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?
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?
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 ?
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).
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
Dear friends and visitors of the site!
Here is our November Problem:
How many 13-digit numbers have an odd sum of digits?
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
June 2018 Problem
Welcome to 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 n3 - 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.
