PROBLEM CORNER

The Department of Mathematics and Computer Science is pleased to announce a project to be known as “PROBLEM COR- NER” and to be:coordinated by Dr. Tomasz Kaczynski. The aim of the project is to make available to students a set of interesting and challenging problems. Another aim is the encouragement of problem solving. : ”

The basic rules of operation of the project are as follows:

— A set of problems shall be posted at the beginning of each

month. — Solutions to any of the problems will be welcomed until the end of the month and should be submitted in writing to Dr. Tomasz Kaczynski, Memorial-104. (Please slide your submission under the door if Dr. Kaczynski is absent).

— Queries about the project and questions should be directed to Dr. Kaczynski. i

— Prizes will be offered to the authors of correct and/or origi- nal solutions of any problem at a social gathering at the end of the semester.

SET 2—-FEBRUARY 1989

1. A hat contains 7 ballots labeled with the numbers 1, 2, 2?, 23, 24, 25, 26, respectively. We randomly select ballots without re- placement until the sum of numbers printed on them exceeds 124. Which value of the obtained sum is most probable?

2. A French boat is fishing on Canadian waters without permis- sion. Each casting of their net into the sea brings a catch of equal value, but during each casting the probability of being caught by the coast guard is z where k is a given integer. We assume that the event of being or not being caught during consecutive castings is independent of the number of previous castings. If the boat is caught by the coast guard, all the fish is confiscated and the fish- ing cannot continue.

The captain plans to return home after n castings. By taking account of the risk, the total gain during the cruise is a random variable. Find the number n which will make the expected value

of that random variable greatest.

3. Decide whether the number z = 1+ 4(1+ ;45(1+ ;Gs(..- is rational or irrational.

4. Prove that, for each positive integer n, the polynomial P(x) = 1+ (%) + (3) + (4) +--+ () has no multiple roots

(notation n! = 1x 2x3x...x (n-1) xn).

Solutions are accepted until the end of February.

Councillor Plans Awareness of the Physically Challenged

by Sam Okello.

Knowing and solving limita- tions of disabled people may not be easy.

Such were the issues discussed last week when Jessie Campbell and I, met with the Students counsellor,Marion Basha.

Basha emphasized the signif- icance of identifying problems faced by certain students. She mentioned that it was important to have resource people come in and point out what can be acces- sible to the Disabled.

Basha said that there were several groups of students with disabilities. For instance, stu- dents with Diabetes, epilepsy,and

Haemopholia were considered as some of the people whose health was at risk. “Students with a health problem should know that there is a health centre on cam- pus”, she added.

Basha sug- gested that the UPEI Disabled association should act as a medi- _ time to employ volunteers. ator to students in “Need” and She suggested that the bring them to services that are should be possible volunteer jg available to them. opportunities on campus. § mentioned possible areas whel disabled students could work ¢ volunteer basis. Such areas ; cluded the vet school, librar Business office, and Cafeteri Basha gave no promises in ensy ing volunteer work:

with limited work experience a find out where their work exper ence lies,” she said.

Meanwhile, these studen should be looking for other jol elswhere. Basha added that | most cases employers don’t ha

It is known that many stu- dents with disabilities don’t have much work exeperience. Basha pointed out that such students be encouraged to join a work Co- operative and do volunteer work. “Employers should get students

Aloud Thought

“Everyone has their

by Richard Whipple [proper] place.”

-Myself in discussion with UPEI Professor and

Poet Richard Lemm, on the topic of Fairness and Equality.

UTOPIA;

A Governing Constitution

When I asked

Doctor Kenneth Clatterbaugh, Associate Professor of Philosophy and adjunct Associate Professor of Women’s Studies and Psychol- ogy at the University of Washing- ton (Seattle) whether or not he jived with my statement, his an- swer was a balanced antithesis: If it’s true, it’s trivial. If it’s not, it’s false.”

I strongly disagree with such rhetoric. The concept of a utopia is an ideal and therefore must be based on ideal circumstances. Ergo, for acheiving Utopia, there must be a viable formula under these circumstances. What are these restrictions or freedoms re- sulting from these circumstances that permit a utopia? And, what shall be my main address; can a universal Utopia exist and, if it can, what is its governing consti- tution?

Doctor Clatterbaugh later qualified his overwhelming optimism by point- ing out that-_ my statement is usu- ally used by the oppressor to sup- press the oppressed. Undaunted by his cynicism, however, my re- buttal rested in my heart. I am

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- sors.

the eztent of an individual’s cz: pability and must exist as an eve lutionary system and _ not be, it self, an insurmountable barrier td the people it serves. This evolu tionary system of social structutt would promote equality amongs the people, it would serve 1 unify! Proper identification ani mature distinction are two sides of the same corner stone of ? utopian society. This is the cor ner stone to the social system structure of just classification.

still of the opinion that if ev- eryone did personally know their [proper] place that there would be few people susceptible to oppres- sion. Furthermore, the place of a leader is to lead the people not to oppress them. In order that the leader remain as utopian as the rest of Utopia, the individual person must be absolutely quali-- fied for the position. Naturally, this would effectively eliminate our current structure for demo- cratic selection, which is noth- ing more than the fasgade of gov- erning will. In application this would mean that the best indi- vidual person would get the job. Consequently my contention with Dr. Clatterbaugh is this: if the statement is true, it is made triv- ial by those with ambition who lack the ability to be responsible. These people who want to bas- tardize this truth are the oppres- But if it is true it is the ground work for a utopia.

This distinction of place de- notes a system of social structure and requires an [official] identity which must evolve to the indi- vidual person it [officially] iden- tifies. Accordingly, this. social system should not represent any- more than a just classification of

_ Ifa government is to hold rea ‘utopian’? power it must realis that this is through its people. ! must realize and understand th power is derived neither fro! force nor from the threat of forct Power is an evolutionary classi fication, just as the social str“ ture must be, and,therefore, is ob tained through love; its demo stration of love for its peop! and the people’s love for it. I has been proven time imme! rial that when society is agai” her government the relations)! breaks down in protest. ——This essay is the begining ' the question of Utopia. It sh? be ongoing in this column until! is answered. Happy Spring Bré from my staff and myself.

Thursday, February 16, 1989 /

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