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_ L S _ Clue
THERE MAY MANY POSSIBLE SOLUTIONS, HERE IS A SIMPLE ONE: THE FIRST PERSON TAKES HIS MONTHLY SALARY (LETS SAY $100), ADDS AN ARBITRARY AMOUNT THAT ONLY HE KNOWS (LETS SAY $475) AND WHISPERS THAT NUMBER ($575) TO THE SECOND PERSON. THE SECOND PERSON THEN ADDS HIS MONTHLY SALARY (LETS SAY $150) TO THAT VALUE AND WHISPERS THE NEW TOTAL ($725) TO THE THIRD PERSON. THE THIRD PERSON ADDS IN HIS SALARY, WHISPERS THE NEW TOTAL TO THE FOURTH PERSON AND SO ON UNTIL THE TENTH PERSON ADDS IN HIS SALARY AND WHISPERS THE FINAL TOTAL TO THE FIRST PERSON. THE FIRST PERSON THEN SUBTRACTS HIS ARBITRARY NUMBER FROM THAT TOTAL, DIVIDES BY 10, WHICH PRODUCES THE AVERAGE MONTHLY SALARY FOR THE GROUP WITHOUT ANYONE HAVING TO DIVULGE THEIR SALARY TO ANYONE ELSE IT IS IMPOSSIBLE. HE TRAVELLED HALFWAY, WHICH IS 30 KM. HE HAS TO TRAVEL ANOTHER 30 KM. IN TOTAL, HE HAS TO TRAVEL 60 KM WITH AN AVERAGE SPEED OF 60 KM/HOUR - THIS MEANS HIS TOTAL TRAVELLING TIME MUST BE 1 HOUR, BUT HE HAS ALREADY TAKEN 1 HOUR FOR HIS FIRST TRIP. UNLESS HE IS ABLE TO TELEPORT HIMSELF FOR THE SECOND TRIP, HE WILL NEVER BE ABLE TO MAKE IT. SOME SAY THAT HE SHOULD TRAVEL AT 90KM/HOUR FOR THE RETURN TRIP. LET'S WORK IT OUT. FOR THE FIRST TRIP, HE TRAVELLED AT 30KM/HOUR AND COVERED 30KM (HALFWAY TO THE TOWN) IN 1 HOUR. FOR THE SECOND TRIP, IF HE TRAVELLED AT 90KM/HOUR, HE WOULD TAKE 20 MINUTES TO COVER 30KM. HIS TOTAL TRAVELLING TIME WILL BE 1HR AND 20 MINS (80 MINS) AND HE WOULD HAVE TRAVELLED 60KM IN TOTAL. HIS AVERAGE SPEED WOULD BE 45 KM/HOUR AND NOT 60 KM/HOUR A HALF DOLLAR, A QUARTER, AND FOUR DIMES. YOU OBVIOUSLY CAN'T HAVE ANY PENNIES, BECAUSE YOU COULDN'T HAVE 1-4 PENNIES, SINCE $1.15 IS A MULTIPLE OF 5, AND IF YOU HAD 5 PENNIES OR MORE YOU COULD CHANGE A NICKEL. YOU CAN'T HAVE MORE THAN 1 NICKEL, OTHERWISE YOU COULD CHANGE A DIME. AND IF YOU HAD 1 NICKEL YOU COULDN'T HAVE BUT 1 DIME, OTHERWISE YOU COULD CHANGE A QUARTER. THEN IF YOU HAD 1 NICKEL AND 1 DIME YOU'D HAVE 15 CENTS. THAT WOULD LEAVE $1.00 AND YOU COULDN'T MAKE THAT REMAINING $1.00 WITH QUARTERS AND HALVES WITHOUT EITHER BEING ABLE TO CHANGE A HALF OR A DOLLAR. SO YOU CAN'T HAVE ANY PENNIES OR NICKELS. SINCE YOU CAN'T HAVE ANY PENNIES OR NICKELS, YOU CAN'T POSSIBLY MAKE $1.15 WITH DIMES AND HALVES ONLY, SO YOU MUST HAVE AT LEAST 1 QUARTER. YOU CAN'T HAVE MORE THAT ONE QUARTER, OTHERWISE YOU COULD CHANGE A HALF. SO YOU MUST HAVE EXACTLY 1 QUARTER. THAT LEAVES 90 CENTS, TO MAKE WITH A HALF DOLLAR AND DIMES. SO THAT'S 1 HALF AND 4 DIMES. AND WITH ONLY 4 DIMES YOU CAN'T CHANGE A HALF DOLLAR THE ELDEST IS 9 YEARS OLD AND THE 2 YOUNGER ONES ARE 2 YEARS OLD. LET'S BREAK IT DOWN. THE PRODUCT OF THEIR AGES IS 36. SO THE POSSIBLE CHOICES ARE: 1,1,36 - SUM(1,1,36) = 38 1,6,6 - SUM(1,6,6) = 13 1,2,18 - SUM(1,2,18) = 21 1,3,12 - SUM(1,3,12) = 16 1,4,9 - SUM(1,4,9) = 14 2,2,9 - SUM(2,2,9) = 13 2,3,6 - SUM(2,3,6) = 11 3,3,4 - SUM(3,3,4) = 10 SIX OF THE SUMS ARE UNIQUE, SO IF IT WERE ONE OF THOSE, TOM WOULD HAVE RECOGNISED THE NUMBER ACROSS THE STREET THAT MATCHES AND HE WOULD KNOW THE ANSWER, BUT HE COULD NOT FIGURE OUT THE ANSWER. THIS MEANS THERE ARE TWO OR MORE COMBINATIONS WITH THE SAME SUM. FROM THE CHOICES ABOVE, ONLY TWO OF THEM ARE POSSIBLE NOW. 1,6,6 - SUM(1,6,6) = 13 2,2,9 - SUM(2,2,9) = 13 WHEN TOM HEARD THAT THE ELDEST IS VISITING HIS GRANDFATHER, WE CAN ELIMINATE COMBINATION 1 SINCE THERE ARE TWO ELDEST ONES. THIS LEAVES US WITH ONLY 1 OPTION LEFT, THAT IS 2, 2 AND 9