The Box of Pythagoras

Once upon a time, a terrible dragon, called a Dorgon was terrorizing the people of the greek island of Samos; it had seven fire breathing heads and each head had hair of hissing snakes.
The only thing that could defeat the Dorgon was the gaze of a male and female Samosian Mongoose.
The gaze of a male and female Samosian mongoose could turn the Dorgon to stone.
Unfortunately, because male and female Samosian Mongeese looked identical it was impossible to tell which was which
"We must have one male and one female to turn the Dorgon to stone", said King Polycrates, the ruler of Samos, "But how do we tell which are male and which are female?".
To solve the Problem, King Polycrates summoned the mathematician and philosopher Pythagoras and, presenting him with four mongeese said "You must find out which of these mongeese are male and which are female because we need one male and one female to gaze at the Dorgon and turn it to stone".
Pythagoras thought about the problem for sometime until, eventually, he had an idea.
He ordered for a glass box to be constructed that was divided into 4 compartments.
Then Pythagoras put one of the four mongeese in each of the compartments.
And once he had done this, he took it to Polycrates to show him.
"Though I have not discovered which mongeese are male and which are female", said Pythagoras, "This box should solve the problem. Each side of the box, you see, shows a different arrangement of the mongeese, thus if, for example there were two female mongeese on the right side of the box and two males on the left side, then through the front and back of the box you would see one male and one female. If on the other hand, there are two females at the front and two males at the back, then through the left side and right side you would see one male and one female. Even if three of the mongeese in the box are male or three female, through one of the sides of the box you would still see one male and one female. Thus, to turn the Dorgon to stone, you simply have to show it all four sides of the glass box and the side that turns it to stone is the side that shows one male and one female".
And when the box was taken before the Dorgon and all its sides shown to the creature, the Male and Female mongoose at the front of the box glared at it and their glare alone turned the monster to stone.
Thus Pythagoras saved the people of Samos.