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M _ N _ T _ S Clue
IF THE GIRLS HAD BEEN ON A STANDING TRAIN, THE FIRST GIRL'S CALCULATIONS WOULD HAVE BEEN CORRECT, BUT THEIR TRAIN WAS MOVING. IT TOOK 5 MINUTES TO MEET A SECOND TRAIN, BUT THEN IT TOOK THE SECOND TRAIN 5 MORE MINUTES TO REACH WHERE THE GIRLS MET THE FIRST TRAIN. SO THE TIME BETWEEN TRAINS IS 10 MINUTES, NOT 5, AND ONLY 6 TRAINS PER HOUR ARRIVE IN THE CITY IT WILL TAKE 10.5 SECONDS FOR THE CLOCK TO STRIKE 10. WHILE STRIKING 7, THE CLOCK STRIKES THE FIRST GONG AT 7 O'CLOCK AND IT STRIKES 6 MORE AT REGULAR INTERVALS. THESE 6 INTERVALS TAKE 7 SECONDS, SO THE INTERVAL BETWEEN GONGS IS 7⁄6 SECONDS. HOWEVER TO STRIKE 10, THERE ARE 9 INTERVALS EACH TAKING 7⁄6 SECONDS. THIS ADDS UP TO A TOTAL OF (9 X 7⁄6) 10.5 SECONDS 25 EGGS WERE BROKEN. THERE IS ONLY ONE WAY OF FINDING A SOLUTION TO THIS PROBLEM: NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 2: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35 NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 3: 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 4: 5, 9, 13, 17, 21, 25, 29, 33, 37 NUMBERS WHICH LEAVE NO REMAINDER WHEN DIVIDED BY 5: 5, 10, 15, 20, 25, 30, 35 THE ONLY NUMBER FULFILLING THE FOUR CONDITIONS IS 25 45 MINUTES. METHOD 1 LET US TALK ABOUT 24 HOURS AS IT WILL SIMPLIFY THE PROBLEM. IN 24 HOURS: THE COLD TAP WILL BE ABLE TO FILL THE BATHTUB 80 TIMES. THE HOT TAP WILL BE ABLE TO FILL THE BATHTUB 96 TIMES. THE DRAIN WILL BE ABLE TO DRAIN THE BATHTUB 144 TIMES. THUS IN 24 HOURS, THE BATHTUB WILL BE FILLED 80 + 96 - 144 = 32 TIMES (IF BOTH TAPS ARE TURNED ON WITH THE PLUG LEFT OUT) THUS IT WILL TAKE 45 MINUTES TO FILL THE TUB ONCE. METHOD 2 THE BATHTUB FILLING RATE IS: THE COLD TAP WILL FILL THE BATHTUB AT 1/18 TUB/MINUTE THE HOT TAP WILL FILL THE BATHTUB AT 1/15 TUB/MINUTE THE DRAIN WILL DRAIN THE BATHTUB AT 1/10 TUB/MINUTE THE NETT BATHTUB FILL RATE IS: 1/18 + 1/15 - 1/10 = 1/45 TUB/MINUTE THE WATER WILL FILL 1/45 OF THE TUB IN 1 MINUTE, SO THE TUB WILL BE FULL IN 45 MINUTES