## Solution to Puzzle #46: A Fork in the Road

Got a pretty enthusiastic response to this puzzle, and I am very happy to see that many people tried it with their children. First person to come back with a correct answer was Anirudh Baddepudi from Singapore. Well done Anirudh! Others to respond correctly were Arunabh Bahadur (great to hear from him…my school time bactmate!), Muskaan Mittal and Adhish+Ameya Kulkarni.

Let’s assume that the native can answer in only “yes” or “no” and lets call the two roads R1 and R2 of which R1 is the correct answer. If we were to ask a simple question – “Does R1 lead to the village?” We will get an answer “yes” from the TRUTH guy and “no” from the “LIE” guy. If we were to apply the principle that truth applied to truth is still truth and lie applied to a lie becomes a truth [effectively 1*1 = 1 and (-1)*(-1)=1], one can ask the following question:

If I were to ask you “does R1 lead to the village”, what would your answer be?….we will get the right and the same answer from both the people.

I am also reproducing the answer from Adhish+Ameya, as I found it to be the easiest to follow. They also did a good role play with their son to show how this works – very innovative!

(L)Liar would say = No it doesn’t

(TT)Truthteller would say = Yes it does

Result: we don’t know if its the right road… because we don’t know if the native is a TT or a L and the answer is different depending on their tribe.

Conclusion: Need to ask a question which gets the same answer from both a TT and an L (in other words, we don’t care if it is an L or a TT we are speaking to).

We then came up with new question variations (with no success):

a) Would a liar tell me to take Road A to reach village (TT = NO; L= YES)

b) If you were a truthteller, would you tell me to take Road A (TT=YES; L=NO)

c) Would it be a lie to say Road A leads to village (TT= NO; L=YES)

Finally, we reformulated the question to avoid labelling the native as an L or a TT:

Question: Would someone from the other tribe say that Road A leads to the Village?

TruthTeller answer : NO (because the other tribe being liars would have said NO the road does not lead to village even though it does, and the TT is just relaying the truth).

Liar answer: NO (because the other tribe being TTs would have said YES the road does lead to village… but being a Liar, the native would answer the opposite of YES, which is NO)

The final piece here is that based on our question construct, if we get a NO, that means it IS the CORRECT Road to the village and if we get a YES, then it is not.

Hope you all enjoyed the puzzle!

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