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r 1 01 0 01 r1 010 0 0 0 r 01100 1 1 01 1 0 0 r 0 1 0 01 1 re 1 0 0 0 0 0 1 1],\

ID: 3729389 • Letter: R

Question

r 1 01 0 01 r1 010 0 0 0 r 01100 1 1 01 1 0 0 r 0 1 0 01 1 re 1 0 0 0 0 0 1 1]," Lo o o o o 1 1 : 0 T6 2 An application: Pentomino The Pentomino is a tiling problem involving 12 different tiles, each of them covering 5 cells . a 6x10 grid The following is one of the many solutions to the Pentomino problem: Design the exact cover matrix for the Pentomino problem: e what should it be represented by its columns? what should each row of the matrix represent? e what is a solution to the problem? Hint: Pentomino is a regular exact cover problem.

Explanation / Answer

In matrix representation, an exact cover is selection rows such that each column contains a 1 in exactly one selected row.

Given information:

1) 12 different tiles, each of them covering 5 cells.

2) a 6x10 grid

To design the Pentomino cover matrix, we go for following approach

Therefore there are 72 columns in the cover matrix.