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UMASS LOWELL/UMASS DARTMOUTH - CyberEd

92.419 Computer Algebra with Mathematica

Kenneth M. Levasseur

Department of Mathematical Sciences

University of Massachusetts Lowell

Lowell, MA 01852



"Wiretap"

Subject

Games, Codes, Programming, Mathematics

Topic

Wiretap is a game by Sid Sackson that appeared in the October 1996 issue of Games magazine. Rules appear below.

Reference(s)

Sid Sackson, "Wiretap: a Two-Player Paper and Pencil Game of DeductiveLogic," Games , October 1996, p 45.

Project Idea(s)

Program the game in some form, to allow the user to play or the computer to play, or both. Programming for play by the user would seem to be easier of the two, but a good interface for input isn't obvious. Explore the phenomonon described in the "Winning" section of the rules where different configurations give exactly the same information. For the different variations listed below, does the same phenomonon occcur?It would seem that linear algebra could be used to provide an explanation.

Prerequisite Mathematics

Programming the game for user play wouldn't appear to require much mathematics. Programming for computer play or idea #2 would require somewhat more, probably linear algebra.

Required Programming Level

To do a good job programming the game, advanced programming would be needed. The second idea would not seem to require much programming other than the use of mathematics packages.

Rules

The Playing Fields

On sheet of paper, draw two 5x5 grids like the ones to the right. Ona separate sheet of paper your opponent does the same. One grid is for setting up secret "network" of wires. The other is used to record information about the opponent's network, the layout of which you will be trying to deduce.

Setting Up the Networks

Draw ten groups of straight lines, known as "wires," in your grid. Each group of wires must be three spaces long, and you must draw one group in each row and one in each column of your playing field. The number of wires in each group must be as follows:

a - Three groups consist of a single wire.

b - Three groups consist of a double wire.

c - Two groups consist of a triple wire.

d - Two groups consist of a quadruple wire.

Example

The accompanying diagram shows one of the many possible networks you can draw.

Tapping the Wires

After each player has secretly drawn a network, each player decides on a space he or she wishes to "tap" for information. This space is announced to the opponent, who reveals the number of wires in that space. For example, if in the previous diagram space A5 is asked, the answer is four wires. In the same diagram, space A4 has one wire and space A2 has none. No information is provided about the number of groups in the space,nor about whether the wires run horizontally or vertically. After each player has recorded the information received, each player taps another space and again told the number of wires located there. Play continues in this way until one player decides that he or she can guess the location of all the wires in the opponent's network.

Variations

Make one each of the single, double, triple and quadruple wire groups four spaces long instead of three.

Use 6x6 playing field. Make the groups four spaces long and use three of each type.

Play the same as in the previous variation but make one of each of the four types of wire groups five spaces long instead of four.

Winning

When a player is ready to guess, he or she tries to draw the opponent's network. This drawing is compared with the opponent's original drawing. If the guessing player is correct, he or she wins a single game; If incorrect, the opponent wins a double game. Since turns are considered to be simultaneous, it's possible for both players to guess at the same time. If both are corrector both are incorrect, the game is a tie. But if one player is correct and the other isn't, the correct player wins a triple game. Sometimes different networks, such as the two shown here, have the same number of wires in each space. If all the corresponding squares in both the guess and the actual network have the same number of wires, the guess is considered correct.

Key Words

games, Mathematica, mathematics, linear algebra, codes, programming

Reviewer

K. M. Levasseur ( kenneth_levasseur@uml.edu )

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