Mma World Programming Competitions

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Mma World Programming Competitions*From*: adams at maths.mu.oz.au (Tim Adam)*Date*: Mon, 30 May 1994 19:20:52 +1000

_Mathematica World_ is an electronic magazine aimed at helping people use Mathematica effectively, and to this end we run two programming competitions. The quarterly "International" competition has Open and Student divisions, and is intended to be more challenging than the monthly "Friendly" competition. Entries are welcomed from anyone, and there are $100 and $50 prizes respectively for the best solutions. Results will be posted to the MathGroup mailing list and sci.math.symbolic. A defensive word: although _Mathematica World_ is available by subscription only, these competitions are open to all and it is our opinion that this article is of interest and relevant to readers of these groups. The current problems are given below: please see a follow-up article for the results of the last International and Friendly competitions. Tim Adam Executive Editor, Mathematica World Mathematica World Friendly Programming Competition This is open to anyone, and the problem is to be seen as an exercise through which we can all learn from each other. We especially encourage inexperienced programmers to attempt the problem in order to improve their programming skills. If this applies to you, please indicate in your entry if you would like some feedback privately on your solution. This month's problem: Consider the cube plotted by the command below to be described by the three-dimensional array {{{1, 2}, {3, 4}}, {{5, 6}, {7, 8}}}. Generate the list of similar descriptions of the cube in all possible orientations. You might want to try to generalize this to n dimensions. Show[Graphics[{ GrayLevel[0.0], Thickness[0.005], Line[{{51.37404, 135.67987}, {109.10594, 175.36909}}], Line[{{51.37404, 135.67987}, {152.40236, 104.10685}}], Line[{{64.00258, 55.39629}, {51.37404, 135.67987}}], Line[{{109.10594, 175.36909}, {110.90954, 103.20505}}], Line[{{110.90954, 103.20505}, {64.00258, 55.39629}}], Line[{{110.90954, 103.20505}, {183.97538, 79.75157}}], Line[{{147.89336, 20.21774}, {64.00258, 55.39629}}], Line[{{147.89336, 20.21774}, {183.97538, 79.75157}}], Line[{{152.40236, 104.10685}, {147.89336, 20.21774}}], Line[{{183.97538, 79.75157}, {194.79865, 156.42628}}], Line[{{194.79865, 156.42628}, {109.10594, 175.36909}}], Line[{{194.79865, 156.42628}, {152.40236, 104.10685}}], Text[FontForm["1", {"Helvetica", 12}], {41.90347, 135.22897}, {-1.0, -1.0}], Text[FontForm["2", {"Helvetica", 12}], {147.44246, 110.87369}, {-1.0, -1.0}], Text[FontForm["3", {"Helvetica", 12}], {106.84977, 175.82166}, {-1.0, -1.0}], Text[FontForm["4", {"Helvetica", 12}], {196.15302, 159.58258}, {-1.0, -1.0}], Text[FontForm["5", {"Helvetica", 12}], {50.02134, 45.92739}, {-1.0, -1.0}], Text[FontForm["6", {"Helvetica", 12}], {139.32459, 5.33303}, {-1.0, -1.0}], Text[FontForm["7", {"Helvetica", 12}], {111.85977, 81.50841}, {-1.0, -1.0}], Text[FontForm["8", {"Helvetica", 12}], {188.03515, 70.28100}, {-1.0, -1.0}] }], AspectRatio->1.10714, PlotRange->{{41.0, 209.0}, {4.0, 190.0}}]; For example, another such description would be {{{6, 8}, {2, 4}}, {{5, 7}, {1, 3}}} because the cube can be rotated to this position: Show[Graphics[{ GrayLevel[0.0], Thickness[0.005], Line[{{51.37404, 135.67987}, {109.10594, 175.36909}}], Line[{{51.37404, 135.67987}, {152.40236, 104.10685}}], Line[{{64.00258, 55.39629}, {51.37404, 135.67987}}], Line[{{109.10594, 175.36909}, {110.90954, 103.20505}}], Line[{{110.90954, 103.20505}, {64.00258, 55.39629}}], Line[{{110.90954, 103.20505}, {183.97538, 79.75157}}], Line[{{147.89336, 20.21774}, {64.00258, 55.39629}}], Line[{{147.89336, 20.21774}, {183.97538, 79.75157}}], Line[{{152.40236, 104.10685}, {147.89336, 20.21774}}], Line[{{183.97538, 79.75157}, {194.79865, 156.42628}}], Line[{{194.79865, 156.42628}, {109.10594, 175.36909}}], Line[{{194.79865, 156.42628}, {152.40236, 104.10685}}], Text[FontForm["6", {"Helvetica", 12}], {41.90347, 135.22897}, {-1.0, -1.0}], Text[FontForm["8", {"Helvetica", 12}], {147.44246, 110.87369}, {-1.0, -1.0}], Text[FontForm["2", {"Helvetica", 12}], {106.84977, 175.82166}, {-1.0, -1.0}], Text[FontForm["4", {"Helvetica", 12}], {196.15302, 159.58258}, {-1.0, -1.0}], Text[FontForm["5", {"Helvetica", 12}], {50.02134, 45.92739}, {-1.0, -1.0}], Text[FontForm["7", {"Helvetica", 12}], {139.32459, 5.33303}, {-1.0, -1.0}], Text[FontForm["1", {"Helvetica", 12}], {111.85977, 81.50841}, {-1.0, -1.0}], Text[FontForm["3", {"Helvetica", 12}], {188.03515, 70.28100}, {-1.0, -1.0}] }], AspectRatio->1.10714, PlotRange->{{41.0, 209.0}, {4.0, 190.0}}]; Solutions will be ranked - and the best and interesting solutions will be published and discussed in the July issue. A prize of US$50 and a commemerative plaque will be awarded to the highest ranked solution. Please send solutions to the Friendly Programming Competition by June 20 1994, notebook or text to: adams at maths.mu.oz.au Subject: MW Friendly Competition Or, on 3.5" diskette (Mac or MS-DOS formatted) to: Programming Competition Mathematica World Ormond College Parkville, Victoria, 3052 Australia Mathematica World International Programming Competition Welcome to our second quarterly competition. There will be prizes for the best solutions (details below). Please send any problems that you think would be suitable for any of these. The second quarter competition closes at the end of June 1994, results will be in the August issue. The best and interesting solutions will be published and discussed. ***************************************************** Anyone can submit a solution to any of the problems below. Solutions will be ranked - and the top few in each section acknowledged. A prize of US$100 and a commemerative plaque will be awarded to the highest ranked solution in each section. To be eligible for the prize in a section you must satisfy the educational criteria. ***************************************************** International Programming Competition - Student For current students who have not completed a university degree. (also includes High School students) Consider a game in which there are a fixed number n of chairs arranged in a circle, and people possessing various positive numbers of chips occupying some or all of these chairs. At each round of the game, everyone moves the same number of chairs to the right (clockwise) as they have chips. If after this move two or more people occupy the same chair, the person there with the least chips gets the chips of the rest of the people at that chair, who are now out of the game. Ties are broken randomly. The game can be represented by a list of n numbers, the numbers of chips held by the person at each chair. The problem is to write a function to take one of these lists and return the corresponding list after one more round of the game. For example, if the initial configuration is {1, 4, 2, 3}, the next one would be {2,5,3,0}, then {0,3,7,0}, etc. International Programming Competition - Open Open to everyone. Consider a game in which there are a fixed number n of chairs arranged in a circle, and people possessing various positive numbers of chips occupying some or all of these chairs. At each round of the game, everyone moves the same number of chairs to the right (clockwise) as they have chips. If after this move two or more people occupy the same chair (a "collision"), one of them is chosen at random to take all the chips of the rest of the people at that chair, who are now out of the game. The game can be represented by a list of n numbers, the numbers of chips held by the person at each chair. The problem is to investigate the game from an initial configuration which is a permutation of Range[n]. The type of thing you could look at might be to identify when there will be no further collisions because there is no point continuing past there, e.g. if there is only one person left. The problem is fairly loosely specified to allow you to decide what direction you take and to use a fuller range of programming and problem-solving skills. As an example of a game, if the initial configuration is {1, 4, 2, 3}, the next one would be {2,5,3,0}, then {0,3,7,0}, {3,7,0,0}, {7,0,0,3}, etc. Judging Criteria Solutions will be judged according to the following criteria: correctness clarity efficiency elegance generality creativity Submitting Solutions Please send solutions to the International Programming Competition by 30 June 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

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