https://projecteuler.net/problem=52
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.
First, write a function same_digits(x,y) that returns True if two integers x and y have the exact same set of digits and multiplicities and False if they have different digits.
In [26]:
def same_digits(x, y):
"""Do the integers x and y have the same digits, regardless of order."""
test1 = True
test2 = True
for a in x:
if a not in y:
test1 = False
break
for b in y:
if b not in x:
test2 = False
break
test = test1 and test2
return test
In [27]:
assert same_digits('132', '321')
assert not same_digits('123', '3')
assert not same_digits('456', '0987654321')
Now use the same_digits function to solve this Euler problem. As you work on this problem, be careful to debug and test your code on small integers before trying it on the full search.
In [28]:
def tester(x):
a = str(x)
b = str(2*x)
c = str(3*x)
d = str(4*x)
e = str(5*x)
f = str(6*x)
u = same_digits(a, b)
v = same_digits(b, c)
w = same_digits(c, d)
y = same_digits(d, e)
z = same_digits(e, f)
if(u and v and w and y and z):
return True
else:
return False
for x in range(1,1000000):
if tester(x) == True:
print(x)
In [31]:
142857
142857*2
142857*3
142857*4
142857*5
142857*6
Out[31]:
In [29]:
assert True # leave this cell to grade the solution