Cool problem of the day!

[AlbertEinstein]

Post more questions please I wanna try solving them.

[qwerty44]

Post more questions please I wanna try solving them.

Here is another good one:


The lengths of the sides of the octagon are 1, 2, 3, 4, 5, 6, 7 and 8 units in some
order. Find the maximum area of the hexagon (square units).

.

[largarithmic]

Here is another good one:


The lengths of the sides of the octagon are 1, 2, 3, 4, 5, 6, 7 and 8 units in some
order. Find the maximum area of the hexagon (square units).

This reminds me of a really neat (but actually pretty hard) problem:

Given a polygon, we define a "flip-stick" to be the following process: take a 'cut' of the polygon (i.e. a line segment that cuts the polygon into exactly two new polygons), then take one of the polygons you produced, reflect it and stick it back on: as long as the flipped thing doesnt overlap with the rest of the polygon, in which case the move is illegal. So essentially you cut of a bit, flip it and stick it back on if its allowed. Does there exist a sequence of "flip-sticks" that can transform a square into an equilateral triangle?

[qwerty44]

Here is another good one:


The lengths of the sides of the octagon are 1, 2, 3, 4, 5, 6, 7 and 8 units in some
order. Find the maximum area of the hexagon (square units).

I got 30 units^2.

Anyone else care to try?

[qwerty44]

The least common multiple of positive integers a, b, c and d is equal to a + b + c + d.
Prove that abcd is divisible by at least one of 3 and 5.