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D _ Y S Clue
IT WOULD TAKE 47 DAYS TO COVER HALF OF THE LAKE, AS THEY DOUBLE IN SIZE EVERY DAY IT WILL TAKE 4 HOURS 43 MINS 16.72 SECONDS TO FILL THE POOL. IN ONE HOUR: 1ST TAP FILLS 1/48 OF THE POOL 2ND TAP FILLS 1/72 OF THE POOL 3RD TAP FILLS 1/96 OF THE POOL 4TH TAP FILLS 1/6 OF THE POOL THIS ADDS UP TO 61/288 (1/48 + 1/72 + 1/96 + 1/6) FOR 1 HOUR. TO FILL THE POOL, IT WILL TAKE 288/61 HOURS IT WILL TAKE 5 DAYS FOR 100 PEOPLE TO BUILD 100 HOUSES. 1 PERSON CAN BUILD 1 HOUSE IN 5 DAYS. SO, 100 PEOPLE CAN BUILD 100 HOUSES IN 5 DAYS THE MATHEMATICIAN MADE A SMALL FENCE AROUND HIMSELF AND DECLARED HIMSELF TO BE ON THE OUTSIDE