SumIt

SumIt.cs

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

namespace SumIt {
	internal static class Program {
		private static void Main() {
			var nums = new List<string[]> { new[] { "+-1", "+1" } };

			for (var i = 2; i < 10; i++)
				nums.Add(new[] {$"{i}", $"+-{i}", $"+{i}"});

			var solutions = M(nums)
				.Select(o => string.Join("", o))
				.Select(o=>new {
					expr = o.TrimStart('+').Replace("+-", " - ").Replace("+", " + "),
					res = o.Split(new[] { '+' }, StringSplitOptions.RemoveEmptyEntries).Sum(int.Parse)
				}).ToArray();
			for (var i = 0; i <= 100; i++) {
				var right = solutions.Where(o => o.res == i).ToList();
				Console.WriteLine($"Solving for {i}, there are {right.Count:N0} correct. {solutions.Length - right.Count:N0} incorrect.");
				foreach (var solution in right)
					Console.WriteLine($"\t{solution.expr}");
			}

			Console.ReadLine();
		}

		public static IEnumerable<IEnumerable<string>> M(List<string[]> list) {
			var m = list.GetRange(1, list.Count - 1);
			if (list.Count == 1)
				foreach (var s in list[0])
					yield return new[] {s};
			else
				foreach (var enumerable in M(m).Select(sublist => sublist as IList<string> ?? sublist.ToList()))
					foreach (var s in list[0])
						yield return Prepend(s, enumerable);
		}

		private static IEnumerable<T> Prepend<T>(T first, IEnumerable<T> rest) {
			yield return first;
			foreach (var item in rest)
				yield return item;
		}
	}
}