## May 2017 Problem

A flooring is done with identical tiles in the form of a regular n-polygon.
What might be the value of n?

A flooring is done with identical tiles in the form of a regular n-polygon.
What might be the value of n?

A three digit number abc when muptiplied by 11n gives the number n n n n.
What is abc ?

Given a number consisting of 2016 digits 1. Prove that it is divisible by 101.

46 Republicans and Democrats are sitting at a round table.

More than a half of them are Republicans.

Is it certain that there are two Republicans facing each other?

x is a prime number greater than 3. Prove that 2x^{2}+190 is a multiple of 48.

Given c^{2} - c + 1 = 0.
Calculate c^{5036} + 1/ c^{5036}

In a dancing school, some students do not have a permanent dancing partner : this concerns 2/7 of the girls and ¼ of the boys. What percentage of the students has a permanent dancing partner ?

Jack picks at random three integers between 7 and 11 (inclusive). Mary picks an integer from 24 to 33 (inclusive). What is the probability that Mary’s number is less than the sum of Jack’s numbers ?

A stock of 650 tons of wood has a 16% moisture content. A month later, as a result of drying, the moisture content reduced to 9 %. What is the new weight of the stock?

A postman has to distribute 10 identical postcards to 5 mailboxes. By how many ways can he do this ?

Ten students are standing in line. How many possibilities do we have to select four out of them, so that no two were neighbors in this line?

One year, August has 4 Wednesdays and 4 Sundays.

How many Mondays does this year have?