# 3. You are given a grid of cells. Each cell has a positive integer written on it. You canmove from a cell x to a cell y if x and y are in the same row or same column, and thenumber in y is strictly smaller than the number in x. You want to colour some cellsred so that:• Every cell can be reached by starting at a red cell and following a sequence ofzero or more moves as de?ned above.• The number of red cells is as small as possible.You should report the following information:2• The number of red cells.• The smallest number appearing amongst all red cells.If there are multiple valid solutions, give any one solution.For example, suppose the grid is as follows:2 2 32 1 23 2 2It is su?cient to colour the two cells labelled 3, and one cannot do better than this.In this case, the number of red cells is 2 and the smallest number appearing amongstall red cells is 3.(a) 55 25 49 40 55 3 5533 32 26 59 41 40 5531 23 41 58 59 14 339 19 9 40 4 40 4055 54 55 46 52 39 4110 41 7 47 5 30 5440 22 31 36 7 40 2821 40 41 59 14 36 31(b) 50 98 54 6 34 94 63 52 3962 46 75 28 65 18 37 18 9713 80 33 69 93 78 19 40 1394 10 88 43 61 72 94 94 9441 79 82 27 71 62 57 67 348 93 2 12 93 52 91 86 9394 79 64 43 32 94 42 91 925 73 29 31 19 70 58 12 11(c) 50 54 6 34 78 63 52 39 41 4675 28 65 18 37 18 13 80 33 6978 19 40 13 10 43 61 72 13 4656 41 79 82 27 71 62 57 67 818 71 2 12 52 81 1 79 64 8132 41 9 25 73 29 31 19 41 5812 11 41 66 63 14 39 71 38 1671 43 70 27 78 71 76 37 57 1277 50 41 81 31 38 24 25 24 81

Apoorva Arora IIT Roorkee
9 years ago
Hello Student,

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