Assessment-quiz, level II

Do not use anything but your knowledge, pen and paper. This quiz has only one purpose: give you a suggestion on which course to do.

Just in case, there**might be several correct answers** to the question. You **need to select all of them to get the question right**!

Just in case, there

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If there is a board of size 11 by 11 that is coloured black and white like in chessboard colouring, how many black cells can it have?

It cannot happen as there is an odd number of cells...

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Suppose that *n*+1 balls are distributed between *n* boxes. Which of the following is a correct thing to say? Select all that apply as always.

No, pigeonhole principle is very much applicable here :)

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What are the answers to the two questions below:

1) How many possible remainders are there modulo 100?

2) Suppose you multiply 2 by itself 100 times. What remainder modulo 7 will you get?

1) How many possible remainders are there modulo 100?

2) Suppose you multiply 2 by itself 100 times. What remainder modulo 7 will you get?

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Ana, Bob and Cara take turns removing stones from a pile of 30 stones. Ana goes first and can remove 1, 2 or 3 stones from the pile. Bob goes next and can remove 0, 1 or 2 stones from the pile. Cara goes next and can remove 1, 2 or 3 stones from the pile. Then Ana removes 1, 2 or 3 stones again, then Bob removes 0, 1 or 2 stones and so on... Player who cannot make a move (i.e all the stones are gone), loses. Which of the following statements are true? As always: select all that apply!

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Can the degrees of a graph be:

a) 1, 2, 3, 3, 3, 3, 3;

b) 2, 2, 3, 3, 5, 6, 7, 7, 8;

c) 0, 2, 3, 3, 4, 5, 6, 7, 8?

(Here the graph stands for something with vertices and edges)

a) 1, 2, 3, 3, 3, 3, 3;

b) 2, 2, 3, 3, 5, 6, 7, 7, 8;

c) 0, 2, 3, 3, 4, 5, 6, 7, 8?

(Here the graph stands for something with vertices and edges)

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What are the correct things to say about invariants and monovariants?

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If you have some experience with olympiad-style maths, then you should go for the course "Basic Olympiad Ideas". Click here. Otherwise go for "Constructions, proofs and a few nice ideas".

Do not worry about the result, it is all fine. We just want to find you a suitable course. So, now it all depends on how much experience you already have with extra-curriculum maths. If almost none, then go for one of the For-beginners courses, namely "Constructions, proofs and a few nice ideas". If you do have some experience, then please go for "Basic Olympiad Ideas", i.e the first course from "Olympiad Maths Training" courses.

Please have a look at the course "Basic Olympiad Ideas". Click here.

The results suggest that you should do the very first course from olympiad maths training, namely "Basic Olympiad Ideas" course.

Please have a look at the course "Basic Olympiad Ideas". Click here.

The results suggest that you should do the very first course from olympiad maths training, namely "Basic Olympiad Ideas" course.

Please have a look at the courses "Basic Olympiad Ideas" or "Two in one: Maths for IT and discrete maths". One of them should do for you. Click here.

The results suggest that you should either do one of the following:

- very first course from olympiad maths training, namely "Basic Olympiad Ideas" course
- or the second course from olympiad maths training, namely "Two in one: Maths for IT and discrete maths"

Let's move on to the harder quiz! Click here.

You got all of the questions but one right, congratulations! This means that we should move on to the harder quiz now... We are not far from finally giving you a course suggestion :)

Let's move on to the harder quiz! Click here.

You got all of the questions right, congratulations! This means that we should move on to the harder quiz now... We are not far from finally giving you a course suggestion :)