Programming Contest: Triangles

From: Max Alekseyev (2:5015/60)
To: All
Date: 2002-07-15T16:56:02Z
Area: RU.ALGORITHMS
* Crossposted in RU.ACM
* Crossposted in RU.GOLOVOLOMKA
* Crossposted in RU.MATH

████ OS/2        Hi, All !

Новое соревнование за $300 на 
http://members.aol.com/bitzenbeitz/Contests/

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Programming Contest
Triangles

*Introduction*

Given any sequence of positive integers we can generate a triangular array of numbers by using the given sequence as the triangles base and then letting each remaining value in the triangle be the absolute difference of the two values immediately below it. For example, starting with the sequence (89, 78, 12, 13) we can construct this triangle:

        10
     55   65
   11   66   1
89   78   12   13

We say that a sequence of positive integers is *acceptable* if no integer appears more than once in the triangle it generates. The sequence (89, 78, 12, 13), whose triangle is shown above, is acceptable. The sequence (19, 80, 51, 77) is not acceptable because its triangle contains two instances of the integer 29:

         29
       32   3
   61   29   26
19   80   51   77

Given an acceptable sequence of positive integers, its *span* is the difference between the largest and smallest values in the corresponding triangle. For example, the span of (89, 78, 12, 13) is 88.

Given two acceptable sequences, the one with the smaller span is considered *better*. For example, (83, 73, 14, 47) is better than (89, 78, 12, 13) because their spans are 73 and 88, respectively.

*The Contest*

The goal is to find acceptable sequences with small spans.

Send me your best (that is, least span) acceptable sequence for each sequence length from 2 to 25. Ill calculate a subscore for each sequence (details of the scoring system are below) and the total of your 24 subscores will be your contest score. The person with the highest contest score wins the contest. In case of a tie, Ill choose a winner at random from among those tied.

*The Prizes*

First prize is $300. Second prize is $50.

*How to Enter*

Send an email containing your entry to bitzenbeitz@aol.com before Noon GMT on October 15, 2002. Put just the word TRIANGLES in the subject line. The body of the email should be formatted as follows.

The first line should contain your sequence of length 2. The second line should contain your sequence of length 3. And so forth through your sequence of length 25. Each sequence should be written as a list of comma-delimited integers. After your last sequence leave a blank line. After that blank line provide your name. On the line after your name provide your city (and state or province, if applicable) and country.

Scoring will be done by computer, so be careful in composing your email.

You may enter as often as you like, but you are only eligible to win one prize. If you enter more than once, you should send from the same email address each time.

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Подробности здесь:
http://members.aol.com/bitzenbeitz/Contests/Triangles/Description.html

Regards,      °°
        Max    ~

--- FleetStreet 1.27.3.8
 * Origin:  (2:5015/60)