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_ S L _ N D Clue
IF THERE WAS ONLY ONE BLUE-EYED PERSON ON THE ISLAND, THEN THAT PERSON WOULD LOOK AROUND AND SEE THAT THERE IS NO OTHER BLUE-EYED PERSON. SO HE REALIZES THAT HE IS THE ONLY PERSON WITH BLUE EYES ON THE ISLAND AND LEAVES ON THE DAY OF THE ANNOUNCEMENT. IF THERE ARE 2 BLUE-EYED PEOPLE, THEN THEY LOOK AT EACH OTHER. EACH ONE EXPECTS THE OTHER TO LEAVE ON THE DAY OF THE ANNOUNCEMENT. HOWEVER, ON THE NEXT DAY, WHEN THEY REALIZE THAT NEITHER OF THEM LEFT THE ISLAND, THEY WOULD BE ABLE TO DEDUCE THAT BOTH OF THEM HAVE BLUE EYES. THEY BOTH LEAVE THE ISLAND ON THE SECOND DAY. THROUGH MATHEMATICAL INDUCTION, THIS LOGIC CAN BE APPLIED TO THE 100 BLUE-EYED PEOPLE ON THE ISLAND. SO ON THE 100TH DAY, ALL THE 100 BLUE-EYED PEOPLE LEAVE THE ISLAND THEIR HATS ARE ALL BLUE IN COLOR. THERE ARE 3 POSSIBLE HAT COLOR COMBINATIONS: [A] 1 BLUE, 2 WHITE [B] 2 BLUE, 1 WHITE [C] 3 BLUE THE COLOR COMBINATION OF 3 WHITE HATS IS NOT POSSIBLE SINCE THE KING HAS ALREADY SAID THAT AT LEAST ONE OF THE WISE MEN HAS A BLUE HAT. SO, LET'S START OUR ANALYSIS. WHAT IF THERE WERE ONE BLUE HAT AND TWO WHITE HATS? THEN THE WISE MAN WITH THE BLUE HAT WOULD HAVE SEEN TWO WHITE HATS AND IMMEDIATELY CALLED OUT THAT HIS OWN HAT WAS BLUE, SINCE HE KNEW THERE IS AT LEAST ONE BLUE HAT. THIS DIDN'T HAPPEN, AND THUS THE HAT COLOR COMBINATION [A] IS RULED OUT. NOW, THE WISE MEN KNEW THAT ONLY 2 HAT COLOR COMBINATIONS ARE POSSIBLE - COMBINATION [B] OR [C]. WHAT IF THERE WERE TWO BLUE HATS AND ONE WHITE HAT? THE MEN WITH THE BLUE HATS WILL SEE ONE WHITE HAT AND ONE BLUE HAT. THEY WILL CONCLUDE THAT COLOR COMBINATION [B] IS THE CASE AND WOULD CALL OUT BLUE AS THEIR HAT COLOR. THIS ALSO DID NOT HAPPEN, AND THUS THE HAT COLOR COMBINATION [B] IS ALSO RULED OUT. AFTER SOME TIME, WHEN NONE OF THE WISE MEN ARE ABLE TO IDENTIFY THE COLOR OF THEIR OWN HATS, COMBINATION [C] (OF 3 BLUE HATS) BECOMES THE ONLY POSSIBLE OPTION LET'S ASSUME THAT THERE IS ONLY 1 CHEATING HUSBAND. THEN HIS WIFE DOESN'T SEE ANYBODY CHEATING, SO SHE KNOWS HE CHEATS, AND SHE WILL KILL HIM THAT VERY DAY. NOW, LET'S SAY THAT THERE ARE 2 CHEATING HUSBANDS. THERE WILL BE 98 WOMEN IN THE TOWN WHO KNOW WHO THE 2 CHEATERS ARE. THE 2 WIVES, WHO ARE BEING CHEATED ON, WOULD THINK THAT THERE IS ONLY 1 CHEATER IN THE TOWN. SINCE NEITHER OF THESE 2 WOMEN KNOW THAT THEIR HUSBANDS ARE CHEATERS, THEY BOTH DO NOT REPORT THEIR HUSBANDS IN ON THE DAY OF THE ANNOUNCEMENT. THE NEXT DAY, WHEN THE 2 WOMEN SEE THAT NO HUSBAND WAS EXECUTED, THEY REALIZE THAT THERE COULD ONLY BE ONE EXPLANATION - BOTH THEIR HUSBANDS ARE CHEATERS. THUS, ON THE SECOND DAY, 2 HUSBANDS ARE EXECUTED. THROUGH MATHEMATICAL INDUCTION, IT CAN BE PROVED THAT WHEN THIS LOGIC IS APPLIED TO N CHEATING HUSBANDS, THEY ALL DIE ON THE N TH DAY AFTER THE QUEEN'S ANNOUNCEMENT. SO WITH 100 CHEATING HUSBANDS, ALL OF THEM WILL BE EXECUTED ON THE 100TH DAY THE KING KEEPS POISON 12 SO THAT HE CAN NEUTRALIZE ANY POISON THAT THE CLOWN GIVES HIM. HE POURS POISON 10 (HIS SECOND STRONGEST POISON) AND GIVES IT TO THE CLOWN TO DRINK. CLOWN CAN DEDUCE THIS SO HE KEEPS POISON 11 FOR HIMSELF TO NEUTRALIZE POISON 10. THAT'S HOW HE SURVIVES. HE ALSO KNOWS THAT THE KING, AFTER DRINKING THE CUP HE GAVE HIM, WILL DRINK POISON 12 TO NEUTRALIZE THE POISON. SO THE CLOWN POURS PLAIN WATER INSTEAD OF POISON INTO THE CUP FOR THE KING. THE KING DRINKS THE WATER (WATER IS NOT POISON) AND RIGHT AFTER THAT HE DRINKS THE STRONGEST POISON POSSIBLE (12) AND DIES