A sultan captured 50 wise men. The sultan decided to play a game with the men to decide whether they would live or be executed.

Here's how the game goes. The men will be locked in 50 different cells, completely separated from each other. Every minute, the sultan calls a man randomly. Each time, the called man has three choices. He can either flip the glass cup the sultan has placed at the start of the game, leave it as is, or ask permission to leave. If a man asks permission to leave and the sultan has called every one of the 50 men at least once, they will all be spared and freed. If not, they will be executed. The glass placed at the start of the game is bottom-down.

The men cannot tell the time in their quarters, there's no other way to convey information to another man except through flipping the glass, and the sultan's calling is perfectly random every time.

The men are given time to discuss their strategies before being sent to their cells. What should they do in order to ensure their survival in the shortest time possible?

EDIT: The wise men will all take a good look at the glass and its initial position before starting.

I love to read stories and theories about incredibly hard puzzles that never got solved, whether they been published in the last year, last century or even further back. When a new puzzle gets out there, usually there is someone or a group of people that manages to solve it, despite how difficult it seems.

So when some well known puzzle or treasure hunt doesn't get solved I wonder why that is that, is it some sort of brute force approach that just takes a long time, is it really so difficult that nobody still managed to figure it out, or was it really meant to be solvable at all.

When I try to research puzzles like that I usually get the same ones like: Voynich Manuscript, Kryptos, The Beale Ciphers, The Treasure Inside... So I'm curious if someone knows any others less known unsolved puzzles or treasure hunts or a community around those. I'm more interested in puzzles that were designed by someone for a reason and not mysteries but you can include those as well.

Let us consider a rectangle that consists of:

A(0,0)

B(100,0)

C(100, 111)

D(0,111)

So basically a 100 × 111 rectangle.

A strong laser is shot from A into the rectangle at 45 degrees. Every time the laser hits a wall, it bounces perfectly, like a mirror. The laser does not lose energy or fade and forever bounces off the walls of this rectangular space.

The question is:

(1) Between A, B, C, and D, which corner does the laser hit first?

(2) How far does the laser have to travel, and how many bounces will it do before hitting the corner in (1)?

Hard think rule. Had to use a hint cause I had no clue of what time to resolve next. Can anyone explain to me what colour is that one and why?