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Problem040.py
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Problem040.py
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"""
Project Euler Problem 40
========================
An irrational decimal fraction is created by concatenating the positive
integers:
0.123456789101112131415161718192021...
123456789012345
It can be seen that the 12th digit of the fractional part is 1.
If d[n] represents the n-th digit of the fractional part, find the value
of the following expression.
d[1] * d[10] * d[100] * d[1000] * d[10000] * d[100000] * d[1000000]
"""
from math import log10, floor
def digit_generator(N=1_000_000):
""" Generator of the N first digits of the concatenation """
i = 0
number = 1
while N > i:
for _i in str(number):
yield _i
i += 1
number += 1
def get_digit(n):
""" Get the digit in nth decimal place"""
"""
9 - 9
10-99 - 2*90
100-999 - 3*900
"""
i = 0
start = 0
done = False
while not done:
step = (i+1)*9*(10**i)
if start + step > n:
done = True
else:
start += step
i += 1
num_digits = i + 1
offset = n - start
number = offset // num_digits + \
(10**(num_digits-1) if (num_digits - 1) else 0)
_i = (offset - 1) % num_digits
return int(str(number)[_i])
result = 1
for i in range(0, 7):
result *= get_digit(10**i)
print(result)