Mobile Technologies Olympiad. Team Tour

Hello, Habravchane! I would like to dedicate this article to interesting and fun tasks in computer science and mathematics.

A bit of history

I am a 4th year student of the Faculty of Mathematics. I will tell you - I am very proud that I will be both a mathematician and a programmer. As my dean-programmer told me: “Without mathematics, this is a programmer with a ceiling.” So, every year for 7 years my university, or rather the faculty holds an open Olympiad in mathematics and computer science, for which he thanks a lot. Everyone can take part in the competition: from schoolchildren to students (in general, the main thing is to assemble a team from at least one of their neighbors).


The Olympiad consists of four rounds:
1. Team tour (tasks, both in mathematics and computer science)
2. Personal math tour
3. Personal Informatics Tour
4. Competition game strategies
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I would like to share with you interesting tasks that our teachers have come up with for us throughout the school year. Every year our Olympiad has a theme to which it is dedicated. This year the competition was devoted to mobile technologies .

I think that I will simply read out the conditions of some tasks and comment on them a bit, and we discuss the solutions in the comments, but how I don’t want to write their solutions.

So let's get started.

Task number 1

The problem is cool. As I found out, it is quite popular in the Internet.

Find the superfluous (2 points)
I'm on the exam on computer science. Task C3:
HARP, BANT, VOLKODAV, YYYY, SAUCH. Of these five “words,” four constitute a pattern, and one is superfluous. Find the extra word.
Help a friend !!!
Received: 10:53:45 Today
From: David

Problem number 2

A good math problem for the equation in integers.

Bonus package “20 SMS per day” (3 points)
The telephone company offered its customers a new bonus system in the “20 SMS per day” package. The package takes into account incoming and outgoing SMS-messages. For each outgoing message, 8 bonuses are charged, and for each incoming message, 5 bonuses are deducted. George connected himself to this package, and by the end of the day he had 13 bonuses on his account. How many SMS-messages George received and sent on this day.

Task number 3

Attention lovers of mathematics, very good, but not an easy task. Many Olympiad participants solved this problem even programmatically, although a mathematical solution is required on the face. The solution in the form of a program was, of course, evaluated at a lower number of points than a mathematical solution.
Perhaps I will give a solution to this problem. Just try to solve first, and then watch.

Checksum (7 points)
A checksum is a value calculated from a set of data by applying a specific algorithm and used to check the integrity of data during transmission or storage. The network signal is transmitted as a sequence of real numbers a ₀ , a ₁ , ..., a _n , ... satisfying the conditions a ₀ = 3, (3-a _{n + 1} ) (6 + a _n ) = 18 for any n ϵ N. The checksum for this sequence is calculated by the formula . Find the checksum value.

Task number 4

Here I really like this task. Here, even if you know the correct drawing, it is difficult to draw it. In general, the task is cool. As it turned out, this problem has several solutions. I will give the solution of our team, but don’t watch it, until you solve the problem yourself :)

Gift to the city (6 points)
The main components of a cellular network are cellular phones and base stations, which are usually located on the roofs of buildings and towers. Being on, the cell phone listens to the air, finding the signal of the base station. After that, the phone sends the station its unique identification code. Telephone and station support constant radio contact, periodically exchanging packages.
The city authorities, concerned about the appearance of the city, demanded that telephone companies streamline the placement of base stations. By City Day, telephone companies made a gift to the city - they put into operation a new base station system. The system includes 16 stations, with original lighting. The BSs are located in such a way that at night, from the planes flying over the city, there is a pattern formed by 12 rows, with 4 stations in each row. Draw a picture that opens with a bird's-eye view (without taking into account the radius of the stations).

Problem number 5

The units seemed to have coped with this simple task. Try it and you solve it. Immediately she says with a poplite :)

Balance Disputes (1 point)
Fatima told Zalina that her husband and son have equal amounts on the personal account balance (rubles without kopecks), Zalina was surprised to see that her husband and son also had equal amounts on the balance and also rubles without kopecks. And when they calculated the total amount of all balances, it was equal to 273 rubles. Can this be and what women understand in mathematics?

Problem number 6

Pretty simple task. But still, to solve it, you need to do a complete search, and with the cut-offs. The maximum score was given for the fastest solution. In general, at each Olympiad we have a task dedicated to complete enumeration, this is a kind of tradition.

Superfood (10 points)
So since ancient times it has become a tradition, if humanity can do something, then it certainly sets records in this. We learned how to produce mobile phones, which means that we must choose the very-most. While in the category “The Most Expensive”, the yellow jersey of the leader is held by the Piece Unique gadget from the Swiss company Goldvish. The device is covered with diamonds, the total mass of which is about 120 carats. Needless to say that the case is made of gold and platinum. With all its magnificence, the telephone also rings, receives messages and plays melodies. Of course, such a work of art is not for industrial production. It is made all in one copy. And now belongs to the Russian.
Our other compatriot ordered a telephone in the form of a cigar, along which the dialer buttons are arranged in a row, and he also demanded that the sum of the digits of the two adjacent buttons be divided either by 5, or by 7, or by 13, in memory of his math teacher . Is it possible to perform the quirks of the oligarch? And how many such phones can be made (if at all possible) for its numerous protection, but with the condition that the order of buttons on all phones should not be repeated?

Task number 7

Come on, solve this popular problem in America. I think many of you know this problem. Of course, the condition of our task composers was embellished ...

Catch up and overtake (2 points)
The biggest mobile phone ad was dedicated to Pantech. It appeared on June 1, 2005 on the walls of the exhibition hall, in which Sotheby's auction takes place regularly. The advertisers spent about one million pounds sterling on its placement and the advertising banner area was 29 m ² . And the official profit from it was about three times more than the cost.
And in St. Petersburg for the upcoming holiday "Scarlet Sails" one telephone company ordered a sail in the form of a right triangle with a hypotenuse of 10 meters and a height of 6 meters to it. Find the area of ​​this triangle. Maybe this will be a record too?

Problem number 8

HERE IT IS A OLYMPIC STAR. This task, on the solution of which the Olympiad participants spent the most time. And she is the easiest of all. By the way, this task is a real story from the life of one of the compilers of the Olympiad.

It's never too late to learn (1 point)
Dad finally began to master sending sms. And on the eve of March 8, my older sister received from him the following message: “Odevatee! Describe the accident "(it seems that the Pope had nothing to hope for intellectual input - mode T9). What did he mean by that? Photo of my father's phone attached

Problem number 9

It is also an interesting, but rather unpretentious task for combinatorics.

Short number (3 points)

A content provider is a company that collects and provides information to customers and organizations.
In mobile communications, a company providing mobile content (mobile ringtones, pictures, real tones, polyphony, Java games, mobile themes, 3gp videos, video tones, ringtones, video calls, Java books, logos, and much more). SMS services are often used to provide services.
The content provider to provide services to cellular subscribers wants to buy short four-digit numbers starting with 5 and consisting of 0, 2, 5, 8, in which all numbers except 5 are found once, and 5 is not more than two time. How many different numbers can a content provider purchase?

Problem number 10

Good geometric problem. Many have coped with this task.

Rational offer (2 points)
Chermen looked at the drawing of the Azamat's “Bee Network” project and began to prove to him that, in order to increase the network capacity, it is possible to put three additional stations into each cell. In addition, each "cell" is divided into three equal pentagons. Azamat did not believe him and demanded to cut his drawing (hexagon) into three equal pentagons.

Conclusion

I think that under the terms of the tasks you understood that our Olympiad is not so serious. The main goal of the Olympiad is to have a good time plus to interest schoolchildren and students in mathematics and computer science.

By the way, lastly I want to say that the prizes of the Olympiad are quite valuable.