Ages Of Three Children Puzzle Solution http://gohighbrow.com/how-old-are-my-children-solution/

FindAges.java

import java.util.*;

public class Main {
    public static void main(String[] args) {
        int max = 72;
        int maxDate = 31;

        Set<Ages> agesPerms = getProducPerms(max, maxDate);
        Map<Integer, List<Ages>> sumToAgesMap = getSumToAgesMap(agesPerms);
        Map<Integer, List<Ages>> sumWithDups = getSumWithDups(sumToAgesMap);
        assert (sumWithDups.size() == 1);

        int found = 0;
        List<Ages> dups = sumWithDups.values().iterator().next();
        for (Ages dup : dups) {
            if (dup.hasDistinctEldest()) {
                found++;
                System.out.println(String.format("\nAnswer: %s", dup));
            }
        }
        assert found == 1;
    }

    private static Map<Integer, List<Ages>> getSumWithDups(Map<Integer, List<Ages>> sumToAgesMap) {
        Map<Integer, List<Ages>> sumWithDups = new HashMap<>();
        for (Map.Entry<Integer, List<Ages>> entry : sumToAgesMap.entrySet()) {
            if (entry.getValue().size() > 1) {
                sumWithDups.put(entry.getKey(), entry.getValue());
            }
        }
        return sumWithDups;
    }

    private static Map<Integer, List<Ages>> getSumToAgesMap(Set<Ages> agesPerms) {
        Map<Integer, List<Ages>> m = new HashMap<>();
        for (Ages ages : agesPerms) {
            int sum = ages.getSum();
            if (!m.containsKey(sum)) {
                List<Ages> agesList = new ArrayList<>();
                m.put(sum, agesList);
            }
            m.get(sum).add(ages);
        }
        return m;
    }

    private static Set<Ages> getProducPerms(int max, int maxDate) {
        Set<Ages> agePerms = new HashSet<>();

        for (int i = 0; i <= max; i++) {
            for (int j = 0; j <= max; j++) {
                for (int k = 0; k <= max; k++) {
                    Ages ages = new Ages(i, j, k);

                    if (!agePerms.contains(ages)
                            && ages.getProduct() == max && ages.getSum() <= maxDate) {
                        agePerms.add(ages);
                        String combo = String.format("%s,%s,%s", ages.x, ages.y, ages.z);
                        System.out.println(String.format("%s - sum(%s) = %s", combo, combo, ages.getSum()));
                    }
                }
            }
        }

        return agePerms;
    }

    static class Ages {
        int x, y, z;

        public Ages(int a, int b, int c) {
            List<Integer> ascAges = Arrays.asList(a, b, c);
            Collections.sort(ascAges);

            this.x = ascAges.get(0);
            this.y = ascAges.get(1);
            this.z = ascAges.get(2);

            assert x <= y && y <= z;
        }

        public boolean hasDistinctEldest() {
            return z > y;
        }

        int getProduct() {
            return x*y*z;
        }

        int getSum() {
            return x+y+z;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Ages ages = (Ages) o;

            if (x != ages.x) return false;
            if (y != ages.y) return false;
            return z == ages.z;

        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            result = 31 * result + z;
            return result;
        }

        @Override
        public String toString() {
            return "Ages{" +
                    "x=" + x +
                    ", y=" + y +
                    ", z=" + z +
                    '}';
        }
    }
}