Assessment-quiz

level III

level III

Do not use anything but your knowledge, pen and paper. This quiz has only one purpose: to 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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Which of the following can be counted as a correct solution to the following problem: What is the biggest possible number of kings can be placed on a chessboard in such a way that none of them attack each other?" Feel free to search for how the chess king moves if you do not know how.

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How many 7-digits numbers are there such that its digits are in strictly decreasing order? (e.g a number 9764310 is one of such numbers)

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There is a graph *G* on 100 vertices such that it is possible to delete one of its edges to get two connected components, each of which is a tree. How many edges can *G* have?

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Let *A* be the number of integers less than 1000000 such that the sum of their digits is 18, and let *B* the number of integers less than 1000000 such that the sum of their digits is 36. What is the value of (*A* - *B*)?

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Which of the following statements are correct? Don't forget to select all that apply!

Nope, S must be equal to 26

The parity of 1 + 4 + 9 + 16 + 25 + .... + 10000 is the same as the parity of 1 + 2 + 3 + 4 + ... + 100 = 5050 which is an even number

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How many zeros does the number 100! end with?

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Which of the statements on the picture are true?

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What is the value of the expression on the picture?

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Initially the number 7^2022 (=7 x 7 x 7 x 7 x ... x 7 (2022) times) is stored in the memory of a computer. Each minute the number in the memory is replaced by the sum of its digits. After 30 minutes, which number will the computer have in its memory?

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Among the statements below select those that are true:

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Please have a look at "Two in one: Maths for IT and discrete maths" course. It seems like the best fit for you. Click here.

Do not worry about the result, it is all fine. We just want to find you a suitable course. The courses #3A,#3B and #3C seem to be too hard for you, therefore we suggest you look at "Two in one: Maths for IT and discrete maths" (course #3). If you did not do the previous quiz well enough, then actually you might even need to do "Basic Olympiad Ideas" course. Check the content of the courses and make your final decision.

Do not worry about the result, it is all fine. We just want to find you a suitable course. The courses #3A,#3B and #3C seem to be too hard for you, therefore we suggest you look at "Two in one: Maths for IT and discrete maths". This is the course#2.

Please have a look at courses #3A, #3B, #3C. We recommend you do courses #3A and #3C at least. As for #3B ("Diving in Geometry") -- take it if you have less than a year of experience with geometry.

Click here to continue.

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The results suggest that you should focus on the courses #3A, #3B, #3C. Since you answered about half of this quiz right, the courses #3A and #3C should be useful for you. As for the course #3B -- it depends on your experience. That course is meant for people interested in doing Geometry but who have little experience with it. Anyway, you can start with #3A.

Please have a look at courses #3A, #3B, #3C. Some of these courses will definitely be useful for you. Click here to continue.

If you mostly failed the first half of this quiz, definitely do the course #3A. Otherwise, definitely do the course #3C. As for #3B ("Diving in Geometry") -- it is for you to decide to take it or not. It depends on your experience. That course is meant for people interested in doing Geometry but who have little experience with it.

If you mostly struggled with the first half of this quiz, do course #3A. Otherwise, do course #3C. As for #3B ("Diving in Geometry") -- it is for you to decide whether or not to take it. It depends on your experience. #3B is meant for people interested in doing Geometry but who have relatively little experience with it.

You should have a look at "Ol-maths for seniors" courses. Click here to continue.

Your results suggest you have a look at the courses #4, #5, #6. Check the content and decide which course to take. You should be able to feel comfortable doing the course #4, but note that it is time-consuming. However, you might need to do the more difficult course than #4.