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M _ N _ T _ S Clue
IF 8 MONKEYS TAKE 8 MINUTES TO EAT 8 BANANAS, THEN 1 MONKEY TAKES 8 MINUTES TO EAT 1 BANANA. SO 3 MONKEYS WILL TAKE 8 MINUTES TO EAT 3 BANANAS. 1 MONKEY CAN EAT 1 BANANA IN 8 MINUTES, SO 1 MONKEY CAN EAT 6 BANANAS IN 48 (8 X 6) MINUTES. THEREFORE, 8 MONKEYS CAN EAT 48 BANANAS IN 48 MINUTES THE SHEEP WILL SURVIVE. IF THERE WERE 1 LION AND 1 SHEEP, THEN THE LION WOULD SIMPLY EAT THE SHEEP. THE SHEEP WILL NOT SURVIVE. IF THERE WERE 2 LIONS AND 1 SHEEP, THEN NO LION WOULD EAT THE SHEEP, BECAUSE IF ONE OF THEM WOULD, IT WOULD SURELY BE EATEN BY THE OTHER LION AFTERWARDS. THE SHEEP WILL SURVIVE. IF THERE WERE 3 LIONS AND 1 SHEEP, THEN ONE OF THE LIONS COULD SAFELY EAT THE SHEEP, BECAUSE IT WOULD TURN INTO THE SCENARIO WITH 2 LIONS, WHERE NO ONE CAN EAT THE SHEEP. THE SHEEP WILL NOT SURVIVE. IF THERE WERE 4 LIONS AND 1 SHEEP, THEN NO LION WOULD EAT THE SHEEP, BECAUSE IT WOULD TURN INTO THE SCENARIO WITH 3 LIONS. THE SHEEP WILL SURVIVE. CONTINUING THIS ARGUMENT, THE CONCLUSION IS AS FOLLOWS: IF THERE IS AN EVEN NUMBER OF LIONS, THEN NOTHING HAPPENS AND THE SHEEP SURVIVES. IF THERE IS AN ODD NUMBER OF LIONS, THEN ANY LION COULD SAFELY EAT THE SHEEP AND THE SHEEP WILL NOT SURVIVE. THIS IS SIMILAR TO THE UNEXPECTED HANGING PARADOX 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