Programming Competition

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Programming Competition*From*: smh at matilda.vut.edu.au (Stephen Hunt)*Date*: Fri, 24 Dec 93 18:50:39 EST

Mathematica World Programming Competitions Judges - Tim Adam, Andrew Conway. Below are details of two competitions: one monthly, the other quarterly. We look forward to receiving your solutions. ____________________________________________________________________________ Mathematica World Friendly Programming Competition - closes 31 January, 1994. ____________________________________________________________________________ Open to anyone. Find the list of 3-D integer points on the surface of the sphere of integer radius r centred at the origin. i.e. list of integer solutions {a, b, c} of a^2 + b^2 + c^2 = r^2, for integer r. Solutions will be ranked - and the top 10 acknowledged. The best and interesting solutions will be published and discussed. A prize of US$50 and a commerative plaque will be awarded to the highest rank eligible solution. To be eligible for the prize you must not have won the prize in any of the previous 5 competitions. Submission details below. ____________________________________________________________________________ Mathematica World International Programming Competition - closes 31 March, 1994. ____________________________________________________________________________ Anyone can submit a solution to any of the problems below. The best and interesting solutions will be published and discussed. Solutions will be ranked - and the top 10 in each section acknowledged. A prize of US$100 and a commerative plaque will be awarded to the highest rank eligible solution in each section. To be eligible for the prize in a section you must satisfy the educational criteria, and have not won the prize in any of the previous 5 competitions High School For students at school up to the high school level, who are not enrolled at a university. (R.W. Hamming) Find the ordered list of positive numbers up to and including a given number which have no prime factors greater than 5. For n = 20 the list is: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20} Undergraduate For current students who have not completed a university degree. (also includes High School students) (T.D. Robb) For any list find the list of objects which occur mo than once in the ven list. For example an input of {1, 2, 3, 1, 2, 4, 1, 7, 8, 9, 6, 6, 6, 6, 8} should return {1, 2, 6, 8} as those elements appear twice or more. If possible, the solution should be efficient for both short and very long lists, and both sparse and densely packed duplicates. Here are two simple inputs to work with: SeedRandom[314159]; input1 = Table[Random[Integer, {0, 10^1}], {10^3}]; (* dense *) input2 = Table[Random[Integer, {0, 10^3}], {10^3}]; (* sparse*) Open Open to everyone. Find the area of the region which is the intersection of a list of two-dimensional convex polygons given in Mathematica Polygon form. eg. Polygon[{x1, y1}, {x2, y2}, {x3, y3}, {x4, y4}] is a quadrilateral with vertices in the given order. The more adventurous may want to allow concave or even self-intersecting polygons, however this will not be taken into account for judging purposes, except to the extent that inherent generality in a solution is a virtue. Judging Criteria Solutions will be judged according to the following criteria: correctness clarity efficiency elegance generality creativity Submitting Solutions Please send solutions by 31 March 1994, notebook or text to: adams at maths.mu.oz.au Subject: MW Competition Or, on 3.5" diskette (Mac or MS-DOS formatted) to: Programming Competition Mathematica World Ormond College Parkville, Victoria, 3052 Australia