Riddle me this

Several young people who appeared to be students of the academy began handing out the numbers one by one. Soon enough James received his and started heading towards his group.

'There's probably around one-thousand five hundred people here, so I guess my group will have fifteen people in it. They really are going after the group mindset, aren't they?'

"Is this group forty-seven?"

After counting the groups of people he could see James found what he believed to be his group, his group was standing uncomfortably close to the old man who was giving the introduction. Apparently, they were eager to make a good first impression.

"Yes, this is the right group, welcome. My name is Elias; I'm from Xinard."

"James; I'm from Angaria."

"Oh, I see.

Okay everyone let's group and make sure we're not in the way. They should tell us what our task is soon."

Apparently, this youth wanted to take charge of the group and run everything. It seemed that he had failed to get in the right mindset for this school already; although he would still be able to redeem himself as long as he wasn't too overbearing.

Once everyone was placed in their correct groups, the students from earlier were each assigned to a group to watch over. They would probably be responsible for reporting the quality of the members of each team.

"Our first round of testing will be conducted right here in your groups. To begin we will be testing logical thinking and problem-solving. The test criteria will be your ability to work effectively as a team and communicate your ideas effectively. Your ability to answer the questions given will be factored as well."

"Seeing as everyone is ready, we may as well begin the first round of tests now."

"Your whole group will be placed in a line in descending height order; you will be facing towards the back of the person in front of you, you will all be given a hat that is either black or white.

You will only be able to say the word black or white to guess the colour of your own hat; you will be disqualified if you make any sort of gesture or another sound to convey information to your teammates.

You must correctly guess the colour of fourteen out of fifteen hats to pass this test. You will be given fifteen minutes to come up with an answer for this riddle then you will be able to put your theory to the test. If you give two wrong answers, your whole team will be disqualified.

If you have prepared your answer early then you will be allowed to take the test early. Naturally, if you are caught passing your answer to another group, you will be disqualified as well.

Begin."

"Okay, did everyone get that. I know they said we couldn't give any cues to our teammates, but this is impossible without it trust me."

'Oh god, why did I have to get paired with a headstrong idiot, the best part is people will believe him because he sounds so sure of himself. What a pain in the ass.'

"What are we going to do for the signal then, I can't think of any ways to cheat without them noticing straight away."

"I don't know either, but this must be what they were talking about when they said looking at something from every angle."

"Or they meant actually trying to solve the riddle, why do you say it's impossible without even trying?" James didn't want to risk his chance of entering the school on these people who were going to flounder about for fifteen minutes and achieve nothing.

Funnily enough, they were approaching the problem from the wrong angle. The problem was definitely solvable, but they hadn't even attempted it. At this rate, Elias would cost them the win.

"I've been tested my whole life, I've answered countless riddles but never heard of anything like this. There's no way it can be done, or I would at least have attempted it before."

"Amazing, you haven't heard of it, so it doesn't exist? I believe that is called a narrow world view."

"Alright, if you're so smart, facer, then tell me, what's the answer?" One of the boys who had been silently revering Elias the whole time finally decided to try and defend him. Naturally, he had to throw in a pointless insult as well.

"Well to start with we pick a colour, white or black it doesn't matter. The person at the back of the line, in this instance that would be you, Elias, calls out either black or white, this doesn't mean the colour this indicates a state.

For example, if our chosen colour were white, then it would be either an odd or even number of white hats depending if you called black or white. We can only say those two words, but that doesn't mean we can't attach a different meaning to them.

Just from that everyone else should be able to work out the colour of their hats with absolute certainty. You would have a fifty per cent chance of guessing your hat colour but seeing as we're allowed one failure then that's fine."

"That would never work, just keep quiet and let us think of an actual answer!" The boy didn't even stop to consider James' answer, he just automatically said it was wrong and moved on. He had just tried to throw away the golden ticket.

"He's not wrong Silas, take a moment to think about it, and you would know that. Don't let your prejudice cost us an easy win."

A stern looking girl gave James a friendly nod as a show of courtesy, clearly, there were at least some sane people in the group. So far the rest of the group had just merely been watching, listening to the conversation.

Taking a look around James realised that most groups had elected a leader of sorts, he saw some of the people from Angaria, it appeared they were being shunned in their groups as well.

It was a shame James had no way to communicate with them, or he would give them the answer to increase the prestige of his city, although if all of them had the answer, then it would definitely be suspicious.

"Okay, does everyone understand the method? Now that we know the correct method I will beat you down if you mess this up for me. We'll use black as odd and white as even." Clearly, Elias wanted to study at Elanaid, and if anyone cost him that, then he would definitely not be happy with them.

After a collective nod from the group, Elias approached their group's examiner and told them the group was ready to take the test.

"Already? It's only been about two and a half minutes, are you sure you want to go?"

"Certain."

"Allow me to conduct this one; they are the first group after all. They deserve a reward for their courage."