100 wise men- with hats!

So a riddle was presented to me as follows (parentheses added for flavour): A mad king had 100 wise men in his court. He told them one day he would line them all up, single file, tallest to shortest (except the last guy who was also tall because why not?) and place on each of their heads a hat (displaying a couple of red and a couple of blue hats as he said this). They could only say the color they thought their hat was, all hats would be of the colors presented. If they guessed correctly they would be silently shuffled into the next room, and allowed to live out their days. If they were wrong, they would be silently shuffled into another room and killed. They were barred from saying anything else, or from doing anything else, so no cheating could occur. They were allowed to confer before lining up though, and anything possible in the universe could be discussed, all manner of logic and possibility used. Once lined up, the king would place one hat atop each head and then ask the man in the back of the line what color his was. The question is, what is the maximum number of wise men that could be saved, guaranteed, given these conditions?

The commonly believed answer is 99. This involves encoding each answer past the first into the answer before it, it involves stacking responses on observation, this answer can be easily found online. This, however, is not the correct answer. Widely believed, yes, but incomplete.

The issue is that there seems to be no way the first man's hat color can be known, he simply had to hope the encoding and structure of the line allowed him to say his own hat color correctly.

Here is my story (from the perspective of the Omega man):

I stood there helpless, unable to contribute, but still nervous. I already knew that all I had to do was say my hat's own color. I didn't even have the illusion of contribution by holding the fate of others in my hand as well.

My turn came and went, and I went with the other men into the room. They had already stopped counting, and looked saddened, each to a degree that corresponded to his proximity to the end of the line. We had lost the first man. What could we do now though? The deed had been done, we had all been spared, was that not enough? It had to be now.

Life went on, and it seemed like everyone else had forgotten, I even did for a time, accepting the facts. But something gnawed at me from within. Perhaps it was the fact that I had no choice from the start, besides my own life or death; nor did I have the illusion of choice, albeit a dark one.

I could not help wondering what might have happened if the hats fell differently. We had a 50/50 shot of coming out unscathed, right? Why was the king so cruel, knowing our plans? I tried to speak to the other men about the issue, but no one seemed to understand why I even brought up that unfortunate sacrifice. At first they declined to speak, and then they mocked me, then they imprisoned me for a time.

This repeated, and I could see in their eyes the pain growing. I could tell they did not dream like I did, nights haunted with nightmares left unremembered or buried. Everything within the crowd cried out, and I heard every scream.  My only solace was a singular beauty that snuck in on occasion.

Time continued to pass, and our knowledge grew as our wisdom shrank. We invented all manner of things and with each step forward I took one back to that fateful night, considering "what if?"

Somehow this kept me ahead of the curve, but in a way I could not explain, and did not understand. That was when I realized time travel was on our horizon. I spoke of it in relation to the initial puzzle, but my words were met with horror. I had not considered that in telling the man his own hat color, he might sacrifice us all to spare his own life, given the circumstances. In my dreams I considered doing it anyway, my lack of choice inverting into grabbing the entire scenario by the horns and giving it up to the first man in line. Alas, true time travel never seemed to happen, there would be evidence in my own personal timeline, right? So I continued dreaming as best I could, trying to drown out the noise.

Then came the day quantum entanglement was discovered. It opened a whole realm of possibility: alternate dimensions, communication across time and space unbound by traditional physics. Eventually time itself was tied up in the grasp of this ground breaking idea, lying just beneath the surface. Even if I could not travel back, I could communicate back, and that was enough. I crafted the machine out of sight of everyone else, although the noises could certainly be heard. As suspicious men came around, I learned to muffle the sound better and better until it was virtually imperceptible. One day it was done, and so was I.

I called back through time to the man: "your hat is red." Every night I sent this message in a new way, still unfamiliar with how the machine worked, but nothing changed. I received dream after dream until I could see the scenario clearly:

The man considered my words, for varying lengths of time, but invariably stuck to the agreed upon plan. Did he not believe me? Or, like I, would he not kill 99 people to save himself? Then I noticed something funny, the timeline changed, I could see it happening. He had a blue hat now! I almost said red again out of habit, but caught myself, and considered maybe that had been the issue? I could have been lying about his hat color, which would have destroyed the whole timeline! What kind of madman would consider that though? But I almost did it on accident. Anyway, I caught myself and called out "your hat is blue." The man once again paused for a long time. That's when I noticed that while his hat had changed, so had everyone else's. If he had said blue, he would have once again killed everyone else in the process. "Red."

I stood in shock. The king was doing this on purpose. Knowing our plans, he was intentionally killing the first man every time. I ran out into the street yelling "@$&# the king!" All night long I yelled it, crying out for my own death, but it did not come. In fact, not a single word was heard that night across the kingdom. I was alone.

I could not reconcile this existence and ranted and raved, nothing made sense, and I made sure everyone knew it, but no one listened. By the dawn's light I was stark raving mad, this was no puzzle I wanted to be a part of, or so I thought. Light brought the men back, and I was once again imprisoned, presumably forever, it felt like forever anyway as my mind raced against every wall and down every corridor. In the prison there were others like myself, and while they could not stop these thoughts, they did manage to slow them down to the point where I desired freedom to the confines, and I was clever enough to get it. I was once again free, but homeless and downtrodden, a pariah.

I was given refuge however, and eventually stood back up, once more considering what was happening. Why was the first man pausing, first long, and then short? It was not to count, that much was clear. The puzzle contained its own puzzle, and so I dove in again, with nothing better to do.

I played the game, keeping a low profile, and wandering the castle. I still observed the king, I always thought his madness obfuscated a kindness, and when my anger subsided, I watched him here and there. I noticed he would get caught up sometimes, staring at the red lights he had hanging everywhere. I grew curious, and so I took a string of them down to examine them myself. I ran all manner of experiments examining these lights, their shape, composition, until I finally recognized something strange about their color. When measured a certain way, half the lights produced one result, and the other half another. I didn't quite catch it at first, but the king seemed to notice something change in me, and left his journal out one night. I snatched it up, reading what appeared to be the ravings of a madman, but they were ravings I had become accustomed to. Ideas flooded my mind, it was truly overwhelming, but one thing stood out. It was the mention of a color I had never seen before. As I read further I considered a new possibility: what if I had been blind to this color all along? It seemed reasonable, with infrared and ultraviolet sneaking into the spectrum long after the visible colors had become known. Then it stood out like a sore thumb. I could hardly sleep, I shouted for joy inside, hope encroaching on me now, rather than vice versa. My dreams became sporadic, but my love was back with much higher frequency than before (she is not unknown to me, by the way). She seemed to be stabilizing the ship as I worked out this last piece.

I saw the lights differently now.

I finally made it back, and simply said. "Your hat is green." The man looked right at me, he did, which was weird because I was pretty sure I would have come across like a ghost or something based on how I was communicating. And he simply said "Green." I noticed a sparkle in his eye that I had not before, and the king, despite the rules, actually whispered "nailed it." I could see the surprise in the other men's eyes, unfamiliar, as I had been, with this color. The next man paused for a very long time, now his own life on the line with nothing but the strange word uttered, confirmed to be correct, but with seemingly no new information. That was until he noticed the string of lights around the room. It took some time for his eyes to adjust, but I could see the shift just the same as before. He called out the color of his hat.

This continued for each man, most unable to comprehend fully until it was their turn, but each considering from that first word spoken.

It got to my turn, it was surreal to see myself in that position, but as soon as I was at the head of the line, I heard a resounding echo from all around. "Your hat is green."

The Christmas lights had been strung up all along. I did not know exactly what to do. I knew my hat color, you see, but I was too stunned to speak. In this, the alternate timeline, I realized that was the moment my blue eyed beauty knew exactly where to find me. But all I saw was her running through the front door of the castle right for me. It was something like a dream. It was something like this. Boy was it something. I Hope it never ends.