# Problem of the Month

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## 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

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What number is greater

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

No calculator!

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## 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?
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## 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
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## November 2016 Problem

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 ?
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## October 2016 Problem

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 ?
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## September 2016 Problem

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?
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## June 2016 Problem

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