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Rigging the Bovine Election
It's election time. The farm is partitioned into a 5x5 grid of cow locations, each of which holds either a Holstein ('H') or Jersey ('J') cow. The Jerseys want to create a voting district of 7 contiguous (vertically or horizontally) cow locations such that the Jerseys outnumber the Holsteins. How many ways can this be done for the supplied grid?
* Lines 1..5: Each of the five lines contains five characters per line, each 'H' or 'J'. No spaces are present.
* Line 1: The number of distinct districts of 7 connected cows such that the Jerseys outnumber the Holsteins in the district.
HHHHH JHJHJ HHHHH HJHHJ HHHHH
The two possible districts are:
Any other possible district with seven cows has fewer than 4 Jerseys.
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