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.
	

	import datetime
	import math

	def MainProc1(y):
		dtStart = datetime.datetime.now()

		print ("Started at: ", dtStart)

		print ("y = ", y, " the power, log(y), is ", math.ceil(math.log(y, 10)))

		nCounter = 0

		bSolution = False

		for j in range (y, y * 10, 1):
			nTemp = j * (j - 1)

			nTemp1 = math.floor(j/math.sqrt(2))

			for i in range (nTemp1, (nTemp1 * 10), 1):
				nTemp2 = 2 * i * (i - 1)

				nCounter += 1

				if nTemp == nTemp2 :
					print(j, i, nTemp2, nTemp)
					print("Solution !!")
					bSolution = True
					break
				elif nTemp < nTemp2 :
					break

			if bSolution == True:
				break

		dtEnd = datetime.datetime.now()

		print("The number of iterations are ", nCounter)

		print("Start time is ", dtStart.time(), " End time is ", dtEnd.time())
		print ("Time span is %s"%(dtEnd-dtStart))

		if bSolution == False :
			print("No solutions are found.")
		else :
			print("*** The solution is found. ***", j, i)

	#################
	MainProc1(math.floor(math.pow(10, 12)))