Greatest product of five consecutive digits in a 1000-digit number

Question

I am working through the problems on project Euler and am not too certain if my understanding of the question is correct.

Problem 8 is as follows:

Find the greatest product of five consecutive digits in the 1000-digit number.

I have taken this to mean the following:

I need to find any five numbers that run consecutively in the 1000 digit number and then add these up to get the total. I am assuming that the size of the numbers could be anything, i.e. 1,2,3 or 12,13,14 or 123,124,124 or 1234,1235,1236 etc.

Is my understanding of this correct, or have I misunderstood the question?

Note: Please don't supply code or the solution, that I need to solve myself.

Answer 1

The number is:

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

• The first five consecutive digits are: 73167. Their product is 7*3*1*6*7=882
• The next five consecutive digits are: 31671. Their product is 3*1*6*7*1=126
• The next five consecutive digits are: 16717. Their product is 1*6*7*1*7=294

And so on. Note the overlap. Now, find the five consecutive digits whose product is maximal over the whole 1000-digit number.

Answer 2

A digit is a single 0-9 in the string representing the number. So the number 12345 has 5 digits. 1234554321 has 10 digits.

The product is the multiplicative total, not the added total. So the product of 3, 5 and 7 is 105.

A (somewhat clunky) way of rephrasing the question would be:

Given a 1000-digit number, select 5 consecutive digits from it that, when taken as individual numbers and multiplied together, give the largest result.

Answer 3

Five single digits. 1, 5, 8... whatever shows up in the big number, all in a row. So if a chunk read "...47946285..." Then you could use "47946", "79462", "94628", "46285", etc.