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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.

Waiting for your solutions.

Serge Hazanov

 

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 ?

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

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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

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

Which factory has a greater number of machines ?

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 2x²+190 is a multiple of 48.

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