Divisiblity of seven digits

Number Theory Level 4

Let $A$ be the set of all 7-digit numbers which use distinct digits $1, 2, 3, 4, 5, 6$ and $7$ . How many ordered pairs $(x,y)$ are there such that both $x$ and $y$ are in $A$ and $x$ divides $y$ ?

The answer is 5040.

1 solution

Fletcher Mattox
Aug 6, 2020

Only the 5040 permutations of $x == y$ .

from itertools import permutations
N = []
for t in permutations([str(i) for i in range(1,8)]):
    n = int(''.join(t))
    N.append(n)
pairs = [[ (i,j) for i in range(len(N)) if N[i] % N[j] == 0] for j in range(len(N))]
print(len(pairs))

Divisiblity of seven digits

The answer is 5040.

1 solution

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