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L _ L Y Clue
THEY ARE BOTH LYING. SCENARIO 1: IF THE CHILD WITH BROWN HAIR IS LYING, HE IS A BOY. THEN THE CHILD WITH BLOND HAIR MUST BE A GIRL SINCE THERE IS A BOY AND A GIRL AND THUS IS ALSO LYING. SCENARIO 2: IF THE CHILD WITH BROWN HAIR IS NOT LYING, THEN SHE'S A GIRL. SINCE AT LEAST ONE OF THEM IS LYING, THE CHILD WITH BLOND HAIR MUST BE LYING AND WOULD BE A GIRL ALSO, WHICH IS IMPOSSIBLE. SO THE ONLY POSSIBILITY IS THE SCENARIO WHERE BOTH ARE LYING VINCE DID IT. JOYCE'S STATEMENTS 1 AND 3 MUST BE TRUE. IF SHE HAD BROKEN THE WINDOW, BOTH STATEMENTS WOULD HAVE BEEN FALSE. BUT SINCE EACH CHILD TOLD ONLY ONE LIE, THESE TWO STATEMENTS MUST BE TRUE. THEREFORE, JOYCE'S STATEMENT 2 IS THE ONE THAT IS FALSE. THE STATEMENT OF ALL THE OTHER CHILDREN CAN THEN BE PROVEN TRUE OR FALSE USING THIS INFORMATION. SINCE WE KNOW THAT JOYCE'S STATEMENT 2 IS FALSE, SALLY'S STATEMENT 1 AND MATT'S STATEMENT 1 HAVE TO BE FALSE. JOE'S STATEMENT 2 HAS TO BE FALSE, SINCE SALLY DID NOT TELL WHO DID IT. NOW WE ARE LEFT ONLY WITH VINCE THE SILVER BOX CONTAINED ANNA'S PICTURE. IF HER PICTURE HAD BEEN IN THE GOLD BOX, THE STATEMENTS ON THE GOLD BOX AND SILVER BOX WOULD HAVE BEEN TRUE. IF HER PICTURE HAD BEEN IN THE BRONZE BOX, THE STATEMENTS ON THE BRONZE BOX AND SILVER BOX WOULD HAVE BEEN TRUE. IF HER PICTURE IS IN THE SILVER BOX, THE STATEMENT ON THE BRONZE BOX WOULD BE TRUE AND THE STATEMENTS ON THE GOLD AND SILVER BOXES WOULD NOT BE TRUE THE COUPLES ARE: GILLES AND LOUISE ROBERT AND LILY MICHAEL AND CAROLE LILY IS AN ONLY CHILD, SO CAROLE HAS TO BE LOUISE'S SISTER. THIS MAKES CAROLE AND MICHEAL A COUPLE. GILLES HAS NEVER MET LILY, SO THIS MAKES GILLES AND LOUISE A COUPLE. THE REMAINING COUPLE IS ROBERT AND LILY