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## June 2019 Problem

In US, when we write a date, month comes before the day.

In Europe, the day comes before the month.

How many dates could be misread during one year?

Difficulty:

## May 2019 Problem

Here is our new Problem:

In an arithmetic sequence, u7+u8+u9 > 0 and u7+u10 < 0.

For what value of n, Sn is maximum ?

## April 2019 Problem

PQR is a right triangle. It is free to move so that P is always on the x-axis and R is on the y-axis. Show that the point Q (right angle) always lies on a straight line passing through the origin.

## March 2019 Problem

Try our March Problem:

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

Difficulty:

## 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 ?

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: