# Problem of the Month

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## February 2018 Problem

Dear Friends and Visitors of the site!

Try our February 2018 Problem:

Given a set of 11 natural numbers, such that the sum of any ten of them is a multiple of 7.

Show that all these numbers are multiples of 7.

Serge Hazanov

Difficulty:

## January 2018 Problem

Dear friends and visitors of the site,

Welcome to a New Year and new problems!

Here is the January Problem:

Vertices A and C of a solid triangle ABC (with a right angle B)

are sliding along the sides of another right angle.

What is the locus of the vertex B ?

Difficulty:

## November 2017 Problem

111 x 111 = 110001

Is this possible?

Difficulty:

## October 2017 Problem

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 ?

Difficulty:

## September 2017 Problem

Welcome back to the site POEMATICS!

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

Serge Hazanov

___________________________________________________

What number is greater

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

No calculator!

Difficulty:

## June 2017 Problem

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

n2 +10n -14 articles. Each machine produced the same number of articles.

Which factory has a greater number of machines ?
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## 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?
Difficulty:

## April 2017 Problem

A three digit number abc when muptiplied by 11n gives the number      n n n n. What is abc ?
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## March 2017 Problem

Given a number consisting of 2016 digits 1. Prove that it is divisible by 101.
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## February 2017 Problem

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?

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## January 2017 Problem

x is a prime number greater than 3. Prove that 2x2+190 is a multiple of 48.
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## December 2016 Problem

Given c2 - c + 1 = 0. Calculate c5036 + 1/ c5036
Difficulty: