data/problems/424.yml
---
:id: 424
:name: Kakuro
:url: https://projecteuler.net/problem=424
:content: " \n\nThe above is
an example of a cryptic kakuro (also known as cross sums, or even sums cross) puzzle,
with its final solution on the right. (The common rules of kakuro puzzles can be
found easily on numerous internet sites. Other related information can also be currently
found at [krazydad.com](http://krazydad.com/) whose author has provided the puzzle
data for this challenge.)\n\nThe downloadable text file ([kakuro200.txt](project/resources/p424_kakuro200.txt))
contains the description of 200 such puzzles, a mix of 5x5 and 6x6 types. The first
puzzle in the file is the above example which is coded as follows:\n\n6,X,X,(vCC),(vI),X,X,X,(hH),B,O,(vCA),(vJE),X,(hFE,vD),O,O,O,O,(hA),O,I,(hJC,vB),O,O,(hJC),H,O,O,O,X,X,X,(hJE),O,O,X\n\nThe
first character is a numerical digit indicating the size of the information grid.
It would be either a 6 (for a 5x5 kakuro puzzle) or a 7 (for a 6x6 puzzle) followed
by a comma (,). The extra top line and left column are needed to insert information.\n\nThe
content of each cell is then described and followed by a comma, going left to right
and starting with the top line. \nX = Gray cell, not required to be filled by a
digit. \nO (upper case letter)= White empty cell to be filled by a digit. \nA
= Or any one of the upper case letters from A to J to be replaced by its equivalent
digit in the solved puzzle. \n( ) = Location of the encrypted sums. Horizontal
sums are preceded by a lower case \"h\" and vertical sums are preceded by a lower
case \"v\". Those are followed by one or two upper case letters depending if the
sum is a single digit or double digit one. For double digit sums, the first letter
would be for the \"tens\" and the second one for the \"units\". When the cell must
contain information for both a horizontal and a vertical sum, the first one is always
for the horizontal sum and the two are separated by a comma within the same set
of brackets, ex.: (hFE,vD). Each set of brackets is also immediately followed by
a comma.\n\nThe description of the last cell is followed by a Carriage Return/Line
Feed (CRLF) instead of a comma.\n\nThe required answer to each puzzle is based on
the value of each letter necessary to arrive at the solution and according to the
alphabetical order. As indicated under the example puzzle, its answer would be 8426039571.
At least 9 out of the 10 encrypting letters are always part of the problem description.
When only 9 are given, the missing one must be assigned the remaining digit.\n\nYou
are given that the sum of the answers for the first 10 puzzles in the file is 64414157580.\n\nFind
the sum of the answers for the 200 puzzles.\n\n"