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S T _ T _ M _ N T Clue
ON THURSDAY. THEY CAN ONLY MAKE THIS STATEMENT DURING THE BORDER DAYS - ON THE BORDER DAY THEY TELL THE TRUTH AND ON THE NEXT DAY THEY LIE, OR VICE VERSE. FOR JAMES, HIS BORDER DAYS ARE ON THURSDAYS AND SUNDAYS. FOR JONATHAN, HIS BORDER DAYS ARE ON MONDAYS AND THURSDAYS. SO, ONLY ON THURSDAYS CAN THEY BOTH MAKE THE STATEMENT THEY SAID THAT ON THURSDAY. AS THERE IS NO DAY WHEN BOTH WOULD BE LYING, AT LEAST ONE OF THEM MUST HAVE SPOKEN THE TRUTH. THEY BOTH SPEAK THE TRUTH ONLY ON SUNDAY. HOWEVER, THE LION WOULD THEN BE LYING IN HIS STATEMENT, SO IT COULDN'T BE SAID ON SUNDAY. SO EXACTLY ONE OF THEM LIED. IF THE UNICORN WAS HONEST, THEN IT WOULD HAVE TO BE SUNDAY - BUT PREVIOUSLY WE PROVED THIS WRONG. THUS ONLY THE LION SPOKE THE TRUTH WHEN HE MET ALICE ON THURSDAY AND SPOKE WITH THE UNICORN ABOUT WEDNESDAY SUNDAY. WHEN THE DAY AFTER TOMORROW IS YESTERDAY, TODAY WILL BE THREE DAYS HENCE, JUST AS WHEN THE DAY BEFORE YESTERDAY WAS TOMORROW CARRIES US BACK THREE DAYS FROM NOW, WHICH MUST BE SUNDAY, TO BE MIDWAY BETWEEN THE TWO "TODAYS". ALTERNATIVELY, WE CAN REPHRASE THE RIDDLE TO: IN 3 DAYS WE WILL BE AS FAR FROM SUNDAY AS WE WERE FROM SUNDAY 3 DAYS AGO SUNDAY IS THE ONLY DAY THAT SATISFIES THAT IT WAS SPOKEN ON WEDNESDAY. "WHEN THE DAY AFTER TOMORROW BECOMES YESTERDAY", LET THE DAY BE (A). LET "TWO DAYS AFTER THAT DAY" BE (B). (A) AND (B) ARE TWO DAYS APART AND EQUALLY FAR FROM SUNDAY, SO THEY MUST BE SATURDAY AND MONDAY, MEANING THE ORIGINAL DAY WAS WEDNESDAY