def cancelling_fractions():
res = []
for n in range(10, 99):
for d in range(n + 1, 100):
if d % 10 == 0 or not _has_common_digit(n, d):
continue
n_digits = number_as_digits(n)
d_digits = number_as_digits(d)
common_digits = set(n_digits) & set(d_digits)
for common_digit in common_digits:
n_digits_except_common = list_except(n_digits, n_digits.index(common_digit))
d_digits_except_common = list_except(d_digits, d_digits.index(common_digit))
reduced_val = float(next(iter(n_digits_except_common))) / float(next(iter(d_digits_except_common)))
val = float(n) / float(d)
if fabs(reduced_val - val) < 0.00000001:
res += [(n, d)]
return res
def test_digit_powers(self):
for num in digit_powers():
digits = number_as_digits(num)
root = int(round(pow(num, 1.0 / len(digits))))
self.assertEqual(num, root ** len(digits))
def digit_factorial():
res = []
for i in range(3, 100000):
if i == sum(map(factorial, number_as_digits(i))):
res += [i]
return res
def _has_common_digit(number_a, number_b):
number_a_digits = set(number_as_digits(number_a))
number_b_digits = set(number_as_digits(number_b))
return len(number_a_digits & number_b_digits) > 0
def powers(a, b):
res = 1
for i in range(1, a + 1):
for j in range(1, b + 1):
res = max(res, sum(number_as_digits(i ** j)))
return res
