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###
# Counting rectangles
# Problem 85
#
# By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains
# eighteen rectangles:
# Although there exists no rectangular grid that contains exactly two million rectangles,
# find the area of the grid with the nearest solution.
###
# blackpenredpend: https://www.youtube.com/watch?v=Uq9OXC0Gzgw
using Base.Iterators
const TARGET_RECTANGLES = 2_000_000
combinations_2(n) = (n * (n - 1)) / 2
dist = Inf
for width in countfrom(1), height in 1:width
count = combinations_2(width + 1) * combinations_2(height + 1)
global dist = min(dist, abs(TARGET_RECTANGLES - count))
if dist < 3 # I just tested a bunch of different threshold
println(width * height)
break
end
end
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