Bear News Beartown News

DECEMBER 1, 2003

MYSTERY

HOW OLD ARE THEY?

1.  Father & Son  If Henry's age is multiplied by the age of his father, the product is a permutation of the digits in their individual ages.  How old are they?

2. John's Cousins  John's age and the ages of his three distant cousins are all prime numbers and the sum of their ages is 50.  How old are they?  (The number 1 is not considered a prime number)

THINK
ABOUT
IT!!!!!!!

Check the next issue of Beartown News for the answer.


FROM LAST MONTH

PROFESSOR'S  TELEPHONE  NUMBER

Professor Americus DeBear is the esteemed Chairman of the Math Department of Beartown University.  However he happens to be extremely absentminded but uses his extraordinary math ability to overcome this problem. 
For example he remembers his seven-digit telephone number as:
THE ONLY SEVEN-DIGIT NUMBER WHICH IS CONVERTED INTO A FACTOR OF ITSELF WHEN THE ORDER OF ITS DIGITS IS REVERSED.
WHAT IS THE PROFESSOR'S PHONE NUMBER???

SOLUTION:  The professor's telephone number is 9899901, which is equal to 9 X 1099989.  Other numbers which have this characteristic may be formed by inserting any number of nines between the 98 and the 01, i.e. 9801, 98901, 989901, etc.  Another number of this type is 8712 which is equal to 4 X 2178.  Finally, additional numbers may be formed by repeating the basic groups, e.g.,  98999019801989901 = 9 X 10998910891099989


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