Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem Solving Competition: 2018/2019

The competitions start annually and last from September to May, but you can enter any time during the academic year.

In Mathematics, there are four different contests, in Physics there are three and in Informatics there are two. The conditions of the respective contests are slightly different. See below for details.

## Entering the competition

Every primary or secondary school student is eligible to participate in the contests.

However, according to the General Data Protection Regulation (GDPR) of the European Union, we need to have a parental consent to handle data for contestants under 16 years. Our data and information policy can be found at https://www.komal.hu/info/adatkezeles.h.shtml.

### Registration

Each participant in the KöMaL contest has a grade number between 1 and 12 (which may differ from their grade in school). A 12th-grade contestant is someone who has just started their last school year before the matriculation examination; 11th- or 10th-grade contestants are expected to finish their secondary education in 2021 or 2020.

Students in different grades might find the same problems but in most cases their work is evaluated within their age group, they compete with students of the same age only. Therefore, it is essential that the paper should indicate the 1 to 12 grade of the contestant in the current school year. The KöMaL contests are individual competitions, solutions produced by a group are not accepted. If two papers turn out to be practically identical, none of them will be marked.

### Contests in mathematics

We have four contests in Mathematics this year.

K contest: this is a joint contest of KöMaL and ABACUS, exclusively for students of grade 9 - beginning the secondary school this year. 5 problems in each Month; each of them is worth of 6 points.
Students are not allowed to participate in both competitions "K" and "B" at the same time.

C contest: easy exercises for practice. 7 problems in each Month; each one for 5 points. The firts 5 exercises are to grades 1 to 10, the last 5 exercises are to grades 11 to 12. There are three age categories:

• grades 11 to 12th (preferably those not studying mathematics in a special advanced class. Those in advanced classes are advised to take part in the B contest).

B contest: this is the traditional contest of KöMaL. 8 problems each month. You can send any number of solutions, but only the highest six scores are entered.
Students are not allowed to participate in both competitions "K" and "B" at the same time.

Age groups:

• up to the 8th grade

A contest: advanced problems, 3 each month. More demainding than the B contest, for those who are preparing for national or international competitions. Here there are no separate age groups.

### Contests in physics

There are three different contests in physics: types M, G and P. A student may participate in more than one type of contest, however, types G and P cannot be chosen simultaneously. Contestants of grade 10 or less should declare which type G or P they choose (see your personal settings on our page).

M contest– experimental problems in physics: In each month, a measurement problem is proposed. This can be submitted by a contestant of any age. Each M problem is worth 6 points.

To carry out an experiment, one can ask someone (a family member, classmate, or a friend) for assistance. Both the contestant's and the assistant's data should appear in the header of the documentation of the experiment. This year, for the first time, it will be possible for two contestants to cooperate and carry out an experiment together. Members of the pair can have different grades or schools, and they should register for the type M contest independently. It is sufficient to submit the experiment documentation only once in each month, but the document header should always contain both names, schools, grades and emails. Points for the documentation will be awarded to both members of the pair.

G contest: 4 easy theoretical problems each month, but we evaluate only 3 problems.
Students are not allowed to participate in both competitions "G" and "P" at the same time.

Age groups:

• up to the 8th grade;

P contest: 10 theoretical problems each month.
Students are not allowed to participate in both competitions "G" and "P" at the same time.

Age groups:

• up to the 8th grade;

Every age group may send solutions to all kinds of problems. In the P contest we evaluate only 3 problems up to the 8th grade and 5 problems from 9th - 12th grade.

### INFORMATICS

We have two contests in Informatics. There are no separate age groups, competition is opened for everyone.

I contest: Three I problems and one I/S problem every month. The I problems can be solved in C, C++, Pascal, Python, Java, Basic or C#. In each month, the three highest scores out of the four problems count in the I contest.

S contest: The S contest consists of one more demanding programming task marked S, and the I/S problem every Month which can be solved in Basic, C, C++, Pascal or Java. Solving these problems need deeper algorithmic thoughts and knowledge.

Please do not send .exe files!

The deadline in all contests is the 10th of the month following the publication of the current issue. Should that be a weekend or bank holiday, the deadline is the next workday.

## Preparing and submitting your solutions:

You cannot submit your solutions in email.

For problems in mathematics or physics, you can use the online editor on our website or upload a file. For problems in informatics, you can only use the Electronic Workbook to upload your solutions.

Handwritten submissions in a non-electronic form are accepted only via regular post. Figures drawn by hand, scanned at a sufficiently high resolution and pasted in your solution are accepted.

The actual state of the contests appears on our web-site (http://www.komal.hu/eredmeny) and it is updated regularly. These data are not official, only for your information. The final results will appear in August on our Internet home page and in the September issue of the following academic year. The cca 10 top contestans are rewarded by a certificate in each category and this is going to be mailed to their schools, and their portraits, additionally, will be presented in the December issue and the Internet.

### Editing your solutions online by using the Electronic Workbook

The Electronic Workbook is part of our website to directly input or edit your solutions. You can modify your solutions anytime before the submission deadline.

Mathematical formulae can be entered by using the TeX system. If you are unfamiliar with TeX, we recommend you take our short TeX course.

If you prepare your solution on a computer, you can upload the complete file on our website. Please use a PDF format for compatibility.

• Each solution should be put in a different file.
• The upper left corner of each submission should contain in block capitals \begin{itemize}
• the type of the problem (A, B, C, K, M, G or P) in red,
• your school's name and location,
• A submission will be disqualified if a file contains solutions to more than one problem.

 C. 593. Robert 314 Smith, 9th grade Philadelphia High School, Boston e-mail: robb@phs.edu.us Denote the age of the captain by C, the age of the ship by S. When the age of the ship was C, the age of the captain was C-(S-C)=2C-S. When the ship was 2C-S ...

## Submission content and format

Please have a look at some sample solutions in our earlier issues or on our website. They indicate the required format and expected level of detail of your submissions.

### Presenting your solutions of theoretical problems in mathematics and physics

It is not enough to state the answer. Results with detailed explanations only will receive full credit. (Reference to standard school math is accepted without proof.)

From time to time it turns out that a proposed ''new'' problem (or its equivalent form or generalization) has already been solved and published elsewhere. We prefer that your problem solving skills improve rather than only use search engines. Hence no points will be awarded if your solution only contains a link or reference, or only shows that the new problem is a special case or corollary of a theorem published elsewhere; your submission should contain the detailed solution steps.

In any case, when you cite something by consulting articles, books or the internet, your submission should explicitly list all the references or sources you used.

A computer program alone is not considered to be a full solution of a mathematics problem. Similarly, it will not be accepted if you examine too many separate cases (e.g. 30 or more): typically one can significantly reduce the number of cases to be considered by thinking a bit more.