Euler 11

gistfile1.txt

#!/usr/local/bin/node

// according to wikipedia, formula for triangle numbers is Tn=n(n+1)/2
// so we can just generate triangle numbers with a while loop, and then check for factors with a for loop
// everytime it finds a factor, add 1 to the limit, end for loop when factors > 500

biggesti = 0;
biggesttriangle = 0;
biggestfactors = 0;


for (i=10000;i<=15000;i++)
	{

	triangle = (i * (i+1))/2;
	factors = 0;
	
	if (triangle%2==0 && triangle%5==0 && triangle%10 == 0)
			{
			for(j=1;j<=triangle;j++)	
				{
				if (triangle%j==0)
					{
					factors+=1;
					}	
				}
			}
		
	if (factors > biggestfactors)		
		{
		biggestfactors=factors;
		biggesti = i;
		biggesttriangle = triangle;
		console.log("our current champion is triangle number " + biggesti + " with value " + biggesttriangle + " which has " + biggestfactors + " factors");
		}
		
	}
	

I hate a few problems here. The first is that my while statement borked- or maybe it didn't- it might have just been running really slow, because this takes forever, and I wasn't sure if it was working at all. So I switched to a for statement so I could control which triangle range we searched. Second, I looked at the triangles which were the high scores in each range, and it seemed like they were all divisible by 0, 5, and 10, so I took a chance and limited the search to that- it helped a little, but not that much. According to http://projecteuler.net/project/resources/012_a86c72e34d4ddac1da5871011962ecba/012_overview.pdf - you could basically count all factors up to the square root of the number you're looking at- and then double it, since factors are symmetrical- the problem is you then have to correct for perfect squares. You could also sieve primes, and then follow a slightly complex formula for deriving the number of divisors from the number of primes.