## Prime Numbers

Any positive integer can be uniquely represented as a product of prime numbers.

Any positive integer can be uniquely represented as a product of prime numbers.

30

minutes

Consider an MxN matrix that represents a population of viruses, which evolves as follows: a virus dies if it has less than 2 neighbors (because of boredom) or more than 3 (suffocated); a virus lives 3 generations at most, after which it dies of old age.

50

minutes

Write an algorithm that checks if a string is a palindrome.

20

minutes

Check if 2 words written on distinct lines rhyme when read from an input file.

30

minutes

Determine the smallest prime number that is on an even position in a given vector.

20

minutes

Which is the minimum number of squares you can split a given rectangle into?

10

minutes

A mechanical device is composed of 3 gears with 6, 4 and 10 cogs that are arranged as in the following figure.

30

minutes

A ray of light comes in from the upper left corner of an MxN sized window, with 45˚ angled edges. The ray is reflected when it reaches the first or the last line, or the first or last column respectively.

50

minutes

A spaceship has exited the Earth atmosphere and is travelling at a speed of S mph.

20

minutes

Given a string, check if the characters can be rearranged to form a palindromic sequence.

20

minutes

Given N threads with different lengths, connect the ropes into one thread.

40

minutes

Design and implement an algorithm that, given any non-zero integer n, computes the last digit of the decimal representation of n ^{n-1} ((n-1)th power of n).

20

minutes

A cell can replicate into 10 copies with only 4 cuts. It is possible to obtain 11 copies with the same number of 4 cuts!

20

minutes

A group of snails is planned to participate in a competition by climbing an N number of poles. Both the height of these poles and the speed of every snail are different.

40

minutes

Write an algorithm which is able to detect a series of 4 pattern types in a poem.

20

minutes

Given a number N, check if it is a Fibonacci number.

30

minutes

Determine if two numbers are consecutive terms of the Fibonacci sequence.

30

minutes

Determine all the prime numbers smaller than a given input value.

20

minutes

Determine the last 2 digits of the multiplication of 2 given numbers.

20

minutes

Determine the last digit of the 2^n number, where n is a given integer.

20

minutes

Write an algorithm that analyzes and decodes a string.

40

minutes

Given a string of words with lots of spaces between the words, remove all the unnecessary spaces.

20

minutes

Write a program that checks that an equation or a program is syntactically correct, meaning that all parentheses are balanced.

40

minutes

Write an algorithm to determine the longest repetition block.

40

minutes

You store all of your passwords for all your accounts in an encrypted file with a password.

40

minutes

Given a vector containing **n numbers**, find the missing number.

30

minutes

Find the numbers that are **repeating **in an array containing numbers from 1 to 1000.

30

minutes

Write an algorithm to check if a number is a power of 2.

20

minutes

Find **the second largest number** in a vector of n numbers.

20

minutes

Given a vector of n positive integers. Write an algorithm that determines whether there are any 2 equivalent elements in the vector.

20

minutes

Determine the **sum of the digits** that compose a given number.

20

minutes

Determine the check digit for a given number n.

20

minutes

Given 2 arrays of integer numbers, with m and n elements each, check if the maximum element from the first array is found in the second one.

20

minutes

Solve this challenge and find meaningful permutations.

20

minutes

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