CyberChallenge.IT 2021

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CyberChallenge.IT 2021 - Test

Demo of the test for the 2021 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

Alice writes down 5 consecutive positive integer, then it takes 4 of them and sum them up, obtaining 217.

What is the sum of the 5 initial integers?

1 point

272

270

271

1024

Clear selection

Question 2

Bob has 120 cards. He decides to give all of them to his 3 children of 4, 7, 9 years.

He gives each child a number that is some positive integer constant c (that is the same for every child) multiplied by his age.

How many cards will receive the oldest child?

1 point

Clear selection

Question 3

What is the smallest positive integer that can be written as the product of 6 different integers (except 0)?

1 point

1440

720

Clear selection

Question 4

Three people are in a room with 4 walls and 4 doors.

The first one says: “No doors are on the north wall”,

the second one: “All the doors are on the south wall”,

the third one: “On every wall there is at most one door”.

Knowing that every person may have lied, what can we say?

1 point

The third one is telling the truth

Everyone is lying

At least one of them is lying

Nothing

Clear selection

Question 5

On a island there are 3 kind of people:

1. truth-tellers, that always say the truth,

2. liars, that always lie,

3. impostors, that can both tell the truth or lie, but if they are not the first to speak they lie if and only if the one that spoke immediatly before them told the truth.

Alice, Bob and Carol tell the following sentences:

- Alice: There is at least a truth-teller among us

- Bob: I am a liar

- Carol: There are no impostors among us

Which of the following is true?

1 point

There are at least two liars

Among the three there is exactly one truth-teller, one liar and one impostor

For at least two of them we don’t have enough information to determine their type

There are at least two truth-tellers

Clear selection

Question 6

Let x and y be two positive integers strictly greater than 1. You know that the product x * y divides 100, that is, the fraction 100/(x * y) is an integer.

What can you say about x and y?

1 point

x is even or multiple of 5 (or both)

At least one of them is even

If x is even then y is a multiple of 5

There are at least 2 correct sentences in the other 3 answers

Clear selection

Question 7

Carol has a bunch of 8 indistinguishable keys on a ring. She wants to color them using n colors in a way such that she can recognize exactly each key.

What is the smallest possible value of n?

1 point

Clear selection

Question 8

In a football championship 20 teams play against each other team exactly one time.

What is the maximum number of teams that can end up with 16 wins or more?

1 point

Clear selection

Question 9

Let Y be a year in the 21st century.

Knowing that the last day of year Y is a Tuesday, the first day of the year Y + 2 is a Friday, on what day will be the last Sunday of January in the year Y + 3?

1 point

Clear selection

Question 10

100 people are in a row, each one being a truth-teller, that always tells the truth, or a liar, that always lies. Each of them says: “Among the people not in front of me, including myself, more than one half are truth-tellers”.

How many possible configurations of truth-teller/liars are possible?

1 point

100

101

102

200

Clear selection

Question 11

Consider the following functions:

What is the result of f(1000000000000)?

1 point

[2, 1, 4, 3, 6, 5, 0]

[6, 3, 0, 5, 2, 1, 4]

[0, 5, 2, 1, 4, 3, 6]

[2, 3, 4, 5, 6, 1, 0]

Clear selection

Question 12

Consider the following function:

What is the results of f(96)?

1 point

-1

Clear selection

Question 13

Consider the following function:

What do you have to put in place of $x, $y and $z to makes f(2, 0, 70), f(3, 20, 70) and f(3, 40, 80) true?

1 point

or, and, or

and, and, and

and, and, or

and, or, and

Clear selection

Question 14

Consider the expression pow(x,15).

Which is the minimum number of multiplications necessary to calculate its value?

1 point

Clear selection

Question 15

Consider the following functions:

How many times the functions are called with x(30000)?

1 point

15000

15001

12001

12000

Clear selection

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