BMAD Posted May 8, 2013 Report Share Posted May 8, 2013 A rectangular floor is composed of whole square tiles. A diagonal line is drawn (corner to corner) and ruins some of the tiles. (on a 2 x 5 floor, 6 tiles are ruined, on a 2 x 4, only 4 are ruined.) a) How many tiles are ruined on a 4 by 6 floor? b) How about a 63 by 81 floor? c) Generalize to an m by n floor. Quote Link to comment Share on other sites More sharing options...
0 witzar Posted May 11, 2013 Report Share Posted May 11, 2013 a) How many tiles are ruined on a 4 by 6 floor? b) How about a 63 by 81 floor? a) 4 + 6 - gcd(4,6) = 4+ 6 - 2 = 8 b) 63 + 81 - gcd(63,81) = 63 + 81 - 9 = 135 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted May 8, 2013 Report Share Posted May 8, 2013 Assume the height H is greater than the width W. Each column will have a number of damaged tiles That number is CEILING (H/W). Where CEILING means least integer greater than. CEILING (3.5) = 4 and CEILING (2) = 2. Multiply by the number of columns. Ruined tiles = W x CEILING (H/W) Quote Link to comment Share on other sites More sharing options...
0 witzar Posted May 8, 2013 Report Share Posted May 8, 2013 m + n - gcd(m,n) Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted May 11, 2013 Author Report Share Posted May 11, 2013 a) How many tiles are ruined on a 4 by 6 floor? b) How about a 63 by 81 floor? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted May 11, 2013 Report Share Posted May 11, 2013 a) How many tiles are ruined on a 4 by 6 floor? b) How about a 63 by 81 floor? 4x6 ceiling (6/4) = 2 2x4 = 8 ruined tiles 63x81 ceiling (81/63) = 2 2x63 = 126 ruined tiles Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted May 11, 2013 Author Report Share Posted May 11, 2013 a) How many tiles are ruined on a 4 by 6 floor? b) How about a 63 by 81 floor? 4x6 ceiling (6/4) = 2 2x4 = 8 ruined tiles 63x81 ceiling (81/63) = 2 2x63 = 126 ruined tiles 6 x 4 should be 2 81 x 63 should be 135 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted May 11, 2013 Report Share Posted May 11, 2013 a) How many tiles are ruined on a 4 by 6 floor? b) How about a 63 by 81 floor? 4x6 ceiling (6/4) = 2 2x4 = 8 ruined tiles 63x81 ceiling (81/63) = 2 2x63 = 126 ruined tiles 6 x 4 should be 2 81 x 63 should be 135 6x4 ruins at least the two corner tiles. Nothing else? Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted May 11, 2013 Author Report Share Posted May 11, 2013 a) How many tiles are ruined on a 4 by 6 floor? b) How about a 63 by 81 floor? 4x6 ceiling (6/4) = 2 2x4 = 8 ruined tiles 63x81 ceiling (81/63) = 2 2x63 = 126 ruined tiles 6 x 4 should be 2 81 x 63 should be 135 6x4 ruins at least the two corner tiles. Nothing else? i missed typed 6x4 ruins 8 Quote Link to comment Share on other sites More sharing options...
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