I5. Circular Prime Sums

'We place some positive whole numbers around a circle. The sum of each
pair of neighbouring numbers is written in a box drawn in the space
between them. We call this arrangement a sum circle.
Like a bracelet, a sum circle is not changed by rotations and
reflections.
If all the boxes contain primes, the sum circle is called a prime sum
circle.

a Find all the different ways of arranging 1, 2, 3, 4, 5, 6, 7, 8, 9,
10 into a prime sum circle with seven different prime numbers in the
boxes. Explain why there are no more such prime sum circles.'

From '2008 MATHS CHALLENGE STAGE MATHEMATICS CHALLENGE FOR YOUNG
AUSTRALIANS MARCH-JUNE INTERMEDIATE STUDENT PROBLEMS AN ACTIVITY OF
THE AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE A SUBCOMMITTEE OF THE
AUSTRALIAN MATHEMATICS TRUST IN ASSOCIATION WITH THE AUSTRALIAN
ACADEMY OF SCIENCE AND THE UNIVERSITY OF CANBERRA'

Now you guys (for a fact which I know for sure) are really good. As
you guys found a way to reduce the guessing and checking in the I1.
Ice creams part c, I'm sure you guys will find a way of narrowing down
the number of possibilities to test out here. Now for I1. Ice creams
part c (http://groups.google.com/group/sci.math/browse_thread/thread/
ca5d8fcb28b870e7/4d1d71ae7d839146?lnk=gst&q=%22copycats
%22#4d1d71ae7d839146 thank you to quasi), I would consider the hint to
be: convert the percentages into fractions.

Could somebody give me a hint here?
.

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