# Project Euler – Problem 8

We had someone leave recently, and as such have been doing interviews. Whenever we start interviewing people I start thinking about algorithms again. Math and algorithms are just fun to work on, they let you explore branches of though in creative ways that UI design doesn’t.

This is the seventh post in my Project Euler series. The seventh problem is here.

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

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

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

Unfortunately today there’s not too much to the problem this time around. Especially in terms of optimization. The only optimization I was able to come up with to prevent having to check every possibility is to ignore any set of 13 adjacent digits if any of them are a 0.

I chose Ruby for this one because it has a really nice method that basically does all of the work. If you get the 1000 digit number into an array of integers, you can use  each_cons to loop through each set of 13 consecutive (adjacent) elements of the array.

Then its just a matter of checking that the array doesn’t have a 0, and getting the product of numbers in the array