Problem #37

For Valentine's Day, a candy manufacturer wants to offer a box of 64 chocolates with 8 horizontal and 8 vertical rows. There are two types of chocolates, milk chocolate and dark chocolate. The manufacturer wants to have at least one dark chocolate in every vertical row, in every horizontal row, and every diagonal.

To illustrate, if n = 4, and the chocolates are labeled as below, in addition to a dark chocolate in each of the horizontal and vertical rows, you'd also need a chocolate in the "southeast" diagonals: "m", "i,n", ..., "c,h", and "d" and in the "northeast" diagonals: "a", "e,b", ..., "o,l", and "p". A solution with 10 dark chocolates is shown below (although this is not the minimum number).

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