# Project Euler: Problem 8

https://projecteuler.net/problem=8

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

(see the number below)

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

Use NumPy for this computation

``````

In [1]:

import numpy as np

``````
``````

In [2]:

d1000 = """
73167176531330624919225119674426574742355349194934\
96983520312774506326239578318016984801869478851843\
85861560789112949495459501737958331952853208805511\
12540698747158523863050715693290963295227443043557\
66896648950445244523161731856403098711121722383113\
62229893423380308135336276614282806444486645238749\
30358907296290491560440772390713810515859307960866\
70172427121883998797908792274921901699720888093776\
65727333001053367881220235421809751254540594752243\
52584907711670556013604839586446706324415722155397\
53697817977846174064955149290862569321978468622482\
83972241375657056057490261407972968652414535100474\
82166370484403199890008895243450658541227588666881\
16427171479924442928230863465674813919123162824586\
17866458359124566529476545682848912883142607690042\
24219022671055626321111109370544217506941658960408\
07198403850962455444362981230987879927244284909188\
84580156166097919133875499200524063689912560717606\
05886116467109405077541002256983155200055935729725\
71636269561882670428252483600823257530420752963450
"""

``````

Turn d1000 into a list I can work with

``````

In [3]:

b = []
for digit in d1000.strip():
b.append(int(digit))
b

``````
``````

Out[3]:

[7,
3,
1,
6,
7,
1,
7,
6,
5,
3,
1,
3,
3,
0,
6,
2,
4,
9,
1,
9,
2,
2,
5,
1,
1,
9,
6,
7,
4,
4,
2,
6,
5,
7,
4,
7,
4,
2,
3,
5,
5,
3,
4,
9,
1,
9,
4,
9,
3,
4,
9,
6,
9,
8,
3,
5,
2,
0,
3,
1,
2,
7,
7,
4,
5,
0,
6,
3,
2,
6,
2,
3,
9,
5,
7,
8,
3,
1,
8,
0,
1,
6,
9,
8,
4,
8,
0,
1,
8,
6,
9,
4,
7,
8,
8,
5,
1,
8,
4,
3,
8,
5,
8,
6,
1,
5,
6,
0,
7,
8,
9,
1,
1,
2,
9,
4,
9,
4,
9,
5,
4,
5,
9,
5,
0,
1,
7,
3,
7,
9,
5,
8,
3,
3,
1,
9,
5,
2,
8,
5,
3,
2,
0,
8,
8,
0,
5,
5,
1,
1,
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7,
6,
6,
8,
9,
6,
6,
4,
8,
9,
5,
0,
4,
4,
5,
2,
4,
4,
5,
2,
3,
1,
6,
1,
7,
3,
1,
8,
5,
6,
4,
0,
3,
0,
9,
8,
7,
1,
1,
1,
2,
1,
7,
2,
2,
3,
8,
3,
1,
1,
3,
6,
2,
2,
2,
9,
8,
9,
3,
4,
2,
3,
3,
8,
0,
3,
0,
8,
1,
3,
5,
3,
3,
6,
2,
7,
6,
6,
1,
4,
2,
8,
2,
8,
0,
6,
4,
4,
4,
4,
8,
6,
6,
4,
5,
2,
3,
8,
7,
4,
9,
3,
0,
3,
5,
8,
9,
0,
7,
2,
9,
6,
2,
9,
0,
4,
9,
1,
5,
6,
0,
4,
4,
0,
7,
7,
2,
3,
9,
0,
7,
1,
3,
8,
1,
0,
5,
1,
5,
8,
5,
9,
3,
0,
7,
9,
6,
0,
8,
6,
6,
7,
0,
1,
7,
2,
4,
2,
7,
1,
2,
1,
8,
8,
3,
9,
9,
8,
7,
9,
7,
9,
0,
8,
7,
9,
2,
2,
7,
4,
9,
2,
1,
9,
0,
1,
6,
9,
9,
7,
2,
0,
8,
8,
8,
0,
9,
3,
7,
7,
6,
6,
5,
7,
2,
7,
3,
3,
3,
0,
0,
1,
0,
5,
3,
3,
6,
7,
8,
8,
1,
2,
2,
0,
2,
3,
5,
4,
2,
1,
8,
0,
9,
7,
5,
1,
2,
5,
4,
5,
4,
0,
5,
9,
4,
7,
5,
2,
2,
4,
3,
5,
2,
5,
8,
4,
9,
0,
7,
7,
1,
1,
6,
7,
0,
5,
5,
6,
0,
1,
3,
6,
0,
4,
8,
3,
9,
5,
8,
6,
4,
4,
6,
7,
0,
6,
3,
2,
4,
4,
1,
5,
7,
2,
2,
1,
5,
5,
3,
9,
7,
5,
3,
6,
9,
7,
8,
1,
7,
9,
7,
7,
8,
4,
6,
1,
7,
4,
0,
6,
4,
9,
5,
5,
1,
4,
9,
2,
9,
0,
8,
6,
2,
5,
6,
9,
3,
2,
1,
9,
7,
8,
4,
6,
8,
6,
2,
2,
4,
8,
2,
8,
3,
9,
7,
2,
2,
4,
1,
3,
7,
5,
6,
5,
7,
0,
5,
6,
0,
5,
7,
4,
9,
0,
2,
6,
1,
4,
0,
7,
9,
7,
2,
9,
6,
8,
6,
5,
2,
4,
1,
4,
5,
3,
5,
1,
0,
0,
4,
7,
4,
8,
2,
1,
6,
6,
3,
7,
0,
4,
8,
4,
4,
0,
3,
1,
9,
9,
8,
9,
0,
0,
0,
8,
8,
9,
5,
2,
4,
3,
4,
5,
0,
6,
5,
8,
5,
4,
1,
2,
2,
7,
5,
8,
8,
6,
6,
6,
8,
8,
1,
1,
6,
4,
2,
7,
1,
7,
1,
4,
7,
9,
9,
2,
4,
4,
4,
2,
9,
2,
8,
2,
3,
0,
8,
6,
3,
4,
6,
5,
6,
7,
4,
8,
1,
3,
9,
1,
9,
1,
2,
3,
1,
6,
2,
8,
2,
4,
5,
8,
6,
1,
7,
8,
6,
6,
4,
5,
8,
3,
5,
9,
1,
2,
4,
5,
6,
6,
5,
2,
9,
4,
7,
6,
5,
4,
5,
6,
8,
2,
8,
4,
8,
9,
1,
2,
8,
8,
3,
1,
4,
2,
6,
0,
7,
6,
9,
0,
0,
4,
2,
2,
4,
2,
1,
9,
0,
2,
2,
6,
7,
1,
0,
5,
5,
6,
2,
6,
3,
2,
1,
1,
1,
1,
1,
0,
9,
3,
7,
0,
5,
4,
4,
2,
1,
7,
5,
0,
6,
9,
4,
1,
6,
5,
8,
9,
6,
0,
4,
0,
8,
0,
7,
1,
9,
8,
4,
0,
3,
8,
5,
0,
9,
6,
2,
4,
5,
5,
4,
4,
4,
3,
6,
2,
9,
8,
1,
2,
3,
0,
9,
8,
7,
8,
7,
9,
9,
2,
7,
2,
4,
4,
2,
8,
4,
9,
0,
9,
1,
8,
8,
8,
4,
5,
8,
0,
1,
5,
6,
1,
6,
6,
0,
9,
7,
9,
1,
9,
1,
3,
3,
8,
7,
5,
4,
9,
9,
2,
0,
0,
5,
2,
4,
0,
6,
3,
6,
8,
9,
9,
1,
2,
5,
6,
0,
7,
1,
7,
6,
0,
6,
0,
5,
8,
8,
6,
1,
1,
6,
4,
6,
7,
1,
0,
9,
4,
0,
5,
0,
7,
7,
5,
4,
1,
0,
0,
2,
2,
5,
6,
9,
8,
3,
1,
5,
5,
2,
0,
0,
0,
5,
5,
9,
3,
5,
7,
2,
9,
7,
2,
5,
7,
1,
6,
3,
6,
2,
6,
9,
5,
6,
1,
8,
8,
2,
6,
7,
0,
4,
2,
8,
2,
5,
2,
4,
8,
3,
6,
0,
0,
8,
2,
3,
2,
5,
7,
5,
3,
0,
4,
2,
0,
7,
5,
2,
9,
6,
3,
4,
5,
0]

``````

create a function that finds the max product of 13 adjacent digits

``````

In [19]:

c = np.array(b)
def product(n):
themax = 0
numbers = []
for i in range(1000):
d = n[i:i+13]     #this is a list of the 13 adjacent digits
p = np.cumprod(d)[len(np.cumprod(d)) - 1]      #this is the product of that list
if p > themax:       #p and d will continue to be replaced by the largest that the for loop finds
themax = p
numbers = d
return themax, numbers

``````
``````

In [20]:

print(product(c))

``````
``````

(23514624000, array([5, 5, 7, 6, 6, 8, 9, 6, 6, 4, 8, 9, 5]))

``````

Success! Worked on this solution with Ryan Werth during pair programming in class.

``````

In [ ]:

assert True # leave this for grading

``````