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C _ N T _ _ N _ R Clue
THE CHILDREN ARE 1, 6 AND 6 YEARS OLD. THE PRODUCT OF THEIR AGES IS 36, SO NONE OF THEM CAN BE OLDER THAN 36. THE NUMBER 36 HAS TO BE EXPRESSED AS THE PRODUCT OF 3 NUMBERS. THEIR POSSIBLE AGES ARE (THE SUM OF THEIR AGES IS IN BRACKETS): 1, 1, 36 (3938) 1, 2, 18 (21) 1, 3, 12 (16) 1, 4, 9 (14) 1, 6, 6 (13) 2, 2, 9 (13) 2, 3, 6 (11) 3, 3, 4 (10) SINCE CHERYL IS TOM'S NEXT DOOR NEIGHBOUR, TOM KNOWS CHERYL'S HOUSE NUMBER. TOM WOULD KNOW THE CHILDREN'S AGES IN EVERY CASE THAT SUMS UP TO A UNIQUE NUMBER EXCEPT FOR THE SUM OF 13, WHICH HAVE 2 COMBINATIONS OF POSSIBLE AGES. AS A RESULT, TOM WOULD BE CONFUSED AS HE HAS TO PICK BETWEEN THE 2 COMBINATIONS: (1,6,6) AND (2,2,9). CHERYL THEN TELLS TOM ABOUT HER YOUNGEST CHILD WHO LIKES STRAWBERRY MILK WHICH TELLS TOM THAT THERE IS ONLY 1 YOUNGEST CHILD 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 SUM OF THE NUMBERS ON THE WATCH FACE IS 78. IF THE TWO LINES CROSS, THERE MUST BE 4 EQUAL PARTS, BUT 78 IS NOT DIVISIBLE BY 4. THEN THE LINES DO NOT CROSS, GIVING THREE PARTS WITH THE SUM OF 26 EACH. ONCE YOU SEE THE PAIRS ON THE FACE THAT ADD TO 13(12+1,11+2, AND SO FAR) THE ANSWER WILL BE EASY TO FIND FILL THE 5 OZ. AND 11 OZ. CONTAINERS FROM THE 24 OZ. CONTAINER. THIS LEAVES 8 OZ. IN THE 24 OZ. BOTTLE. NEXT EMPTY THE 11 OZ. BOTTLE BY POURING THE CONTENTS INTO THE 13 OZ. BOTTLE. FILL THE 13 OZ. BOTTLE FROM THE 5 OZ. CONTAINER (WITH 2 OZ.) AND PUT THE REMAINING 3 OZ. IN THE 11 OZ. BOTTLE. THIS LEAVES THE 5 OZ. CONTAINER EMPTY. NOW POUR 5 OZ. FROM THE 13 OZ. BOTTLE INTO THE 5 OZ. BOTTLE LEAVING 8 OZ. IN THE 13 OZ. BOTTLE. FINALLY POUR THE 5 OZ. BOTTLE CONTENTS INTO THE 11 OZ. BOTTLE GIVING 8 OZ. IN THIS CONTAINER