Kerstprobleem 2003 *** Christmas Problem 2003

CLICK HERE FOR THE NEW 2004 PROBLEM

click now here for the solutions

You can win twenty euro with this Christmas prize problem.
I will also send a anthology of the contributions to the Nieuwe Wiskrant, of course with the names of the contributors.
First read all conditions below.

Answer each of both following questions, number 1) and number 2).

1) Ten pirates are landing with a space-ship on a newly discovered planet. They decide to settle there, but as far away from each other as possible.

We have a sphere with a radius of one thousand kilometers.
Find the positions of ten points on the sphere such that the smallest distance between two distinct points out of these ten is as large as possible. Distances are not measured through space, but following shortest paths on the sphere.
Describe this optimal configuration of ten points in geometrical terms. Give also the minimum distance between two distinct points in this configuration.

2) Like 1), but now with twelve pirates instead of ten. So replace now in 1) everywhere ten by twelve.

Demonstrate clearly how you search the points, how you find them, and how you verify the answers.

prizes

There is one prize in each of both following categories.

category A: professionals. In this category there is one prize of twenty euro. Everybody may subscribe in this category. Winner is the competitor who gives the correct and exact answers and, in my opinion, the best demonstration.

category B: amateurs. In this category there is also one prize of twenty euro. People who have completed a maths or physics education at university cannot subscribe in this category.
In this category you can win with answers that are not exact, but nearly correct. You may use a computer or a measuring tape.

other conditions

The winning contribution in each category will be published in this website, together with my own solutions, with the name of the contributor. I will also send a anthology of the contributions to the Nieuwe Wiskrant.
If you don't win, but you do give correct answers, I would like to mention your name under the head 'other contributors who gave correct answers'. Please indicate whether you wish to be mentioned in this case.

You may send your contribution by e-mail (but then without appendices), or in a letter by traditional mail. I'll send you a confirmation of receipt as soon as possible. Send your solutions with complete name and address, and indication of the category in which you wish to subscribe, to
H.Reuvers, Brusselsestraat 92, 6211 PH Maastricht, the Netherlands
(e-mail info@petericepudding.com) .

All contributions must be sent at last on 6 januari 2004. At that day I must have your answers. After that, it may last two weeks before I publish the results.