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Hill's data (Posted on 2018-03-03) Difficulty: 4 of 5
“I am old,” said Mr Methuselah, “but not as old as the Hills.
Did you know that if you add up the ages of all the Hills exceptin’ Mr Hill you get his age?
And did you know that if you multiply the ages of all the Hills except Mr Hill you get a number which contains ones only, and as many ones as there are Hills, not counting Mr Hill?
Every Hill has a different age less than 100, and every Hill’s age in years is odd, exceptin’, of course, Mr Hill.”

I didn’t know this. How could I? I had only just arrived in Rome, Georgia, and knew nothing of the locality. But once he had told me it sure set me to wondering:

How old is Mr Hill?
How old is Mrs Hill?
And how old are the Hillocks?

Hope you give me the answers...

See The Solution Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Solution answers | Comment 5 of 6 |
Given the first n factors, the number of digits in the product exceeds the number of factors when n ≥ 11, therefore n < 11.

Iterating through the ten numbers comprised of n 1's, there are only four where all factors are < 100. The set of these numbers are {1, 11, 111, 111111}.
Reducing the set to include only those where the sum of the factors is even gives {11, 111111).

Factors         Sum
1,11             12
1,3,7,11,13,37   72

Therefore, there are two valid answers:
(1) Mr.  Hill     is age  12.
    Mrs. Hill     is age  11.
   *The Hillock   is age   1.
*An unknown quantity is referred to in the plural even if it be one.

(2) Mr.  Hill     is age  72.
    Mrs. Hill     is age  37.
    The Hillocks are ages 13, 11, 7, 3 & 1.

Society generally frowns of preteens being parents, thus, the expected answer would be that for (2).

  Posted by Dej Mar on 2018-03-03 23:01:44
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