CyberChallenge.IT 2024

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CyberChallenge.IT 2024 - Test

Demo of the test for the 2024 edition of CyberChallenge.IT

Additional material for other tests is available at the link https://cyberchallenge.it/training

Note: the expression pow(x, y) indicates x to the power of y.

Question 1

Four cards are on a table. On each card a character is written, respectively M, I, 9, 7. We also know that every card has a letter on one side, and a positive integer on the other one. Francesco says “If a card has an even number on one side, then it has a consonant on the other side”. Paolo disproves Francesco’s sentence by turning over a card.

Which character is on the card turned over by Paolo?

1 point

Clear selection

Question 2

Alice and Bob play a game. Alice chooses N distinct real numbers between 0 and 1000 (inclusive). Bob lists down the absolute difference of all possible pairs (a, b) such that a ̸ = b. Bob wishes to find 10 distinct numbers on his list not exceeding 100.

What is the least value of N such that Bob can always accomplish this?

1 point

101

501

There is no such N

201

Clear selection

Question 3

A TeamItaly class has 42 people. All the 42 people are either tutors or students. The first tutor gives a challenge to 23 students, the second to 24 students, the third to 25 students and so on until the last tutor, which gives a challenge to all the students.

How many students are there in the class?

1 point

Clear selection

Question 4

1000 students participated in the admission test for CyberChallenge.IT. Each of the 1000 participants scored an integer number of points between 0 and 15 (included).

Given that the average score among all of them is 6, what is the maximum number of participants that could have scored exactly 15 points?

1 point

500

250

400

Clear selection

Question 5

Alice and Bob both have a secret number. They don’t tell anyone, not even each other. Bob’s number is between 1 and 100 (included) and Alice’s between 1 and 20 (included) and they know that their numbers are different. Yesterday I heard a conversation between them:

- Bob: “My number has (bzzzz) divisors.”
- Alice: “Now I know your number!”

- Bob: “Interesting, now I know your number too!”
Unfortunately, I couldn’t hear Bob’s first statement completely due to an interference!

What is Alice’s number?

1 point

Clear selection

Question 6

Four hackers are interviewed. We know that all of them are either black-hat or white-hat. Black-hat hackers always lie, while white-hat hackers always tell the truth:
- Hacker One said that exactly one of the four hackers is a black-hat.
- Hacker Two said exactly two of the four hackers are black-hat.
- Hacker Three said that exactly three of the four hackers are black-hat.
- Hacker Four said that exactly four of the four hackers are black-hat.

How many of the hackers are black-hat?

1 point

Clear selection

Question 7

A special knight is moving on a board. The board is 15 × 15 and the knight can move 1 square in one direction and 3 squares in a perpendicular one (which is a diagonal of a 1 × 4 rectangle instead of a 1 × 3 like in chess).

What is the maximum number of squares that a knight can reach within the board, among all the possible starting positions?

1 point

113

163

225

112

Clear selection

Question 8

10 people are sitting in a circle. They are sitting one behind the other. Each person picks either rock, paper, or scissors, with 2 people picking rock, 4 people picking paper, and 4 picking scissors. A move consists of an operation of one of the following three forms:

- If a person picking rock sits behind a person picking scissors, they swap places.
- If a person picking paper sits behind a person picking rock, they swap places.
- If a person picking scissors sits behind a person picking paper, they swap places.

What is the maximum number of moves that can be performed, over all possible initial configurations?

1 point

Clear selection

Question 9

Lorenzo is writing numbers on a board. He starts writing the number 152. For 7 times he takes a random number x between {pow(2, 0), pow(2, 1), pow(2, 2), . . . , pow(2, 7)} and substitutes the number n on the board with n ⊕ x, where ⊕ is the bitwise xor operator.

Note: The bitwise XOR, denoted with ⊕, is the bit-by-bit operation defined by the following truth table: 0 ⊕ 0 = 0, 1 ⊕ 0 = 1, 0 ⊕ 1 = 1, 1 ⊕ 1 = 0.

What is the probability that in the end the number written on the board is 255?

1 point

735 / pow(2, 17)

405 / pow(2, 17)

175 / pow(2, 17)

Clear selection

Question 10

There are 60 knights and knaves sitting on a round table, evenly distributed. Knaves always lie, while knights always tell the truth. Each person says ”The two people next to me and the one in front of me are all knaves”.

How many knights are there at most?

1 point

Clear selection

Question 11

Consider the following function, where x**n is the power function pow(x, n).

For how many integer values of n the function f(n) returns 3?

1 point

99999999

999900000000

99000000

999999000000

Clear selection

Question 12

Consider the following functions, where ord is the function that maps A to 0, B to 1 and so on, while chr is its inverse function.

Assuming that there is exactly one error and that the encryption function is correct, which line of code is incorrect?

1 point

Clear selection

Question 13

Consider the following function:

What is f(n) computing?

1 point

pow(2, n)

pow(2, n) -1

2*n

2*n-1

Clear selection

Question 14

Consider the following functions:

What is the value of f(1234567890)?

1 point

[0, 0, 0, 1, 1, 1, 0, 1, 1, 1]

[1, 0, 0, 0, 1, 0, 0, 0, 0, 0]

[0, 0, 0, 0, 0, 1, 1, 1, 0, 0]

[0, 0, 0, 0, 1, 0, 0, 0, 1, 0]

Clear selection

Question 15

Consider the following function:

What does f(l) compute?

1 point

Average of the elements of l

Sum of the elements of l

Product of the elements of l

Maximum of the elements of l

Clear selection

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