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edited Jun 18 at 15:24

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Without further restrictions on the types of questions that may be asked or further knowledge the guards have about each other, it is open to being achieved in one question as follows.

Ask to Guard #1

"If I were to ask Guard #2 to ask Guard #3, 'behind which door would Guard #3 say is the pot of gold?', to which door would Guard #2 say that Guard #3 would point?"

Then, the door which Guard #1 indicates leads to the pot of gold.

Analysis

If Guard #1 is the truthteller then Guard #3 is a liar and would point to a door leading to a hungry lion. However, Guard #2, being also a liar, would indicate a door that Guard #3 would not pick and would have to choose the door leading to the pot of gold to guarantee their lie. This would also be assumed by Guard #1

Alternatively, if Guard #2 or #3 is the truthteller, then Guard #2 would indicate that Guard #3 would point to a door, behind which is a hungry lion. Guard #1, not knowing which of the hungry lion doors Guard #2 would indicate must point to the door leading to the pot of gold to guarantee their status as a liar.

Thanks to justhalf and Brendan Mitchell for helpful comments on the wording of the question.

Without further restrictions on the types of questions that may be asked or further knowledge the guards have about each other, it is open to being achieved in one question as follows.

Ask to Guard #1

"If I were to ask Guard #2 to ask Guard #3, 'behind which door is the pot of gold?', to which door would Guard #2 say that Guard #3 would point?"

Then, the door which Guard #1 indicates leads to the pot of gold.

Analysis

If Guard #1 is the truthteller then Guard #3 is a liar and would point to a door leading to a hungry lion. However, Guard #2, being also a liar, would indicate a door that Guard #3 would not pick and would have to choose the door leading to the pot of gold to guarantee their lie. This would also be assumed by Guard #1

Alternatively, if Guard #2 or #3 is the truthteller, then Guard #2 would indicate that Guard #3 would point to a door, behind which is a hungry lion. Guard #1, not knowing which of the hungry lion doors Guard #2 would indicate must point to the door leading to the pot of gold to guarantee their status as a liar.

Without further restrictions on the types of questions that may be asked or further knowledge the guards have about each other, it is open to being achieved in one question as follows.

Ask to Guard #1

"If I were to ask Guard #2 'behind which door would Guard #3 say is the pot of gold?', to which door would Guard #2 point?"

Then, the door which Guard #1 indicates leads to the pot of gold.

Analysis

If Guard #1 is the truthteller then Guard #3 is a liar and would point to a door leading to a hungry lion. However, Guard #2, being also a liar, would indicate a door that Guard #3 would not pick and would have to choose the door leading to the pot of gold to guarantee their lie. This would also be assumed by Guard #1

Alternatively, if Guard #2 or #3 is the truthteller, then Guard #2 would indicate that Guard #3 would point to a door, behind which is a hungry lion. Guard #1, not knowing which of the hungry lion doors Guard #2 would indicate must point to the door leading to the pot of gold to guarantee their status as a liar.

Thanks to justhalf and Brendan Mitchell for helpful comments on the wording of the question.

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created Jun 18 at 9:17

hexomino

137.6k
10
391
569

Without further restrictions on the types of questions that may be asked or further knowledge the guards have about each other, it is open to being achieved in one question as follows.

Ask to Guard #1

"If I were to ask Guard #2 to ask Guard #3, 'behind which door is the pot of gold?', to which door would Guard #2 say that Guard #3 would point?"

Then, the door which Guard #1 indicates leads to the pot of gold.

Analysis

If Guard #1 is the truthteller then Guard #3 is a liar and would point to a door leading to a hungry lion. However, Guard #2, being also a liar, would indicate a door that Guard #3 would not pick and would have to choose the door leading to the pot of gold to guarantee their lie. This would also be assumed by Guard #1

Alternatively, if Guard #2 or #3 is the truthteller, then Guard #2 would indicate that Guard #3 would point to a door, behind which is a hungry lion. Guard #1, not knowing which of the hungry lion doors Guard #2 would indicate must point to the door leading to the pot of gold to guarantee their status as a liar.