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ABEL HAS 50, BILL HAS 20 AND CLARK HAS 30. ABEL ON HIS FIRST TURN OBVIOUSLY DOESN'T KNOW WHETHER HIS NUMBER IS 50 OR 10. SIMILARLY NEITHER BILL NOR CLARK CAN IMMEDIATELY FIGURE OUT THEIR NUMBERS. HOWEVER, ON HIS SECOND TURN ABEL CAN REASON: IF MINE IS A 10, THEN CLARK WOULD KNOW HIS NUMBER IS EITHER 10 OR 30. IF IT IS 10, BILL WOULD IMMEDIATELY KNOW HIS NUMBER IS 20. BUT HE DIDN'T KNOW. SO CLARK SHOULD KNOW HIS NUMBER IS 30. NOW SINCE CLARK DIDN'T KNOW, MY NUMBER MUST BE 50. WITH THIS KIND OF REASONING WE CAN ALSO RULE OUT ALL OTHER COMBINATIONS. SO [50, 20, 30] IS THE ONLY SOLUTION TO THIS PUZZLE 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 MAN 2 WILL SHOUT FIRST. MAN 3 AND MAN 4 WILL NOT BE ABLE TO TELL WHAT COLOUR HATS THEY ARE WEARING SINCE THEY CANNOT SEE THE OTHER MEN. MAN 1 CAN SEE MAN 2 AND MAN 3 BUT IS NOT ABLE TO TELL WHAT COLOUR HAT HE IS WEARING AS MAN 2 AND MAN 3 ARE WEARING DIFFERENT COLOUR HATS. SO MAN 1 WILL NOT SHOUT OUT. THEN BASED ON MAN 1'S SILENCE, MAN 2 IS ABLE TO INTERPRET THAT HE (MAN 2) AND MAN 3 ARE WEARING DIFFERENT COLOUR HATS. SINCE MAN 3 IS WEARING A BLACK COLOUR HAT, SO MAN 2 KNOWS THAT HE IS WEARING A WHITE COLOUR HAT THE ADDRESS IS 1460 SUNSET BOULEVARD. YOU KNOW THAT THE HOUSE NUMBERS ARE EVEN AND CONSECUTIVE, SO THEY MUST BE APPROXIMATELY 1/6TH THE VALUE OF THE SUM 8790. IN FACT, THE NUMBER THAT IS 1/6TH THE TOTAL IS THE MEAN (AVERAGE) FOR ALL 6 HOUSES. THE AVERAGE NUMBER IS 1465 (8790 / 6). THERE MUST BE 3 HOUSE NUMBERS GREATER THAN THAT NUMBER, AND 3 HOUSE NUMBERS LESS THAN THAT NUMBER, ALL BEING EVEN AND CONSECUTIVE. THEREFORE, THE 6 HOUSE NUMBERS ARE 1460, 1462, 1464, 1466, 1468, 1470. THE LOWEST HOUSE NUMBER, AS PER THE QUESTION, IS THE ANSWER: 1460