abachler, I don't even start college until August and won't be taking an A.I. class for at least a year after that. You jumping to conclusions is slightly insulting and annoying. You got your first solution from 64*63*62*61*60*59*58*57. However, any fool would write the loops like this:
Code:
for (Q1 = 0; Q1 < 57; Q1++)
{	
	for (Q2 = Q1; Q2 < 58; Q2++)
	{
		for (Q3 = Q2; Q3 < 59; Q3++)
		{
			for (Q4 = Q3; Q4 < 60; Q4++)
			{
				for (Q5 = Q4; Q5 < 61; Q5++)
				{
					for (Q6 = Q5; Q6 < 62; Q6++)
					{
						for (Q7 = Q6; Q7 < 63; Q7++)
						{
							for (Q8 = Q7; Q8 < 64; Q8++)
							{
								
							}
						}
					}
				}
			}
		}
	}
}
That's 10.4 billion. Then you realized that when you place the queens, you can do it one column at a time and check that no queens are in the same row giving you 8*7*6*5*4*3*2*1. This can still be easily beaten with a hill-climbing algorithm starting in random places.