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THE QUESTION IS: "WHAT WOULD THE OTHER ANGEL SAY, IF I ASKED WHICH GATE LEADS TO HEAVEN?". AND DO EXACTLY THE OPPOSITE OF WHAT THE ANGEL SAYS. IF THE LEFT GATE LEADS TO HEAVEN: THE ANGEL THAT TELLS THE TRUTH WILL SAY THAT IT'S THE RIGHT GATE SINCE IT KNOWS THAT THE OTHER ANGEL WILL LIE. THE ANGEL THAT LIES WILL ALSO SAY THAT IT'S THE RIGHT GATE SINCE IT KNOWS THAT THE OTHER ANGEL WILL TELL THE TRUTH. THE SAME EXPLANATION APPLIES IF THE RIGHT GATE LEADS TO HEAVEN THE TRAVELER ASKED, "WHICH ROAD GOES TO YOUR VILLAGE". HE WOULD THEN TAKE THE ROAD THE VILLAGER POINTED TO. IF THE MAN IS A TRUTHFUL PERSON, HE WOULD POINT TOWARDS THE TRUTHFUL VILLAGE. IF HE'S A LIAR, HE WOULD ALSO POINT TO THE TRUTHFUL VILLAGE THE MAN ASKS: IF YOU WERE THE OPPOSITE ONE (MEANING IF THE TRUTH-TELLING ONE WAS THE LIAR, ETC.), WHO WOULD YOU SAY IS THE ORACLE? THEN THE TRUTH-TELLER WOULD HAVE TO POINT TO THE FAKE ONE AND THE THE LIAR WOULD HAVE TO POINT TO HIMSELF YOU ASK EACH TWIN WHAT WOULD YOUR BROTHER SAY?. THIS WORKS BECAUSE.... WELL LET'S SAY THE CORRECT PATH IS ON THE LEFT SIDE. SO SAY YOU ASKED THE LIAR "WHAT WOULD YOUR BROTHER SAY?" WELL, THE LIAR WOULD KNOW HIS BROTHER WAS HONEST AND HE WOULD SAY THE LEFT SIDE, BUT SINCE THE LIAR LIES, HE WOULD SAY RIGHT. IF YOU ASKED THE HONEST TWIN THE SAME QUESTION, HE WOULD SAY RIGHT, BECAUSE HE KNOWS HIS BROTHER WILL LIE. THEREFORE, YOU WOULD KNOW THAT THE CORRECT PATH WAS THE LEFT!