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 ?
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
n2 +10n -14 articles. Each machine produced the same number of articles.
Which factory has a greater number of machines ?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?
