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Unformatted text preview: 7 board with any one square missing can be tiled using trominos. (This is lengthy, and done by considering several possible cases of missing square. So if you can’t ﬁnd an answer just assume that this can be done). (d) Show that a 11 × 11 board, with any one square missing can be tiled using trominos. Hint: Divide the board into a subboard of size 7 × 7 (which contains that missing square), a subboard of size 5 × 5 with a corner missing, and two subboards of size 4 × 6. (e) By induction show that, for n > 11, any n × n board with one square missing can be tiled using trominoes as long as n is odd and not a multiple of 3. Hint: Divide the board into four parts, One of size ( nm ) × ( nm ) containing the missing square (which can be solved using induction), two boards of sizes ( nm1) × m , which can be solved using part (a), and one board of size ( m +1) × ( m +1), with a missing corner. 1...
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This note was uploaded on 01/06/2012 for the course CS 3230 taught by Professor Sanjay during the Fall '10 term at National University of Singapore.
 Fall '10
 sanjay
 Algorithms, Sort

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