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1 Clue
THE PROFESSOR HAS TO ADD THE REST OF THE DIGITS, FIND THE NEAREST NUMBER TO THE SUM THAT IS DIVISIBLE BY 9 AND GET THE DIFFERENCE. SO, JOHN GAVE THE NUMBER 9646 TO THE PROFESSOR. THE PROFESSOR WILL ADD THE NUMBERS (9 + 6 + 4 + 6) TO GET 25. THE NEAREST NUMBER TO 25 THAT IS DIVISIBLE BY 9 IS 27. AND THE CROSSED OUT NUMBER IS 27 - 25. THIS IS A MATHS TRICK THAT RELIES ON THE POWER OF 9 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 THE TOTAL IS 2. WHEN THE BOOK ON THE LEFT IS UPSIDE DOWN THEN THE PAGE NUMBER ON THE EXTREME LEFT IS 1 AND THE RIGHT HAND SIDE BOOK'S EXTREME RIGHT HAND SIDE PAGE NUMBER IS ALSO 1. ANOTHER WAY TO LOOK AT THE PROBLEM: IF TWO BOOKS ARE STANDING SIDE BY SIDE TO EACH OTHER, PAGE 1 IS ON THE RIGHT SIDE OF EACH BOOK (ASSUMING YOU ARE LOOKING AT THE SPINE OF THE BOOKS). TURNING THE ONE ON THE LEFT UPSIDE DOWN (WITH THE BOOK SPINE STILL POINTING OUT), BRINGS PAGE 1 TO THE LEFT SIDE. AND SO AT THE "EXTREME LEFT" OF THE BOOK ON THE LEFT IS PAGE 1, WHILE THE "EXTREME RIGHT" OF THE BOOK ON THE RIGHT IS ALSO PAGE 1 THE STUDENT IS DOUBLE COUNTING A LOT OF THE DAYS. A LOT OF THE TIME SPENT SLEEPING, EATING, AND RELAXING OCCURS DURING WEEKENDS AND THE SUMMER. WEEKENDS ALSO OCCUR DURING THE SUMMER, SO ALL OF THESE HOURS ARE GETTING COUNTED SEVERAL TIMES. AND, SCHOOL IS NOT AN ALL DAY AFFAIR. SO THE 4 DAYS ACTUALLY REPRESENTS MORE DAYS OF SCHOOL. IF SCHOOL IS 6 HOURS PER DAY, THOSE FOUR DAYS REPRESENTS 16 DAYS OF SCHOOL