Enigma 1566 - Consistently older
Chappy
New Scientist magazine, 7 October 2009.
By Richard England.
Yesterday was Harry's birthday and also
Tom's birthday. Harry is the older. Harry's
current age, Tom's current age and the
difference between their ages are each the
product of two primes. The six primes are
all different.
Before Harry reaches the age of 90, there
will be three further years during which his
age, Tom's age and the difference between
their ages will again each be the product of
two primes, the six primes all being
different.
What is Harry's current age?
Ciao,
Chappy.
jonnie303
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Harry is 57
The numbers between 1 and 90 which are the product of 2 primes are
6,10,14,15,21,22,26,33,34,35,38,39,46,51,55,57,58,62,65,69,74,77,82,85,86,87.
The difference between Harry's age and Tom's age is constant, and must
be one of these numbers; their ages at the 4 relevant years must share
no common factor with this difference. If the difference has a factor
of 2 or 3 then there are not enough possible numbers left to provide
for 4 matching pairs of ages. Trying a difference of 35 quickly
provides us with the necessary 4 matching pairs - 22/57, 34/69, 39/74,
and 51/86.
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jonnie303
sevenoaks, uk