Pandigital products

Problem 32

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.

HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

Answer:

45228

Completed on Sat, 25 Jul 2015, 15:13

python code:

from math import sqrtdef func(x):    s0=set(str(x))    for i in range(2,min(100,int(sqrt(x)+1))):        if x%i==0:            s1=set(str(i))            s2=set(str(x//i))            s=s0|s1|s2            if len(s)==9 and '0' not in s:                return True    return Falseresult=0for i in range(1000,9999):    Pstr=str(i)    if len(set(Pstr))==4 and '0' not in Pstr:        if func(i):            result+=i            print(i)print(result)

这里由于要求乘积不能反复，能够考虑对乘积候选项循环推断，把满足条件的加起来，而且非常easy反证证明乘积项数字位数仅仅能为4。

数字1-9是一个有趣的问题，很多其它问题能够參考