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 sqrt
def 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 False
result=0
for 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
http://www.worldofnumbers.com/ninedig1.htm