Tag Archive for 'curiousFraction'

Problem 33 in Project Euler says there are 4 non-trivial curious fractions which satisfy the following properties:

where a, b and x are all single digit numbers and a < b

The solution was pretty simple.

Similarly solving for the other form gives the answer .

Implementing this solution in java:

public class Problem_33 {
	/**
	 * @return All the proper non-trivial curious fractions having numerator, denominator < 100
	 */
	public static List<Fraction> getCuriousFractions() {
		List<Fraction> curiousFractions = new ArrayList<Fraction>();

		for (int a = 1; a < 10; a++)
			for (int b = a + 1; b < 10; b++)
				if (Problem_33.checkCondition(a, b))
					curiousFractions.add(new Fraction(a, b));

		return curiousFractions;
	}

	/**
	 * Checks if the number is of the form xa/bx = a/b or ax/xb = a/b
	 *
	 * @param a The numerator of the fraction
	 * @param b The denominator of the fraction
	 * @return true if it can be formed into a curious fraction, false otherwise
	 */
	private static boolean checkCondition(int a, int b) {
		int numerator = 9 * a * b;
		int denominatorA = 10 * b - a;
		int denominatorB = 10 * a - b;
		return numerator % denominatorA == 0 && numerator / denominatorA < 10 || numerator % denominatorB == 0
		        && numerator / denominatorB < 10 ? true : false;
	}
}

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