## November 2017 Problem

111 x 111 = 110001

Is this possible?

111 x 111 = 110001

Is this possible?

What factor should be crossed out of the product

1! х 2! х 3! х ............х 16! ,

to make the remaining expression a perfect square ?

Welcome back to the site POEMATICS!

The September Problem is a warming up. It is so easy, that even I can solve it.

Go ahead!

Serge Hazanov

___________________________________________________What number is greater

sqrt(109) - sqrt(106) or sqrt (104) - sqrt (101) ?

No calculator!

n machines of factory A and 13 machines of factory B has produced together

n^{2} +10n -14 articles. Each machine produced the same number of articles.

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 ?