コマ大数学科「入社試験に挑戦」に挑戦

読売新聞社の入社試験問題より。A～Eの発言から順位を導き出す（ただし1人だけ嘘つきがいる）。

Program.cs

using System;
using System.Collections.Generic;
using System.Linq;

namespace KomaUniv
{
    static class Ex
    {
        public static IEnumerable<IList<T>> Permutation<T>(
            this IList<T> source, int count)
        {
            return PermutationRec(source, count, new List<int>(),
                Enumerable.Range(0, source.Count).ToList());
        }

        private static IEnumerable<IList<T>> PermutationRec<T>(
            IList<T> source, int count, List<int> indices, List<int> candidates)
        {
            if (count == indices.Count)
            {
                yield return indices.Select(x => source[x]).ToArray();
                yield break;
            }
            for (var i = 0; i < candidates.Count; i++)
            {
                var v = candidates[i];
                candidates.RemoveAt(i);
                indices.Add(v);
                foreach (var l in PermutationRec(source, count, indices, candidates))
                    yield return l;
                indices.RemoveAt(indices.Count - 1);
                candidates.Insert(i, v);
            }
        }

        public static Func<T, bool> And<T>(this Func<T, bool> p1, Func<T, bool> p2)
        {
            return x => p1(x) && p2(x);
        }

        public static Func<T, bool> Or<T>(this Func<T, bool> p1, Func<T, bool> p2)
        {
            return x => p1(x) || p2(x);
        }

        public static Func<T, bool> Not<T>(this Func<T, bool> p)
        {
            return x => !p(x);
        }

    }

    class Program
    {
        static void Main(string[] args)
        {
            var all = new[] { 1, 2, 3, 4, 5 }
                .Permutation(5)
                .Select(x => new { A = x[0], B = x[1], C = x[2], D = x[3], E = x[4] });
            var a = Predicate(all, x => x.C < x.A && x.D < x.A);
            var b = Predicate(all, x => x.D < x.B && x.B < x.A);
            var c = Predicate(all, x => x.C < x.D && 2 < x.C);
            var d = Predicate(all, x => x.C < x.D && x.D < x.B);
            var e = Predicate(all, x => x.E == 1);
            var result = all.Where(
                    ((a.Not()).And(b).And(c).And(d).And(e))
                    .Or(a.And(b.Not()).And(c).And(d).And(e))
                    .Or(a.And(b).And(c.Not()).And(d).And(e))
                    .Or(a.And(b).And(c).And(d.Not()).And(e))
                    .Or(a.And(b).And(c).And(d).And(e.Not()))
                ).First();
            Console.WriteLine(result.ToString());
        }

        static Func<T, bool> Predicate<T>(IEnumerable<T> dummy, Func<T, bool> pred)
        {
            return pred;
        }
    }
}