Why maths ?
Ok, here is the description of the two problems you should try to solve.
1. An easy one to start : A winter fairy-tale
Two years ago it snowed for
days together that acute, that the two assistants of the Lineare Algebra
Lectures had to shovel snow away. They shoveld during continous snow
drifts for 8 days one quarter of the university snow free. Then they
abandoned.
The next year in addition to the two assistants the two lecturers and
aunt Hilda ( the inventor of the same named biscuits ) had to shovel
snow. They shovelled during same conditions as the year before half
of the university snow free in 6 days. Then they abandoned.
We also expect this year again a winter entry and want for amplification
to pull up the 6 students for shoveling snow, who have thrown the most
paper flyers during the exercises. How long do these 11 persons need
to get the whole university snowfree ?
Hint : As in every text exercise we make some assumptions : Shoveling starts first after a certain amount of snow has fallen ( every year the same amount ), every day falls the same amount of snow ( also during the shoveling !), all persons shovel the same amount. Don’t abandon !
2. A bit more complicated : WEMI – Task
In a land far away, Ellatien recently the following has occurred. The ministery for waste economy, matehematics and industry (WEMI ) has been flushed by the LISA-survey, which was judging the quality of teaching. Immediately starting with activism, WEMI asked the popular Prof. Dr. No-Way, to pursue a survey about the attendance of lectures at the university. Surveyed was the lecture in background studies, respectively the subject Ella. Prof. Dr. No-Way finished after a nearly representative survey to the following conclusion. Not all of the 880 signed in students always go to the lectures ! More detailed he came up with :
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Out of 10 students, who are going on any day in the Ella lectures, only 7 students return the next time. 2 are going in a pub and one is going into anonther lecture by mistake.
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Out of 10 students, who are going on any day into another lecture by mistake, one is doing it the next time again. 4 prefer to going to the pub, 3 stay in bed and 2 are going in the Ella lectures.
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Out of 10 students, who prefer going to a pub instead of going to the Ella lectures, 4 are repeating this the next time again. 4 instead stay in bed, 1 is going to the correct lecture and 1 is going to the wrong lecture.
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Out of 10 students, who prefer to stay in bed on any day, 7 will repeat this the next time. The 3 other people distribute equally to pub, correct and wrong lecture.
WEMI can make nothing of this. Help WEMI !
Calculate how many students will be in the correct lecture, pub, bed and wrong lecture at the end of the lecture time (15 weeks with 2 lectures )! Show also, that the result doesn’t change, if already at the start of the semester only half of the students is going in the correct lecture.
Steps how to solve these tasks are given in the process page.
Last updated : 24.2.2004
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