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+1 vote

A rectangle of height 100 squares and width 200 squares is drawn on a graph paper. It is colored square by square from top left the corner and moving across in a spiral turning right whenever a side of the rectangle or a colored square is reached. Which square is colored last? (give its row and column numbers – the bottom right square is on row 100 and column 200)

a) 50,50

b) 51,50

c) 51,150

d) 50,150

0 votes

I think answer shold be B(51,50)

you can take first small size for understanding

suppose i took (4,8) rectangle that ends at (3,2).

(1,1) – – – – – – (1,8)

…..so on

so on …..it's end at (3,2).

For(2,4), ends at (2,1)

For(3,6) ends at (2,5)

For(4,8) ends at (3,2)

For(5,10) ,ends at (3,8)

For(6,12) ends at (4,3).

For(7,14) rectangle ends at (4,11)

For (8,16) ...ends at (5,4)

We can get some idea that,

For Even number of rows, column increases 1 by previous column.

For Odd number of rows, difference of the present column and the previous even number column we get that particular column.

For row, the value repeats two times from row 2.

In this problem, (100, 200) i.e.

Even number row,

So column value must be 50 for 200 columns and row value must be 51 for 100 rows.

For even number of rows and columns,

Condition: Column =2*Row

(R, C) = {((Row/2) +1), Column/4} (this is generalize formula for this type of question).

you can take first small size for understanding

suppose i took (4,8) rectangle that ends at (3,2).

(1,1) – – – – – – (1,8)

…..so on

so on …..it's end at (3,2).

For(2,4), ends at (2,1)

For(3,6) ends at (2,5)

For(4,8) ends at (3,2)

For(5,10) ,ends at (3,8)

For(6,12) ends at (4,3).

For(7,14) rectangle ends at (4,11)

For (8,16) ...ends at (5,4)

We can get some idea that,

For Even number of rows, column increases 1 by previous column.

For Odd number of rows, difference of the present column and the previous even number column we get that particular column.

For row, the value repeats two times from row 2.

In this problem, (100, 200) i.e.

Even number row,

So column value must be 50 for 200 columns and row value must be 51 for 100 rows.

For even number of rows and columns,

Condition: Column =2*Row

(R, C) = {((Row/2) +1), Column/4} (this is generalize formula for this type of question).

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