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The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $(0,0),(0,21)$ and $(21,0)$ is
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190
$x+y=21$
The number of integral solutions to the equations are $x+y < 21$, i.e., $x < 21-y$
$\therefore$ Number of integral coordinates $=19+18+\ldots+1$
$=\frac{19(19+1)}{2}=\frac{19 \times 20}{2}=190$
The number of integral solutions to the equations are $x+y < 21$, i.e., $x < 21-y$
$\therefore$ Number of integral coordinates $=19+18+\ldots+1$
$=\frac{19(19+1)}{2}=\frac{19 \times 20}{2}=190$
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