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V _ N C _ Clue
ROGERS COULD NOT HAVE KNOWN THAT HIS EX-WIFE HAD BEEN SHOT UNLESS HE HAD THE GUILTY KNOWLEDGE OF THE CRIME. THE MAID DID NOT SAY WHY SHE HAD BEEN TAKEN TO THE HOSPITAL. YET ROGERS' FIRST WORDS ON ENTERING THE HOSPITAL WERE, "WHO SHOT HER?" ZOE'S SMALLEST POSSIBLE NUMBER IS 6. BASED ON THE FIRST STATEMENT OF ALI, IT INDICATES THAT HE HAS NEITHER 1 NOR 9. IF HE HAD EITHER 1 OR 9 THEN HE WOULD KNOW THAT ZOE MUST HAVE A BIGGER OR SMALLER NUMBER. NOW ZOE, BASED ON ALI'S FIRST STATEMENT, KNOWS THAT ALI DOESN'T HAVE 1 OR 9. ZOE'S FIRST STATEMENT INDICATES THAT SHE DOES NOT HAVE 2 OR 8 (NEITHER 1 NOR 9). IF SHE HAD 1, 2, 8 OR 9, THEN SHE COULD HAVE CONCLUDED THAT ALI HAS A BIGGER OR SMALLER NUMBER. NOW ALI KNOWS THAT ZOE DOESN'T HAVE 1, 2, 8 OR 9. ALI'S SECOND STATEMENT INDICATES THAT HE DOES NOT HAVE 3 OR 7 AND ALSO NOT 1, 2, 8 OR 9. ZONE CAN CONCLUDE THAT ALI DOESN'T HAVE 1, 2, 3, 7, 8 OR 9. IN SHORT, ALI MUST HAVE EITHER 4, 5 OR 6. NOW WHEN ZOE SAYS THAT SHE HAS A BIGGER NUMBER THEN IT MUST BE EITHER 6, 7, 8 OR 9 AND ALI HAVING 4 OR 5. ZOE CAN'T SAY CONFIDENTLY THAT SHE HAS A BIGGER NUMBER IF SHE HAD A 4 OR 5, AS IT COULD BE SMALLER THAN WHAT ALI COULD HAVE. SO ZOE'S SMALLEST POSSIBLE NUMBER IS A 6 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 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