MATRIX
(CAT 2018)
You are given an n×n square matrix to be filled with numerals so
that no two adjacent cells have the same numeral. Two cells are called adjacent
if they touch each other horizontally, vertically or diagonally. So a cell in
one of the four corners has three cells adjacent to it, and a cell in the first
or last row or column which is not in the corner has five cells adjacent to it.
Any other cell has eight cells adjacent to it.
1) What is the minimum number of different numerals needed to
fill a 3×3 square matrix?
2) What is the minimum number of different numerals needed to
fill a 5×5 square matrix?
3) Suppose you are allowed to make one mistake, that is, one
pair of adjacent cells can have the same numeral. What is the minimum number of
different numerals required to fill a 5×5 matrix?
a) 4
b) 16
c) 9
d) 25
4) Suppose that all the cells adjacent
to any particular cell must have different numerals. What is the minimum number
of different numerals needed to fill a 5×5 square matrix?
a) 9
b) 25
c) 16
d) 4
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