Comment by selcuka
6 hours ago
So it was more of a physical problem rather than a mathematical one [1]:
> Harshbarger says he and his colleagues always knew the dice were mathematically possible.
> The mystery was whether that mathematical solution could be translated into the physical geometry of a die — something that could actually be manufactured and rolled.
> “I knew there was a solution with something crazy like 1,440 sides for each die,” he said. “That's not makeable.”
[1] https://www.cbc.ca/radio/asithappens/dice-mystery-board-game...
I think it is not a matter of whether it is more of a "physical problem" or a "mathematical one". They knew a solution existed but it was physically unfeasible, which prompted them to mathematically optimize the solution by using fewer sides. They found a solution using only 120 sides, and a lower bound of 30 is known but brute-forcing it is still computationally expensive.
Reword it as “the smallest possible set where X is still true” and you combine both.