A family consists of Mum, Dad and the three children, Gerald, Fred and
Angela.
Gerald is four times older than Angela. He is also the sum of Fred's and Angela's ages. And if
Gerald's age is added to Mum's, you get Dad's age. Dad is nine times older than Fred. All the
family's ages added together come to 58 years. (For the sake of the problem, we assume they
all have a birthday on the same date so that their ages are all whole numbers of years.) What
are the ages of each member of the family?
Please send your answers to me, David Broughton (see page 3 for addresses), to arrive by
Wednesday 6th August.
ANSWER TO THE MAY PUZZLE
This puzzle was to draw a diagram with E (the number of edges) = 15; V (the number of
vertices) = 10 and F (the number of faces) = 7. Only three edges were permitted at each
vertice. I was also interested in how many different diagrams could be produced with these
constraints. By "different", of course, I mean different topologically. I found 6 which are
shown above. Peter Greenhalgh, Ray Boote, Rosemary West and Bill Woodmore sent in
diagram D1, the double pentagon. Gordon Stonham and John Bownas found D2. Les
Burridge sent in the interesting D4b which he described as a tetrahedron with the top vertice
chamfered off on three edges. At first I thought this was a new form but later realised it was
topologically equivalent to my own D4a. It is an interesting exercise to check that this is so.
Notice that D4a is a cube with a corner cut off. John Moxon sent in D6. All the diagrams have
been redrawn by me (using Paint) so that all polygon faces have internal angles not exceeding
180 degrees with the external face having angles not less than 180 degrees. If anyone can find
a new diagram that is not topologically equivalent to one of the six above, I shall be very
interested. The numbers in each polygon, plus the external face, are the number of sides for
each polygon and their total must be 30. This was one way of checking the validity of the
answers. Can you prove that this is a sufficient check?
Many thanks to the eight members who sent in answers to this interesting and novel puzzle.
As usual, one was chosen at random for the £5 book token and this was won by John Bownas.
Congratulations to all eight and thank you for your answers.
PRIZE PUZZLE CORNER
JULY2003
by David Broughton
3
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