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Question Number 22043 by Tinkutara last updated on 10/Oct/17

In how many ways we can choose 3

squares on a chess board such that one

of the squares has its two sides common

to other two squares ?

Answered by Rasheed.Sindhi last updated on 10/Oct/17

Let the square which shares its

two sides is named as^{'} {main}^{'} .

Case - 1 : When the main is on

the corner . 4 squares

Making corner square as main

only one triple of squares can be

slected .

4 corners \to 4 triples of squares .

Case - 2 : When the main is on the

edge but not the corner . 24 squares

Making edge square (without

corners) as main 3 triples of

squares can be acieved .

24 squares \to 72 triples .

Case - 3 : When the main is other

than corner and edge squares .

36 squares .

Making any non - edge square

as main 6 triples can be achieved .

36 squares \to 216 triples .

4 + 72 + 216 = 292 triples of squares .

In 292 ways such triples of squares

can be chosen .

Commented by Tinkutara last updated on 11/Oct/17

Thank you very much Sir!