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Grade: 10
        


3. You are given a grid of cells. Each cell has a positive integer written on it. You can


move from a cell x to a cell y if x and y are in the same row or same column, and the


number in y is strictly smaller than the number in x. You want to colour some cells


red so that:


• Every cell can be reached by starting at a red cell and following a sequence of


zero 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 3


2 1 2


3 2 2


It 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 amongst


all red cells is 3.


 


(a) 55 25 49 40 55 3 55


33 32 26 59 41 40 55


31 23 41 58 59 14 33


9 19 9 40 4 40 40


55 54 55 46 52 39 41


10 41 7 47 5 30 54


40 22 31 36 7 40 28


21 40 41 59 14 36 31


 


(b) 50 98 54 6 34 94 63 52 39


62 46 75 28 65 18 37 18 97


13 80 33 69 93 78 19 40 13


94 10 88 43 61 72 94 94 94


41 79 82 27 71 62 57 67 34


8 93 2 12 93 52 91 86 93


94 79 64 43 32 94 42 91 9


25 73 29 31 19 70 58 12 11


 


(c) 50 54 6 34 78 63 52 39 41 46


75 28 65 18 37 18 13 80 33 69


78 19 40 13 10 43 61 72 13 46


56 41 79 82 27 71 62 57 67 81


8 71 2 12 52 81 1 79 64 81


32 41 9 25 73 29 31 19 41 58


12 11 41 66 63 14 39 71 38 16


71 43 70 27 78 71 76 37 57 12


77 50 41 81 31 38 24 25 24 81


7 years ago

Answers : (1)

Apoorva Arora
IIT Roorkee
askIITians Faculty
181 Points
							Hello Student,

Your question is not clear and seems to be incomplete. Please recheck your question and post it again..

I am not able to interpret your query. Please write down the problem clearly so that I can provide you the meaningful answer

Thanks
5 years ago
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