Tasks EGE on computer science

In Russia, the practice of evaluating school graduates using the Unified State Exam (USE) is becoming increasingly common.

For several years in experiments across the country passed the exam in a variety of subjects. This year, for the first time, the Unified State Exam in computer science will be given in bulk.

What is inside?

The unified state examination takes 4 hours, contains quite a lot of questions (in this version 32) and requires a decent level of knowledge for passing it to a high rating.
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Before the story itself about the tasks I want to share two thoughts.
1. The USE has drawbacks, but the main positive point is that an almost objective assessment of the student’s real knowledge is introduced. Previously, within the school, the teacher / director had the opportunity to draw any marks with almost no responsibility for the real level of knowledge. Cases of non-admission to universities were rare (well, in the extreme case - another university / faculty) and few people worried. Now it’s scary for a teacher to put 5 and run into the USE, which was passed by 3. This drastically changed the very atmosphere of preparation.
However, there are drawbacks. Example: according to many experts, schools almost stopped teaching geometry, since in the USE it is represented by only three tasks.
2. The main goal of the exam is to rank students according to their level of knowledge. Additional - put a mark on the school 4-point system.
For the ranking of a large number of students it is NOT IMPORTANT what level the exam will average. It is necessary only that the weakest decide at least something, and the strongest decide almost everything. Suppose the exam is too complicated, and the vast majority will solve only half of the tasks. Well, the best 20% of them will be able to get into the university to the relevant department.
The unified state examination does not so much value (absolute score) as it ranks (relative score).

Tasks
Below, with my comments, are some approximate tasks proposed by the Federal Institute for Educational Measurement (FIPI).
Link to the full version of the tasks of 2009: fipi.ru/binaries/731/infZIP%20-%20WinRAR.zip and 2008: fipi.ru/binaries/518/inform.rar (there mime-type is incorrectly specified, save as rar and open).

In my opinion, the tasks are complex (I remind you, on average, 7.5 minutes are allocated for a task). I propose to evaluate and you.

I. 119 athletes participate in cycling race. A special device registers the passage of each intermediate finish by recording its number using the minimum possible number of bits that are the same for each athlete. What is the information volume of the message recorded by the device after 70 cyclists passed the intermediate finish?
1) 70 bits 2) 70 bytes 3) 490 bits 4) 119 bytes

It requires an understanding of the information capacity of a sequence of several bits, the ability to operate with powers of two, just an understanding of the essence of the term “information” and the principles of its measurement.
The average student, I think, will solve it only if he studied computer science beyond the school minimum.

Ii. The light board consists of light bulbs. Each light can be in one of three states (“on”, “off” or “flashing.”) What is the smallest number of light bulbs that must be on the board in order to use it to transmit 18 different signals?

It requires an understanding of the existence of number systems with any bases and the principles of coding such signals. In this case, the ternary system.
The average student, I think, will not solve it. It is possible to solve and search all the options and count them, but this is a long time and there is a risk of being mistaken.

Iii. What is the largest integer X for which the statement is true
(50 <X • X) → (50> (X + 1) • (X + 1))?

It requires knowledge of logical operations (functions of the algebra of logic) and good analytical skills (check how much time you will decide for yourself and allow any schoolchild or junior student).

Iv. Enter a comma in ascending order all bases of the number systems in which the record of the number 23 ends with 2.

The task at first glance is not particularly difficult, but it has to be solved either by brute force (that is, to make many translations into number systems such as sevenfold or eleven-decimal, which is extremely tedious), or develop a system and understand that
23 mod X = 2, where mod is the remainder of division, and X is the answer.
Guess from my friends IT shnik far from all.

V. The class teacher complained to the director that he had a company of 3 students in his class, one of whom always tells the truth, the other always lies, and the third tells through the lie, then the truth. The director knows that their name is Kolya, Sasha and Misha, but he does not know which of them is truthful and who is not. Once all three of them skipped the astronomy lesson. The director knows that never before have any of them skipped astronomy. He called all three into the office and talked to the boys. Kohl said: “I always skip astronomy. Do not believe what Sasha will say. ” Sasha said: "This was my first absenteeism of this subject." Misha said: “Everything that Kolya says is true.” The director understood who of them who. Arrange the first letters of the boys' names in the order: “always speaks the truth”, “always lies”, “speaks the truth through time”. (Example: if the names of the boys were Roma, Tolya and Vasya, the answer could be: PTB)

Reminds tasks on sharpness, isn't it?
It can be solved with the help of a logical apparatus, which is obviously unknown to schoolchildren (for example, propositional / predicate calculus) or logic.
I, frankly, do not understand what relation this task has to computer science.

Vi. Two players play the next game. On the coordinate plane is a chip. Players take turns. At the beginning of the game, the chip is at the point with coordinates (5.2). A move is that the player moves a chip from a point with coordinates (x, y) to one of three points: either to a point with coordinates (x + 3, y), or to a point with coordinates (x, y + 3), or to a point with coordinates (x, y + 4). The player wins, after the course of which the distance in a straight line from the chip to the point with coordinates (0,0) is not less than 13 units. Who wins in the error-free play of both players — the player making the first move, or the player making the second move? What should be the first move of the winning player? Justify the answer.

The task is interesting. I suggest you solve it. In the decisions of the authors it is proposed to solve it by enumerating all possible moves of each player.
Again, the question is, what does this difficult task have to do with computer science? Checking logical thinking?

VII.

It’s a paradox, but many don’t understand what the program does and consider all 2x2 squares that do not contain lines.

Viii.

The task requires care and experience. For example, not everyone can see that there are 2 errors, both of which must be corrected.

These approximate assignments are made public and are actively studied by all who will have to pass the EGE.
Many computer science teachers are shocked by the assignments. Let me remind you that now in many schools they are studying Word, Paint, typing texts or listening to stories about Charles Bebbidge’s car and Byron’s first daughter programmer. All this is good and useful, but does not help passing this exam.

Many schoolchildren to whom to take this exam, rushed to look for a tutor.
But in my opinion, an average savvy student who taught computer science just like a school subject (I taught geography so much that I didn’t even imagine a map of Europe to grade 11), it’s almost impossible to prepare for the hot 3 months to pass this decent exam. evaluation.

Your opinion, IT shniki? How many tasks would you decide on an average of 7.5 minutes each?