Added solution to problem 34

Problem34.lua

@@ -0,0 +1,66 @@
+--ProjectEuler/ProjectEulerLua/Problem34.lua
+--Matthew Ellison
+-- Created: 06-01-21
+--Modified; 06-01-21
+--Find the sum of all numbers which are equal to the sum of the factorial of their digits
+--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
+--[[
+	Copyright (C) 2021  Matthew Ellison
+
+	This program is free software: you can redistribute it and/or modify
+	it under the terms of the GNU Lesser General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	This program is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU Lesser General Public License for more details.
+
+	You should have received a copy of the GNU Lesser General Public License
+	along with this program.  If not, see <https://www.gnu.org/licenses/>.
+]]
+
+
+require "Stopwatch"
+require "Algorithms"
+
+
+--Setup the variables
+local timer = Stopwatch:create();
+local MAX_NUM = 1499999;	--The largest num that can be the sum of its own digits
+local numberFactorials = {};	--Holds the pre-computed factorials of the numbers 0-9
+local sum = 0;	--Holds the sum of all numbers equal to the sum of their digit's factorials
+
+--Start the timer
+timer:start();
+
+--Pre-compute the possible factorials from 0! to 9!
+for cnt = 0, 9 do
+	numberFactorials[cnt] = factorial(cnt);
+end
+--Run through all possible numbers from 3-MAX_NUM and see if they equal the sum of their digit's factorials
+for cnt = 3, MAX_NUM do
+	--Split the number into its digits and add each one to the sum
+	local numString = tostring(cnt);
+	local currentSum = 0;
+	for numCnt = 1, string.len(numString) do
+		currentSum = currentSum + numberFactorials[tonumber(string.sub(numString, numCnt, numCnt))];
+	end
+	--If the number is equal to the sum add the sum to the running sum
+	if(currentSum == cnt) then
+		sum = sum + currentSum;
+	end
+end
+
+--Stop the timer
+timer:stop();
+
+--Print the results
+io.write("The sum of all numbers that are the sum of their digit's factorials is " .. sum .. "\n");
+io.write("It took " .. timer:getString() .. " to run this algorithm\n");
+
+--[[ Results:
+The sum of all numbers that are the sum of their digit's factorials is 40730
+It took 1.308 seconds to run this algorithm
+]]