February 2019 Problem

A right triangle has a hypotenuse with the length equal to 12 cm.

What is the greatest possible area of this triangle ?

Difficulty:

January 2019

Dear friends and visitors of the site.

Welcome to our first 2019 Problem:

Prove that 23 is a factor of 211 - 1 (without direct computation).

Difficulty:

December 2018

Dear friends and visitors of the site.

Try our December Problem.

 

Take numbers from 1 to 10000.

How many permutations of them exist such that neighbouring numbers differ at most by 1 ?

Difficulty:

November 2018 Problem

Dear friends and visitors of the site! Here is our November Problem:  

How many 13-digit numbers have an odd sum of digits?

Difficulty:

October 2018 Problem

Dear friends and visitors of our site! Welcome back to Poematics. here is our new Problem:

The front tyre of a racing bike is guaranteed for 9000 km and the rear tyre – for 3000 km.

How long can the bike run on these tyres ?

Waiting for your solutions.

Serge Hazanov

 
Difficulty:

June 2018 Problem

Welcome to June 2018 Problem:  

Does equation

2018(x+y) =xy

have integer solutions ?

No calculator !

 
Difficulty:

May 2018 Problem

Find for what values of natural n

the expression n- 7 is divisible by (n-1).

No Euclidean division!

April 2018 Problem

Dear friends and visitors of the site,

this is the April 1st problem:

Prove that for any prime number m > 3, m4 -1 is a multiple of 48.

Difficulty:

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.

Waiting for your solutions.

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: