## March 2019 Problem

Try our March Problem:

How many ways are there to roll a sum of 9 with 4 standard dice?

## February 2019 Problem

What is the greatest possible area of this triangle ?

## January 2019

Dear friends and visitors of the site.

Welcome to our first 2019 Problem:

Prove that 23 is a factor of 2^{11} - 1 (without direct computation).

## 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 ?

## November 2018 Problem

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

## October 2018 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

## June 2018 Problem

Does equation

2018(x+y) =xy

have integer solutions ?

No calculator !

## May 2018 Problem

Find for what values of natural n

the expression n^{3 }- 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, m^{4} -1 is a multiple of 48.

## 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

## 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 ?