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MathGroup Archive 1993

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Programming Competition

  • To: mathgroup at
  • Subject: Programming Competition
  • From: smh at (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 

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 

(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}


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 

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: 

input1 = Table[Random[Integer, {0, 10^1}], {10^3}]; (* dense *)
input2 = Table[Random[Integer, {0, 10^3}], {10^3}]; (* sparse*)


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: 


Submitting Solutions

Please send solutions by 31 March 1994, notebook or text to:

adams at
Subject: MW Competition

Or, on 3.5" diskette (Mac or MS-DOS formatted) to:

Programming Competition
Mathematica World
Ormond College
Parkville, Victoria, 3052

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