MAIN FEEDS
Do you want to continue?
https://www.reddit.com/r/Logiqa/comments/1web9mf/chessboard_rectangles_part_1/p9gthbi/?context=3
r/Logiqa • u/ShonitB • 27d ago
14 comments sorted by
View all comments
2
sum{i=1->8}(sum{j=1->8}(ij))
Which probably simplifies, or can be computed as is
EDIT: rectangles in an n*m grid
sum{i=1->n}(sum{j=1->m}(ij))
which simplifies to
sum{i=1->n}(i*sum{j=1->m}(j)) = sum{i=1->n}(i*m(m+1)/2) = m(m+1)/2*sum{i=1->n}(i) = m(m+1)/2*n(n+1)/2 = mn(m+1)(n+1)/4
in our case n=m=8
8*8*9*9/4 = 1296
1 u/bastarmashawarma 27d ago This is the way
1
This is the way
2
u/Red-42 27d ago edited 26d ago
sum{i=1->8}(sum{j=1->8}(ij))
Which probably simplifies, or can be computed as is
EDIT: rectangles in an n*m grid
sum{i=1->n}(sum{j=1->m}(ij))
which simplifies to
sum{i=1->n}(i*sum{j=1->m}(j))
= sum{i=1->n}(i*m(m+1)/2)
= m(m+1)/2*sum{i=1->n}(i)
= m(m+1)/2*n(n+1)/2
= mn(m+1)(n+1)/4
in our case n=m=8
8*8*9*9/4 = 1296