai, or Foresaken)
σ(NHD)	NHD,DNH,HDN, NDH,HND,DHN	N (Eelfinn)	N or H (Eelfinn or Aes Sedai)	N, H, or D (Eelfinn, Aes Sedai, or Foresaken)
σ(RHD)	RHD,DRH,HDR,RDH,HRD,DHR	R (Myrddraal)	H (Aes Sedai)	H or D (Aes Sedai, or Foresaken)

The next step is to observe that, regardless of the first question that you broadcast to the three villages, and regardless of the association of each village to tribal type, there are only 8 possible responses (arbitrarilly order the responses as the first response is from the village to the North, the second is from the village to the Southeast, and the third is from the village to the Southwest):

1. YYY
2. YYN
3. YNY
4. NYY
5. YNN
6. NYN
7. NNY
8. NNN

Observation 1: Regardless of your first question, you must partition the 40 possible Configurations (28 distinct Configurations, with 12 of these (the ones with 'R' present) appearing twice) into the 8 possible responses. Namely, you must distribute/assign the 40 Configurations to one of the 8 possible rows of the following "Assignment Table:"

Q1 Response	Configurations
YYY	???
YYN	???
YNY	???
NYY	???
YNN	???
NYN	???
NNY	???
NNN	???

Before attempting to assign the 40 Configurations into the 8 response rows of the above table, it will be useful to make an additional observation on a required property that any 'valid' assignment must satisfy. This requirement comes from considering the necessary outcome of your second question: namely, that you can necessarily associate each village to precisely one tribe after your second question. In particular, suppose that after your first question (and based on the assignment of each of the 40 Configurations to the 8 possible response rows), that it remains a possibility that Myrddraal ('R') is one of the three villages. This means that when you direct your second question to this village, the response you get from them could be 'Yes' or 'No'. We can now think about partitioning the remaining possible Configurations (after your first question rules out some of them) into the 8 possible responses of your second question. For example, if RHH is one of the possible Configurations after your first question, and you want to (say) assign the response 'NYY' to your second question to this Configuration, then you must also assign 'YYY' to it. Essentially what this means is that each Configuration that has an 'R' in it must be assigned to two different response rows for the Assignment Table of the second question. Since the second question must uniquely identify each village with the Charin tribe living there, this means that the Assignment Table based on your first question must satisfy:

Observation 2: For any possible Response to your first question (e.g. 'YYY' is one of the 8 possible responses), you must assign some subset of the (28 possible) Configurations to this Response (on average, 5 Configurations must be assigned to each of the 8 possible responses).
If 'r' counts the number of Configurations assigned to this Response that include 'R' (Myrddraal) and 's' counts the number of Configurations assigned to this Response that do not include 'R', then:

2r + s ≤ 8

Actually, Observation 2 can be made stronger by applying a counting argument. Namely, across the 8 total Response rows, we must assign 24 Configurations that have an 'R' and another 16 that do not. Then applying the inequality of Observation 2 simultaneously to all 8 rows would imply: 2*R + S ≤ 64. Indeed, this shows that none of the rows can exhibit the inequality, and all must actually be equality:

Observation 2': If 'r' counts the number of Configurations assigned to any Response row in the Assignment Table that include 'R' (Myrddraal), and 's' counts the number of Configurations that do not include 'R', then:

2r + s = 8

For example, Observation 2' says that there can't be a row in your Assignment Table that has 5 (or more) Configurations with 'R'. Similarly, if a row has 4 Configurations with 'R' (so r = 4), then it must be s = 0 (so there are no other Configurations on this row). Similarly, if a row has 3 Configurations with 'R' (so r = 3), then it must be s = 2 (so there are exactly two Configurations that don't include 'R' on this row). When combining these facts with the fact that 24 Configurations involving 'R' (12 distinct Configurations that have 'R' in them, with each one needing to appear twice in the Assignment Table) and 16 not involving 'R' must be assigned, this limits the number of ways the Assignment Table can be constructed (even disregarding for the moment an actual question that would generate such a table).

***Solution for Medium Variant***

Before specifying (one possible) Assignment Table, we need one final observation that applies for the Medium variant (but not the Easy variant) of this riddle. Namely, we need to determine where to send the Children after just the first question and response. Because the Myrddraal ('R') is the only tribe that is absolutely hostile towards Children (adult men can be sent to Aelfinn and Eelfinn villages to protect Children sent to them), a minimum requirement to ensure the safety of the Children is that after the first question/response, (no matter which of the 8 Responses you receive) you will know for certain the identity of (at least) one village that is NOT 'R'. This is captured by the following:

Observation 3: In every row of the Assigment Table, there must be (at least one) village position (North, Southwest, or Southeast) such that no Configuration on that row has Myrddraal ('R') assigned to that position.

With these observations in hand, there are many possible ways to create a valid Assignment Table that partitions the 40 Configurations into the 8 responses (subject to the constraint that whenever/wherever a Configuration with 'R' appears in one of the rows, then this Configuration must also appear in the other row that has flip-flopped Y/N in the position that 'R' is in). Perhaps one of the most natural ways to do this -- an the way that was used in the provided Solution for the Easy Variant of this riddle -- is:

Q1 Response	Configurations
YYY	YYY, HHH, RHH, HRH, HHR
YYN	YHD, HYD, RHD, HRD, HHR
YNY	YDH, HDY, RDH, HRH, HDR
NYY	DHY, DYH, RHH, DRH, DHR
YNN	HND, HDN, RDD, HRD, HDR
NYN	NHD, DHN, RHD, DRD, DHR
NNY	NDH, DNH, RDH, DRH, DDR
NNN	NNN, DDD, RDD, DRD, DDR

Unfortunately, the above Assignment Table fails to satisfy Observation 3. For example, if the response to your first question is (row) 'YYN,' then notice that the set of possible Configurations have the Myrddraal tribe ('R') as a possibility for all three of the positions (North, Southwest, Southeast). Thus, you have no village that you can be assured is safe to send the Children.

Going back to counting arguments: we know that (on average) each row of the Assignment Table will have 3 Configurations involving 'R' (and by Observation 2', no row can have more than 4 Configurations involving 'R'). By Observation 3, any such row with 3 (or more) Configurations involving 'R' must leave one position (North, Southwest, or Southeast) that does not assign 'R' to that position for any of the Configurations of that Response row. This makes the above Assignment Table, which was a natural (simple, symmetric) choice, invalid. Perhaps the next natural choice (in terms of simplicity and symmetry) that does respect Observation 3 is to have each Response row that involves 'R' in the corresponding Configurations do so in such a way that there are 4 Configurations involving 'R' in each such row, where these 4 Configurations are such that the 'R' is in one position (say, North) for 2 of the 4, and 'R' is in a second position (say, Southwest) in the other 2. Note that by Observation 2', this would mean that any such row would contain only these four Configurations (i.e. any such row would not have any Configurations that don't include 'R'). This would mean that all the Configurations containing 'R' -- of which there are 12, or 24 total by Observation 1 -- would be distributed across 6 of the 8 rows of the Assignment Table, leaving the other 16 Configurations that don't include 'R' to be distributed in the remaining two rows of the Assignment Table. The following is a natural example of one such possible Assignment Table:

Q1 Response	Configurations
YYY	YYY, HHH, YHD, YDH, HYD, DYH, HDY, DHY
YYN	RHH, RDH, DRD, DRH
YNY	RDD, RHD, HHR, DHR
NYY	HRH, HRD, DDR, HDR
YNN	DRD, DRH, HHR, DHR
NYN	RHH, RDH, DDR, HDR
NNY	RDD, RHD, HRH, HRD
NNN	NNN, DDD, NHD, NDH, HND, DNH, HDN, DHN

This Assignment Table successfully respects the three Observations; but there remain two outstanding issues that must be specified/checked:

1. Is there a Q1 that partitions the 40 Configurations as per this Assignment Table (and if so, what is it)?
2. Given such an Assignment Table, can (the set of Configurations in) each row be successfully "separated" by a second question (i.e. does there exist a second question, such that the response will select the unique Configuration, amongst those that remain); and if so, what is the second question (can depend on the specific relevant row of the Assignment Table based on the Q1 response)?

Q1: Are any of the following three statements true?:

1. Your clockwise neighbor village has the same Charin tribe type as you, AND your counter-clockwise neighbor is a Myrddraal ('R') village;  OR
2. The Charin tribal types of your two surrounding villages are Aes Sedai ('H') and Eelfinn ('N') (in either order);  OR
3. The Charin tribal types of your two surrounding villages are Foresaken ('D') and Aelfinn ('Y') (in either order).

Next, depending on which response (row) you receive from your first question, you must determine a second question that will allow you to narrow down the remaining possible Configurations down the unique (one) Configuration that you are in. Again, there are numerous possible solutions, and your second question can depend on which (of the 8 possible) Response you get to your first question.

The table below is one possible solution for what to ask for Q2 (based on the Response you got to your Q1):

Q1 Response	Configurations	Q2
YYY	YYY, HHH, YHD, YDH, HYD, DYH, HDY, DHY	There is exactly one Aes Sedai ('H') village, AND it is clockwise from you
YYN	RHH, RDH, DRD, DRH	Are the three villages, in clockwise order (i.e. up to rotational shift), equal to 'HDR' (Aes Sedai, Foresaken, Myrddraal)?
YNY	RDD, RHD, HHR, DHR	Same as 'YYN' (above) row
NYY	HRH, HRD, DDR, HDR	Same as 'YYN' (two above) row
YNN	DRD, DRH, HHR, DHR	Are the three villages, in clockwise order (i.e. up to rotational shift), equal to 'HRD' (Aes Sedai, Myrddraal, Foresaken)?
NYN	RHH, RDH, DDR, HDR	Same as 'YNN' (above) row
NNY	RDD, RHD, HRH, HRD	Same as 'YNN' (two above) row
NNN	NNN, DDD, NHD, NDH, HND, DNH, HDN, DHN	There is exactly one Foresaken ('D') village, AND it is clockwise from you

It is left to the reader to verify that the above Q2's for each Response row indeed partition each of the possible Configurations into distinct Q2 response rows.

Note that the Q2a, Q2b, Q2c, and Q2d at the top (in the "Succinct Answer") matches the Q2 column above.

Note that the separation of Q2 into Q2a - Q2d could be avoided so that there is a single Q2. While this is not strictly necessary to solve the riddle, it may be more satisfying to some readers (albeit less explicitly clear) to do so. Namely, notice all Q2's are exactly the same if you appropriately swap occurrences of 'H' and 'D' and/or 'R' with 'Y' or 'N'. Thus, you could use the number of "YES" responses to Q1 (0, 1, 2, or 3) as an indicator function on whether or not to perform these swaps when asking about the (up to rotation) assignments of Tribes to villages in the Q2a - Q2d above.

1. Your spaceship lands in the middle of three villages, and you must decide which village to head to (not all passengers on you spaceship need go to the same village).
2. Each village is home to a tribe, with each tribe having different tendancies (in terms of Honesty and Hostility; see chart at the top).
3. Tribes are identified by their (primary, secondary) colors (as per chart at the top).
4. As you flew in, your spotted the roof (secondary) colors of the three villages: Yellow, Black, and Black. However, as your spaceship spun out of control for a crash landing, when you actually land and look out your window, you don't know which village corresponded to which roof color.
5. The villages are now so far from your landed spacecraft that you are unable to identify their primary (or secondary) colors.
6. The crash landing rendered your spacecraft almost completely useless. Only the broadcast PA communication works, which can broadcast a single message to each of the three villages simultaneously. Based on the primitive communication of the alien lifeform, which is akin to Morse code, it will take about 5 minutes to broadcast any communication to the 3 surrounding villages.
7. Similarly, it will take about 5 minutes for the response from each village to reach your spaceship (you will be able to distinguish which response is coming from which village).
8. While you know that "Foog" and "Goof" are the words for 'YES' and 'NO' in the Charin language, you cannot remember which is which! (Charin creatures can understand English, but they are unable to speak it).
9. You estimate it is about 30 minutes until sundown, at which point the Trollocs will start hunting any human that is not already in a village.
10. You estimate it will take 20 minutes for the children on board to reach any of the three villages, and 10 minutes for your adult passengers.
11. Thus, you have time to broadcast one (YES/NO) question to the villages (5min) and await the response (5min), at which point in time you'll need to choose a destination village for the children to start walking to (in order for them to have time to reach it by sundown, when the countryside will be crawling with hungry Trollocs). You'll then have time to broadcast a second (YES/NO) question to the villages (5min) and await the response (5min) before you need to decide which village to send the adult (male and female) passengers.

Observations:

The Hard variant of this riddle is very similar to the Easy and Medium variants; if you haven't solved those variants yet, it may be worth visiting the Hints (and Solutions?) to them first. These first set of Hints are the same as the Easy Variant:

• In order to know where to send each passenger (man, woman, child), you need to consider the Hostilities of each Charin tribe type. In particular, solving the riddle requires you to exactly identify the tribe type of each of the three surrounding villages.
• You saw two Black-roofed villages. These are either Aes Sedai or Foresaken (or one of each).
• You saw one Yellow-roofed village, which is either Myrddraal, Aelfinn, or Eelfinn.
• As a result, the following 12 scenarios enumerates all possible scenarios, where 'H' denotes Honest (Aes Sedai), 'D' denotes Dishonest (Foresaken), 'R' denotes Random (Myrddraal), 'Y' denotes YES (Aelfinn), 'N' denotes NO (Eelfinn), and τ denotes an arbitrary translation (rotational shift) of the three villages:
• τ(RHH)
• τ(RHD)
• τ(RDH)
• τ(RDD)
• τ(HHH)   ←  (from τ(NHH), since (per the "Exceptions" of the Tribal Chart) Eelfinn ('N') act like Aes Sedai ('H') when surrounded by two Aes Sedai villages.)
• τ(DDD)   ←  (from τ(YDD), since (per the "Exceptions" of the Tribal Chart) Aelfinn ('Y') act like Foresaken ('D') when surrounded by two Foresaken villages.)
• τ(YYY)   ←  (from τ(YHH), since (per the "Exceptions" of the Tribal Chart) two adjacent Aes Sedai ('H') villages will each act like Aelfinn ('Y') when there is a nearby Aelfinn village.)
• τ(NNN)   ←  (from τ(NDD), since (per the "Exceptions" of the Tribal Chart) two adjacent Foresaken ('D') villages will each act like Eelfinn ('N') when there is a nearby Eelfinn village.)
• τ(YHD)
• τ(YDH)
• τ(NHD)
• τ(NDH)
• Before attempting to identify specific questions, it may be useful to think about the universe of possible Responses, independent of what the actual question(s) are. Namely, regardless of the first question, there are just 8 possible universes of responses (based on receiving a "Yes" vs. "No" response from each of the 3 villages).
• Namely, for each possible "configuration" (assignment of the 3 villages to a Charin tribe type), one (or more) of the 8 possible Responses to your first question must include that configuration as a possibility. In particular, we can construct an "Assignment Table", that distributes/assigns all possible configurations to one of the 8 possible Responses:

  Q1 Response	Configurations
  YYY	???
  YYN	???
  YNY	???
  NYY	???
  YNN	???
  NYN	???
  NNY	???
  NNN	???

• Before thinking about the actual concrete questions you will ask, it may be useful to think about how the Responses may (in an ideal world) partition the possible configurations amongst them, in such a way that the configurations are balanced (in terms of how many configurations are assigned to each of the eight possible Responses), logically sound (see next bullet), and suitably diverse (i.e. the set of configurations that correspond to any single Response type -- e.g. YNY ("Yes", "No", "Yes") -- are suitably distinct from one another so that they can be easily separated/distinguished by the second question).
• In terms of the "logically sound" criteria: Consider any single possible configuration in which the Yellow roof building you saw is a Myrddraal ('R') village; for example one such possibile configuration is: (R, H, H), in which the Northern village is Myrddraal ('R'), and the Southwestern and Southeastern villages are both Aes Sedai ('H'). Suppose, as per the previous hint, you assign row 'YNY' for this Configuration in the Assignment Table. Then, regardless of what your first question actually is, notice that 'NNY' is necessarily also a possible response for this (R, H, H) Configuration. This is because Myrddraal respond to questions Randomly, which means (regardless of the question) they can respond with either 'Yes' or 'No'.
• In particular, this means that as you fill in the Assignment Table, any Configuration that has an 'R' in it must actually appear in (at least) two rows of the table: once for whichever row you choose to put it in, and a second time in the row that has the same response pattern but has flip-flopped the Myrddraal response in terms of 'Y' vs. 'N'.

• The three tribes that are violent towards Children are the Myrddraal, Aelfinn, and Eelfinn, with the latter two only dangerous if the Children are sent their without adult male supervision. Since you saw a Yellow roof as you approached your landing site, you know one of the three villages must be one of those three tribe types. Therefore, your first question/response must seek to identify which of the three villages had the Yellow roof.
• However, because the presence of adult males can protect Children from the Aelfinn and Eelfinn, it is less vital that you identify these (if you happen to send your children to an Aelfinn or Eelfinn village, then you'll be able to send adult males to catch up with them -- and thus ensure their safety -- before they reach the village).
• Thus, if you are limited in how much information you can deduce from just one question/response, it is more important to identify villages that are/aren't Myrddraal ('R'), as opposed to the broader question of identifying which of the three villages has the Yellow-roofed buildings.
• If attempting to use the Assigment Table approach (from above hint) to solve this riddle, what this concretely means is that (amongst the 8 possible Reponse rows) there cannot be a Row that has a set of corresponding Configurations that include an 'R' in all three positions. Namely, as you think about how to distribute all the Configurations with an 'R' in them amongst the 8 possible response rows, you need to cluster them so that, in each row, there is at least one village position (North, Southwest, or Southeast) that never has Myrddraal ('R') assigned to it.

• There are two sources of uncertainty: The association of alien words {'Foog', 'Goof'} ↔ {"Yes", "No"}; and the association of which Charin tribe is in which village. A correct strategy will not be able to resolve both of these uncertainties (and, in particular, the riddle only requires you to resolve the latter).
• You must use the fact that the villages know which tribes occupy the two neighboring villages.
• Your question(s) can (and must) be understandable to the aliens, but not necessarily to you. Namely, at least one of your questions must refer to the aliens' language for Yes/No, e.g. "Is 'Goof' the correct response to the question 'Does 2 plus 2 equal 5?'?"
• Some of your questions must involve hypothetical scenarios, e.g. "If you were X, then would you answer Y if I asked you Z?"

Succinct Answer:

Q1: Is 'Foog' the honest response to the question: "Are any of the following statements A, B, C, or D true?"?

1. Your clockwise neighbor village has the same Charin tribe type as you, AND your counter-clockwise neighbor is a Myrddraal ('R') village;  OR
2. Aes Sedai ('H') is the Charin tribal type of one of your two surrounding villages, and the other is the Charin tribe that always responds 'Goof' to questions;  OR
3. Foresaken ('D') is the Charin tribal type of one of your two surrounding villages, and the other is the Charin tribe that always responds 'Foog' to questions.
4. The other two villages are the same Charin tribe as you.

Then, letting:

In the 'Q1 Response' column: 'F' denotes a 'Foog' response and 'G' denotes a 'Goof' response
In the 'Possible Configurations' column: 'σ' denotes an arbitrary (not just rotational) permutation of the three villages
In the Q2 column: 'H' denotes Aes Sedai, 'D' denotes Foresaken, 'R' denotes Myrddraal, and 'F' (resp. 'G') denotes the Charin tribe (Aelfinn or Eelfinn) that always respond 'Foog' (resp. 'Goof') to questions

Then do the following based on the responses to your first question:

Q1 Response	Possible Configurations	Send Children	Q2
FFF	If 'Foog' = 'Yes':  HHH, YYY, σ(HDY) If 'Foog' = 'No':   HHH, NNN, σ(HDN)	Any (e.g. North)	Is exactly one statement below true?:   1. There is exactly one Aes Sedai ('H') village, AND it is clockwise from you   2. 'Foog' means 'No'
FFG	RHH, RDH, DRD, DRH	Southwest (the 'G' response)	Is 'Foog' the hoest response to the question?:   "Are the three villages, in clockwise order (i.e. up to rotational shift), equal to HDR?"
FGF	RDD, RHD, HHR, DHR	Southeast (the 'G' response)	Same as 'YYN' (above) row
GFF	HRH, HRD, DDR, HDR	North (the 'G' response)	Same as 'YYN' (two above) row
FGG	DRD, DRH, HHR, DHR	North (the 'F' response)	Is 'Foog' the hoest response to the question?:   "Are the three villages, in clockwise order (i.e. up to rotational shift), equal to HRD?"
GFG	RHH, RDH, DDR, HDR	Southeast (the 'F' response)	Same as 'YNN' (above) row
GGF	RDD, RHD, HRH, HRD	Southwest (the 'F' response)	Same as 'YNN' (two above) row
GGG	If 'Foog' = 'Yes':  DDD, NNN, σ(HDN) If 'Foog' = 'No':   DDD, YYY, σ(HDY)	Any (e.g. North)	Is exactly one statement below true?:   1. There is exactly one Foresaken ('D') village, AND it is clockwise from you   2. 'Foog' means 'No'

Explanation: The solution for the Hard Variant of this riddle is basically a combination of the solution to the riddle of the Medium Variant, plus a solution for how to deal with the alien language wrinkle (not understanding which word 'Foog' vs. 'Goof' means 'Yes' (and which means 'No'). Therefore, the first step is understanding the solution to the Medium variant (go and visit the Solution section of the "Medium Variant" tab now, if you haven't already).

Then, to account for the alien language wrinkle (not knowing which of 'Foog' vs. 'Goof' means 'Yes'): first you need to abandon hope of ever resolving knowledge of what 'Foog' and 'Goof' are; you simply do not have enough information from two sets of question/response to learn both the association of {'Foog', 'Goof'} ↔ {'Yes', 'No'} and the association of which village is which Charin tribe type. However, the riddle only requires knowledge of the second association (which village is which); so this means that a correct solution will not (even attempt to) learn the association of {'Foog', 'Goof'} ↔ {'Yes', 'No'}.

With this in mind, we know that the questions themselves must involve 'Foog' and/or 'Goof' in them. By carefully modifying the questions used for the solution to the Medium Variant, a similar Assignment Table (modulo not being able to distinguish between Aelfinn ('Y') and Eelfinn ('N') villages, which stems from your uncertainty of 'Foog' vs. 'Goof') can be constructed, which then allows you to solve the Hard variant in the same way. The following table enumerates all 64 possible responses to your questions, and specifies which Configurations correspond to each and where to send the Children, Women, and Men for each scenario. We leave it as an exercise to the reader to verify that each Configuration has the indicated responses, and that all 28 possible Configurations appear in (at least one) cell of column 5, and furthermore that, modulo uncertainty in Aelfinn ('Y') vs. Eelfinn ('N') villages, each cell in column 5 corresponds to exactly one Configuration (this is important, as it means that given any particular combination (of the 64 possible) response, you know the exact Configuration (assignment of Charin tribe type to village), which is exactly what you need in order to solve the riddle (i.e. to know where to send each Child, Woman, and Man). The only exception is that there is ambiguity in distinguishing Aelfinn ('Y') vs. Eelfinn ('N') villages; but since these villages have the same hostility property, this ambiguity does not at all impact your decision on where to send your passengers.

Q1 Response	Possible Configurations	Send Children	Q2 Response	Configuration	Destination Villages Send Women Send Men
FFF	If 'Foog' = 'Yes':  HHH, YYY, σ(HDY) If 'Foog' = 'No':   HHH, NNN, σ(HDN)	Any (e.g. North)	FFF	YYY or NNN	Same place as Children Same place as Children
			FFG	DYH or DNH	Southeast (Y or N) Southeast (Y or N)
			FGF	YHD or NHD	North (Y or N) North (Y or N)
			GFF	HDY or HDN	Southwest (Y or N) Southwest (Y or N)
			FGG	YDH or NDH	North (Y or N) North (Y or N)
			GFG	HYD or HND	Southeast (Y or N) Southeast (Y or N)
			GGF	DHY or DHN	Southwest (Y or N) Southwest (Y or N)
			GGG	HHH	Any (e.g. same place as Children) None (Trollocs)
FFG	RHH, RDH, DRD, DRH	Southwest (the 'G' response)	FFF	DRD	None (Trollocs) Southeast (R)
			FFG	RDH	Southwest w/ Children (H) North (R)
			FGF	DRD	None (Trollocs) Southeast (R)
			GFF	DRH	Southwest w/ Children (H) Southeast (R)
			FGG	RHH	Southeast (H) or Southwest w/ Children (H) North (R)
			GFG	RDH	Southwest w/ Children (H) North (R)
			GGF	DRH	Southwest w/ Children (H) Southeast (R)
			GGG	RHH	Southeast (H) or Southwest w/ Children (H) North (R)
FGF	RDD, RHD, HHR, DHR	Southeast (the 'G' response)	FFF	RDD	None (Trollocs) North (R)
			FFG	RHD	Southeast w/ Children (H) North (R)
			FGF	DHR	Southeast w/ Children (H) Southwest (R)
			GFF	RDD	None (Trollocs) North (R)
			FGG	DHR	Southeast w/ Children (H) Southwest (R)
			GFG	RHD	Southeast w/ Children (H) North (R)
			GGF	HHR	North (H) or Southeast w/ Children (H) Southwest (R)
			GGG	HHR	North (H) or Southeast w/ Children (H) Southwest (R)
GFF	HRH, HRD, DDR, HDR	North (the 'G' response)	FFF	DDR	None (Trollocs) Southwest (R)
			FFG	DDR	None (Trollocs) Southwest (R)
			FGF	HDR	North w/ Children (H) Southwest (R)
			GFF	HRD	North w/ Children (H) Southeast (R)
			FGG	HDR	North w/ Children (H) Southwest (R)
			GFG	HRH	Southwest (H) or North w/ Children (H) Southeast (R)
			GGF	HRD	North w/ Children (H) Southeast (R)
			GGG	HRH	Southwest (H) or North w/ Children (H) Southeast (R)
FGG	DRD, DRH, HHR, DHR	North (the 'F' response)	FFF	DRD	None (Trollocs) Southeast (R)
			FFG	DRH	Southwest (H) Southeast (R)
			FGF	DRD	None (Trollocs) Southeast (R)
			GFF	DHR	Southeast (H) Southwest (R)
			FGG	DRH	Southwest (H) Southeast (R)
			GFG	DHR	Southeast (H) Southwest (R)
			GGF	HHR	Southeast (H) or North w/ Children (H) Southwest (R)
			GGG	HHR	Southeast (H) or North w/ Children (H) Southwest (R)
GFG	RHH, RDH, DDR, HDR	Southeast (the 'F' response)	FFF	DDR	None (Trollocs) Southwest (R)
			FFG	DDR	None (Trollocs) Southwest (R)
			FGF	RDH	Southwest (H) North (R)
			GFF	HDR	North (H) Southwest (R)
			FGG	RHH	Southwest (H) or Southeast w/ Children (H) North (R)
			GFG	HDR	North (H) Southwest (R)
			GGF	RDH	Southwest (H) North (R)
			GGG	RHH	Southwest (H) or Southeast w/ Children (H) North (R)
GGF	RDD, RHD, HRH, HRD	Southwest (the 'F' response)	FFF	RDD	None (Trollocs) North (R)
			FFG	HRD	North (H) Southeast (R)
			FGF	RHD	Southeast (H) North (R)
			GFF	RDD	None (Trollocs) North (R)
			FGG	HRD	North (H) Southeast (R)
			GFG	HRH	North (H) or Southwest w/ Children (H) Southeast (R)
			GGF	RHD	Southeast (H) North (R)
			GGG	HRH	North (H) or Southwest w/ Children (H) Southeast (R)
GGG	If 'Foog' = 'Yes':  DDD, NNN, σ(HDN) If 'Foog' = 'No':   DDD, YYY, σ(HDY)	Any (e.g. North)	FFF	DDD	None (Trollocs) None (Trollocs)
			FFG	HDY or HDN	North (H) or Southwest (Y or N) Southwest (Y or N)
			FGF	DYH or DNH	Southwest (H) or Southeast (Y or N) Southeast (Y or N)
			GFF	YHD or NHD	Southeast (H) or North (Y or N) North (Y or N)
			FGG	YDH or NDH	Southwest (H) or North (Y or N) North (Y or N)
			GFG	HYD or HND	North (H) or Southeast (Y or N) Southeast (Y or N)
			GGF	DHY or DHN	Southeast (H) or Southwest (Y or N) Southwest (Y or N)
			GGG	NNN or YYY	Same place as Children Same place as Children