Задачи по программированию на шахматной доске. Chessboard programming problems. And other problems.

• Knight's tour
• 8 queens.
• Project Euler problem 100 elementary mathematics solution.

Arranged probability

	If a box contains twenty-one coloured discs, composed of fifteen blue discs and six red discs, and two discs were taken at random, 
	it can be seen that the probability of taking two blue discs, P(BB) = (15/21)×(14/20) = 1/2.

	The next such arrangement, for which there is exactly 50% chance of taking two blue discs at random, is a box containing 
	eighty-five blue discs and thirty-five red discs.

	By finding the first arrangement to contain over 1012 = 1,000,000,000,000 discs in total, determine 
	the number of blue discs that the box would contain.
	

	#define _CRT_SECURE_NO_WARNINGS

	#include <iostream>
	#include <math.h>
	#include <ctime>
	#include <string>

	int main(int argc, char* argv[])
	{
		const clock_t begin_time = clock();
		
		long long y = (long long) pow(10, std::stoi(argv[1]));

		std::cout << "Calculation for " << y << std::endl;

		long long nCounter = 0;

		bool bSolution = false;

		long double sqrt2 = sqrt(2);

		for (long long j = y; j < y * 10; j++)
		{
			long long nTemp = j * (j - 1);

			long long nTemp1 = (long long) floor(j / sqrt2);

			for (long long i = nTemp1; i < nTemp1 * 10; i++)
			{
				long long nTemp2 = 2 * i * (i - 1);

				nCounter++;

				if (nTemp == nTemp2)
				{
					std::cout << "Solution is found for x=" << i << " and y=" << j << std::endl;
					bSolution = true;
					break;
				}
				else if (nTemp < nTemp2)
				{
					break;
				}
			}

			if (bSolution) break;
		}

		if (!bSolution) std::cout << "No solution was found." << std::endl;

		float dtDifference = float(clock() - begin_time) / CLOCKS_PER_SEC;

		std::cout << "The number of iterations is " << nCounter << std::endl;
		std::cout << "Execution time is " << dtDifference << " seconds." << std::endl;

		return 0;
	}