REMEMBER
YOU WILL APPRECIATE THESE SOLUTIONS
MORE IF YOU
STRUGGLE WITH THE PROBLEM YOURSELF
FIRST
Louise Anderton' s Solutions
SPHINX 5
SPHINX 6
SPHINX 7
Since Louise made inroads into this problem, the students at Thorne Grammar, near Doncaster, England and several adults have also become involved.
Hypotheses
From England
Andy Martin is the Head of Department at
Thorne Grammar, and the Task Centre Project Officer for the UK.
- Andy is always looking for ways
to involve more students in problem solving. Noting the interest
in Sphinx that was developing across the school he engaged the
Design & Technology Department to mass produce Sphinx shapes.
He now has over 1000 pieces made from waste plastic which are cut to
fit 20mm isometric paper.
- The learning power of concrete materials
is again highlighted by the use of these pieces. In simple terms,
they provide access to the problem.
I quote here from a fax I received which discussed the Sphinx
developments at Thorne:
- "I enclose work from Sarah Hutchinson
who found 4 Size 3 Sphinx solutions. She has conjectured 9 Size 5,
16 Size 7 to relate the sequences of square numbers and
primes."
Andy also sent 3 solutions for Size 5 and 3 for Size 9, from Steven, Catherine and Richard in Year 8, and copies of a Size 5
solution from Sarah Steadman & Catherine Finnegan and a Size 7
solution from Steven Tootel.
More than a year later I received another set of solutions from Andy. In the interim, Year 7 & 8 classes had been working on Sarah's hypothesis of 9 Size 5 Sphinxes. They found 10 and Andy was able to illustrate the mathematical process of disproof by counter example. He felt is was a good thing that Sarah had been part of the group which had continued the challenge!
With this remarkable work came 10 different solutions for the Size 7 Sphinx AND an attempt at formal proof by a Year 9 boy, Paul Elliott, that argued at least 92 solutions to the Size 7 Sphinx and suggested a direction to find even more!
An example of one of these solutions is shown in this photograph.
Andy would be very pleased to share his students work with other teachers, and even happier to extend the Sphinx Search beyond the boundaries of his school. Establishing problem solving teams of students who communicate over the Internet is one potentially exciting way to do this.
Interested teachers can email Andy at: andy@1martin1.freeserve.co.uk
From Sweden
A second hypothesis comes from Johan
Öberg who conjectures that the
number of solutions for Size N sphinx is (N -1)^2 - ie: (N-1)
squared.
From Australia
David Shield, a retired mathematician from Australia, became engaged in the Sphinx puzzles through the student work described above. He set to work building a formal proof of the number of solutions of various sizes. Part of his work is reproduced here. David has written his proof in a form that Junior Secondary students could follow:
Size 4 and More Proofs
- Move on to:
- Patterns &
Powers
Lesson Set A based on
Sphinx - Curriculum Corporation Task 166
Patterns & Powers contains a number of photos. It will take
longer to down load than normal. However you will be able to read
through the text while the photos are being brought in. They are
worth the wait.
- Shapes &
Perimeter
Lesson Set B based on
Sphinx - Curriculum Corporation Task 166
- Task Centre Home Base
- Return to: