Cheryl's Age
Albert and Bernard now want to know how old Cheryl is.
Cheryl: I have two younger brothers. The product of all our ages (that is my age and the ages of my two brothers) is 144, assuming that we use whole numbers for our ages.
Albert: We still don't know your age. What other hints can you give us?
Cheryl: The sum of all our ages is the bus number of this bus that we are on.
Bernard: Of course we know the bus number, but we still don't know your age.
Cheryl: Oh, I forgot to tell you that my brothers have the same age.
Albert and Bernard: Oh, now we know your age.
So what is Cheryl's age?
This problem is the sequel of Cheryl's Birthday .
The answer is 9.
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1 solution
There are 18 unique was for three numbers to multiply to 1 4 4 : 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 4 4 1 2 3 4 6 8 9 1 2 2 3 4 6 8 3 4 6 4 6 1 4 4 7 2 4 8 3 6 2 4 1 8 1 6 1 2 3 6 2 4 1 8 1 2 9 1 6 1 2 8 9 6 Sum 1 4 6 7 5 5 2 4 1 3 1 2 7 2 6 2 5 4 0 2 9 2 4 2 0 1 9 2 2 1 9 1 7 1 7 1 6 There are two sums -- 1 7 and 1 9 -- for which knowing the sum doesn't uniquely determine the ages. Of these, only one -- ( 4 , 4 , 9 ) -- has two of the ages the same. Thus Cheryl, the oldest sibling, is 9 .