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7 Clue
THE FOUR SOLUTIONS ARE 2-3, 3-4, 9-8 AND 8-7. THE TRICK IS TO UNDERSTAND THAT A PERSON IS ABLE TO DETERMINE THE UNKNOWN CONSECUTIVE NUMBER CORRECTLY ONLY WHEN THERE IS ONLY 1 POSSIBLE CHOICE. AFTER THE 1ST STATEMENT, WHEN A SAYS "I DO NOT KNOW YOUR NUMBER", IT IS CLEAR THAT THE NUMBER KNOWN TO HIM IS NEITHER 1 NOR 10, OTHERWISE HE WOULD HAVE KNOWN B'S NUMBER. SO, NOW, B KNOWS THAT A KNOWS SOME NUMBER OTHER THAN 1 OR 10. IF THE NUMBERS KNOWN TO B WERE 2 OR 9, HE COULD HAVE IMMEDIATELY DEDUCED THE FACT THAT THE NUMBER KNOWN TO A IS 3 OR 8. BUT SINCE, HE SAYS "NEITHER DO I KNOW YOUR NUMBER", IT MEANS THAT B'S NUMBER IS NOT 1, 2, 9, OR 10. HOWEVER, THIS DOES NOT MEAN THAT THE NUMBERS KNOWN TO A CAN'T BE 2 OR 3. FROM THE 3RD STATEMENT, A NOW KNOWS THE NUMBER, THEREFORE A'S NUMBER MUST BE 2, 3, 8 OR 9. SO, IF A'S NUMBER IS 2, THEN HE CAN BE SURE THAT B'S NUMBER IS 3, IF A'S NUMBER IS 3, THEN HE CAN BE SURE THAT B'S NUMBER IS 4, IF A'S NUMBER IS 9, THEN HE CAN BE SURE THAT B'S NUMBER IS 8, IF A'S NUMBER IS 8, THEN HE CAN BE SURE THAT B'S NUMBER IS 7 THE KING KEEPS POISON 12 SO THAT HE CAN NEUTRALIZE ANY POISON THAT THE CLOWN GIVES HIM. HE POURS POISON 10 (HIS SECOND STRONGEST POISON) AND GIVES IT TO THE CLOWN TO DRINK. CLOWN CAN DEDUCE THIS SO HE KEEPS POISON 11 FOR HIMSELF TO NEUTRALIZE POISON 10. THAT'S HOW HE SURVIVES. HE ALSO KNOWS THAT THE KING, AFTER DRINKING THE CUP HE GAVE HIM, WILL DRINK POISON 12 TO NEUTRALIZE THE POISON. SO THE CLOWN POURS PLAIN WATER INSTEAD OF POISON INTO THE CUP FOR THE KING. THE KING DRINKS THE WATER (WATER IS NOT POISON) AND RIGHT AFTER THAT HE DRINKS THE STRONGEST POISON POSSIBLE (12) AND DIES 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 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