Count 'em All 7!

Probability Level 2

Count the total number of $3\times2$ rectangles in the $5\times5$ grid above.

Details and assumptions:

Dimensions are expressed as width $\times$ height . Thus a $3\times2$ rectangle (that is, a rectangle of width 3 and height 2) is considered to be different to a $2\times3$ (width 2 height 3) rectangle, in this case, you only want the $3\times2$ rectangles, not the $2\times3$ ones.

This is one part of Quadrilatorics .

The answer is 12.

1 solution

Kenneth Tan
Mar 17, 2016

From this note , we know that the number of $x\times y$ rectangles in an $a\times b$ grid given that $x\leqslant a$ and $y\leqslant b$ is $(a-x+1)(b-y+1)$

Now, substitute $a=b=5$ , $x=3$ , $y=2$ into the equation above we would get $12$ .

Count 'em All 7!

This is one part of Quadrilatorics .

The answer is 12.

1 solution

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