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_ T C Clue
ANY NUMBER. IF A NUMBER IS DOUBLED AND MULTIPLIED BY 4, IT'S ACTUALLY BEEN MULTIPLIED BY 8, SO DIVIDING BY 8 WILL GET YOU THE ORIGINAL NUMBER AGAIN THERE ARE 19 KIDS IN THE CLASS. TOTAL NUMBER OF BOYS IN THE CLASS = BOYS WHO WEAR BLUE SHIRTS + BOYS WHO DO NOT WEAR BLUE SHIRTS. THERE ARE 3 BOYS (8 WEAR BLUE - 5 GIRLS WEARING BLUE) WHO WEAR BLUE SHIRTS. THERE ARE 2 BOYS WHO DO NOT WEAR A BLUE SHIRT. THEREFORE, THERE ARE 5 BOYS IN THE CLASS. IN TOTAL, THERE ARE 14 GIRLS + 5 BOYS IN THE CLASS 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 27 STUDENTS. THE NUMBER OF BOYS MUST BE A MULTIPLES OF 3 (3, 6, 9, 12, ...) SO THAT IT CAN BE SPLIT IN THE RATIO OF 2:1 (NO WATCH:WATCH). THE NUMBER OF GIRLS IS DOUBLE THE NUMBER OF BOYS - 6, 12, 18, 24, ETC. SO THE TOTAL NUMBER OF STUDENTS CAN ONLY BE 9, 18, 27, 36, ETC