"So I have 3 thoughts just from the first 2 dice rolls: first, the numbers are fairly low. So this means that it's unlikely that there's some kind of system where you have pluses and minuses. Because it's unlikely that they'd cancel each other out to get close to zero?

Second, the first 2 rolls have many of the same numbers in both, but not in the same order. But the values are super-close to each other. So it's unlikely that you have a system where the position matters, because then it's unlikely for the numbers be placed in the new order in a way that cancels each other out so you get close to the last order of essentially the same numbers?

Third, they're also both even. Which is a vague hint that the end result only grows by an even amount?

So now I'm thinking, we probably have a rule where order doesn't matter, and we add an even number of points, and there are only a few different dice results that can add points. 

If we compare the numbers in roll 1 and roll 2, the second one has the same numbers except for one more 3, and it has an associated number 2 more. So 3 increases the answer-number by 2 is a perfectly fine and good hypothesis to get started with.

That means that all the other numbers in the first two sequences put together, the 1, 4, 5 and 6, add 4 to the answer-number, right?

After this, you mentioned one sequence that resulted in 12, and another sequence that resulted in 12. And what I noticed was that both had two 3s and two 5s. So two 5s add 8 to crate 12, or one 5 adds 4 was a hypothesis explaining all outcomes. 2s add 8 also technically speaking make sense for the two sequences resulting in 12, but it's unlikely that the the one die we didn't see was a 2. So I think the rule is: 3s adds two to the number, and 5s add four to the number, because it explains the pattern perfectly, and 2s add eight required the one die we didn't get to see to be a two, making it a shakier hypothesis."

"Very good that's correct. Does anyone want to give a guess as to how the rule relates to the name of the puzzle?"

The kids seem to have no idea.

"Alright, let's start by breaking down the name. Who can tell me what petals are?"

"They're analogous to leaves, placed at the end of a flower's stem, where they help with photosynthesis?"

"That's a very technical answer, petals do help with photosynthesis but they also help attract pollinators and when people, at least where I come from, think about flowers they're often thinking about how the petals of the flower look. A Rose is a type of flower. Does that give anyone any ideas?"

It really doesn't, actually!

"Alright, I'll just explain, the name of the puzzle is meant to be a hint at the arrangement of the dots on the dice. If there's a dot in the center of the face that's the rose and the petals are the dots arranged around it. 2, 4, and 6 don't have a dot in the center so they don't have any petals and 1 has a rose but no petals around it."

The children just seem weirded out. "It's a good mnemonic, I guess?"

"Alright, for the rest of the time you can either do your normal work or form small groups and take turns making up your own rules and seeing if the other people can figure them out."

They spend the time inventing their own rules, or just using their phones to take cloze tests and going over flashcards, very intently. The children display a very intense level of concentration. One of them is very slowly pacing the classroom, trying to understand some particularly tough concept and explain it to themselves.

"Should one of us see if they need help?" she whispers to Clarissa regarding the pacing child.

"They know to ask for help! It's one thing that really gets drilled into them." Eventually, someone walks up to Clarissa. "Could you explain the parts of the entropy formula, again?"

"Well, the first part, the innermost part, is how many 1s and 0s you'll need. Then of course you have to multiply that by the chance that you get that symbol. You do this for all your possible symbols. But of course, the innermost part is always negative, and you want a positive value. So you negate it again.

And you want the biggest number, right? And the way you do that is that you try making a square: basically, you want the 2 inner parts to both be the same, because going from 5*3 to 4*4 is bigger than vice versa, it's a bigger percentage increase for the smaller one of the two."