def problem56():
# As a and b increase, the number of digits of a**b increase and thus the
# sum of digits will also likely increase.
# For example 90**90 has 176 digits, so a number around it should have a digit sum of around 5*176
# And it keeps increasing from there.
return max(applyToDigits(a ** b, lambda x: x) for a, b in permutations(range(90, 100), 2))
def problem20(): return applyToDigits(factorial(100))
def problem16(): return applyToDigits(2**1000)