matlab 欧拉计划 34

problem 34

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
Find the sum of all numbers which are equal to the sum of the factorial of their digits.
Note: as 1! = 1 and 2! = 2 are not sums they are not included.

思路

1.要求：找到满足如下条件的数：位数大于1位；各位数字阶乘相加等于本身。并求出所 有满足该条件的数之和；
2.首先需要确定范围，按9!来估算：9!×8=2903040，结果为一7位数，最大的8位数字阶乘和都达不到8位数，因此范围肯定小于8位数；9!×7=2540160，结果位数相符，因此可以将范围定为[10,2540160].（就是运行时间有点长）

程序

clc;clear all;
t=[];
for i=10:2540160
    t1=0;
    y=num2str(i);
    for j=1:length(y)
        t1=t1+factorial(str2num(y(j)));
    end
    if t1==i
        t=[t i];
    end    
end