## Problem:

It is possible to write five as a sum in exactly six different ways:

4 + 1
3 + 2
3 + 1 + 1
2 + 2 + 1
2 + 1 + 1 + 1
1 + 1 + 1 + 1 + 1

How many different ways can one hundred be written as a sum of at least two positive integers?

983

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 26 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */import java.util.HashMap;import java.util.Map;public final class p026 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p026().run());	}			public String run() {		int bestNumber = 0;		int bestLength = 0;		for (int i = 1; i <= 1000; i++) {			int len = getCycleLength(i);			if (len > bestLength) {				bestNumber = i;				bestLength = len;			}		}		return Integer.toString(bestNumber);	}			private static int getCycleLength(int n) {		Map<Integer,Integer> stateToIter = new HashMap<Integer,Integer>();		int state = 1;		int iter = 0;		while (!stateToIter.containsKey(state)) {			stateToIter.put(state, iter);			state = state * 10 % n;			iter++;		}		return iter - stateToIter.get(state);	}	}