Given big rectangle of size $x, y$, count sum of areas of smaller rectangles.
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Let's say we have two integers $x$ and $y$ that describe one rectangle, if this rectangle is splitten in exactly $xcdot y$ squares, each of size $1cdot 1$, count the sum of areas of all rectangles that can be formed from those squares.
For example if $x = 2, y = 2$, we have $4$ rectangles of size $(1,1)$, $2$ rectangles of size $(1, 2)$, $2$ rectangles of size $(2, 1)$ and $1$ rectangle of size $(4,4)$. So the total answer is $4cdot 1+ 2cdot2 + 2cdot2+1cdot4 = 16$
Is there easy way to solve this for different $x$ and $y$?
combinatorics summation area
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someone123123
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up vote
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Let's say we have two integers $x$ and $y$ that describe one rectangle, if this rectangle is splitten in exactly $xcdot y$ squares, each of size $1cdot 1$, count the sum of areas of all rectangles that can be formed from those squares.
For example if $x = 2, y = 2$, we have $4$ rectangles of size $(1,1)$, $2$ rectangles of size $(1, 2)$, $2$ rectangles of size $(2, 1)$ and $1$ rectangle of size $(4,4)$. So the total answer is $4cdot 1+ 2cdot2 + 2cdot2+1cdot4 = 16$
Is there easy way to solve this for different $x$ and $y$?
combinatorics summation area
asked 1 hour ago
someone123123
411214
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let's say we have two integers $x$ and $y$ that describe one rectangle, if this rectangle is splitten in exactly $xcdot y$ squares, each of size $1cdot 1$, count the sum of areas of all rectangles that can be formed from those squares.
For example if $x = 2, y = 2$, we have $4$ rectangles of size $(1,1)$, $2$ rectangles of size $(1, 2)$, $2$ rectangles of size $(2, 1)$ and $1$ rectangle of size $(4,4)$. So the total answer is $4cdot 1+ 2cdot2 + 2cdot2+1cdot4 = 16$
Is there easy way to solve this for different $x$ and $y$?
combinatorics summation area
asked 1 hour ago
someone123123
411214
Let's say we have two integers $x$ and $y$ that describe one rectangle, if this rectangle is splitten in exactly $xcdot y$ squares, each of size $1cdot 1$, count the sum of areas of all rectangles that can be formed from those squares.
For example if $x = 2, y = 2$, we have $4$ rectangles of size $(1,1)$, $2$ rectangles of size $(1, 2)$, $2$ rectangles of size $(2, 1)$ and $1$ rectangle of size $(4,4)$. So the total answer is $4cdot 1+ 2cdot2 + 2cdot2+1cdot4 = 16$
Is there easy way to solve this for different $x$ and $y$?
combinatorics summation area
combinatorics summation area
asked 1 hour ago
someone123123
411214
asked 1 hour ago
someone123123
411214
asked 1 hour ago
someone123123
411214
asked 1 hour ago
someone123123
411214
asked 1 hour ago
someone123123
411214
411214
add a comment |
add a comment |
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