# Project Euler Problem 8: Largest Product In A Series¶

The source code for this problem can be found here.

## Problem Statement¶

The four adjacent digits in the $$1000$$-digit number that have the greatest product are $$\color{red}{9} \times \color{red}{9} \times \color{red}{8} \times \color{red}{9} = 5832$$.

$\begin{split} & 73167176531330624919225119674426574742355349194934 \hookleftarrow \\ \hookrightarrow & 96983520312774506326239578318016984801869478851843 \hookleftarrow \\ \hookrightarrow & 85861560789112949495459501737958331952853208805511 \hookleftarrow \\ \hookrightarrow & 12540698747158523863050715693290963295227443043557 \hookleftarrow \\ \hookrightarrow & 66896648950445244523161731856403098711121722383113 \hookleftarrow \\ \hookrightarrow & 62229893423380308135336276614282806444486645238749 \hookleftarrow \\ \hookrightarrow & 30358907296290491560440772390713810515859307960866 \hookleftarrow \\ \hookrightarrow & 70172427121883998797908792274921901699720888093776 \hookleftarrow \\ \hookrightarrow & 65727333001053367881220235421809751254540594752243 \hookleftarrow \\ \hookrightarrow & 52584907711670556013604839586446706324415722155397 \hookleftarrow \\ \hookrightarrow & 53697817977846174064955149290862569321978468622482 \hookleftarrow \\ \hookrightarrow & 83972241375657056057490261407972968652414535100474 \hookleftarrow \\ \hookrightarrow & 821663704844031\color{red}{9989}0008895243450658541227588666881 \hookleftarrow \\ \hookrightarrow & 16427171479924442928230863465674813919123162824586 \hookleftarrow \\ \hookrightarrow & 17866458359124566529476545682848912883142607690042 \hookleftarrow \\ \hookrightarrow & 24219022671055626321111109370544217506941658960408 \hookleftarrow \\ \hookrightarrow & 07198403850962455444362981230987879927244284909188 \hookleftarrow \\ \hookrightarrow & 84580156166097919133875499200524063689912560717606 \hookleftarrow \\ \hookrightarrow & 05886116467109405077541002256983155200055935729725 \hookleftarrow \\ \hookrightarrow & 71636269561882670428252483600823257530420752963450\end{split}$

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

## Solution Discussion¶

We’ll simply iterate over all $$13$$-long sub-strings in a sliding window fashion. For each sub-string, compute the product of the integers. The maximum of these individuals products is the answer.

## Solution Implementation¶

from functools import reduce
from operator import mul

def solve():
""" Compute the answer to Project Euler's problem #8 """

# Build a list of the individual digits as integer objects
series = """
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
"""
series = series.replace(" ", "").replace("\n", "")
integers = [int(character) for character in series]

# Perform the search through all overlapping m-long subsets
n = len(integers)
m = 13

solutions.problem8.solve()