# Thread: Cool problem of the day!

1. ## Re: Cool problem of the day!

Post more questions please I wanna try solving them.

2. Originally Posted by AlbertEinstein
Post more questions please I wanna try solving them.
Originally Posted by 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).
.

3. ## Re: Cool problem of the day!

Originally Posted by 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).
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?

4. ## Re: Cool problem of the day!

Originally Posted by 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?

5. ## Re: Cool problem of the day!

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.

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