The definition of Problem 8 suggests some flexibility on how you treat the 1000-digit number: as a number or as a string. I decided that it would be easier to understand as the latter – using mod to extract digits seemed a little redundant and not really the point of the problem, which treats each digit as a distinct object. Why make things more complex than they need to be?

Because performance clearly isn’t an issue for this type of problem, I chose a slightly verbose style to see how self-documenting I could make it.

(defn euler-8 [string]
  "Finds the greatest product of five consecutive digits in string."
  (letfn [(by-fives   [s] (partition 5 1 s))
          (chars2ints [v] (map #(Integer/parseInt (str %)) v))
          (multiply   [v] (reduce * v))
          (max-of     [v] (reduce max v))]
    (max-of (map multiply (map chars2ints (by-fives string))))))
        
(euler-8 (concat "73167176531330624919225119674426574742355349194934"
                 "96983520312774506326239578318016984801869478851843"
                 "85861560789112949495459501737958331952853208805511"
                 "12540698747158523863050715693290963295227443043557"
                 "66896648950445244523161731856403098711121722383113"
                 "62229893423380308135336276614282806444486645238749"
                 "30358907296290491560440772390713810515859307960866"
                 "70172427121883998797908792274921901699720888093776"
                 "65727333001053367881220235421809751254540594752243"
                 "52584907711670556013604839586446706324415722155397"
                 "53697817977846174064955149290862569321978468622482"
                 "83972241375657056057490261407972968652414535100474"
                 "82166370484403199890008895243450658541227588666881"
                 "16427171479924442928230863465674813919123162824586"
                 "17866458359124566529476545682848912883142607690042"
                 "24219022671055626321111109370544217506941658960408"
                 "07198403850962455444362981230987879927244284909188"
                 "84580156166097919133875499200524063689912560717606"
                 "05886116467109405077541002256983155200055935729725"
                 "71636269561882670428252483600823257530420752963450"))

The choice of strings and concat to represent the 1000-digit number is just to help me display it properly on the internet; clearly it could be written without line breaks, as a vector, or in several other forms.

Looking at other people’s solutions, I noticed that I was using the wrong function to convert characters to integers:

;; Original
(chars2ints [v] (map #(Integer/parseInt (str %)) v))

;; Better
(chars2ints [v] (map #(Character/getNumericValue %) v))

That’s good enough for government work, as they say. I’m not interested in nitpicking this uninteresting problem any further.