Project Euler 52

题目

Permuted multiples

It can be seen that the number, \(125874\), and its double, \(251748\), contain exactly the same digits, but in a different order.

Find the smallest positive integer, \(x\), such that \(2x, 3x, 4x, 5x,\) and \(6x\), contain the same digits.

解决方案

直接枚举。可以发现，如果要满足上面的条件，那么\(x\)和\(6x\)的位数必须相同。

因此，对于一个\(n\)位数而言，只需要枚举这些\(n\)位数的前\(\dfrac{1}{6}\)的部分。

代码

from itertools import count

for i in count(1, 1):
    l = 10 ** (i - 1)
    r = 10 ** i // 6
    ok = False
    for x in range(l, r + 1):
        st = set()
        for i in range(1, 7):
            st.add("".join((lambda x: (x.sort(), x)[1])(list(str(x * i)))))
        if len(st) == 1:
            ok = True
            ans = x
            break
    if ok:
        break
print(ans)