Pyraminx - Unscrambled tips (fairness) ?

Radu (2011-11-26 13:28:34 +0000)
This topic might sound silly, but I think this “problem” is much more interesting than it appears. It came to my mind while I was practicing the pyraminx and realized I scramble every time all the tips, even if the scramble didn't show that. I just want to make the solve as hard as possible every time. I asked myself how fair is not scrambling all the tips? Below is the explanation I find most realistic. What I’m going to explain in this topic is why I think that in a pyraminx scramble all tips should be scrambled and not let the actual random state scrambler decide about it. For me it’s obvious… unless we consider a solved puzzle = scrambled one, if the scramble gives us a solved puzzle – which I understand is not true after the last e-mails. For the beginning, the main point is that the pyraminx can be regarded as 2 puzzles in 1…we just don’t see it like this. It’s the puzzle scrambled by the big letters (U, D, R, B), the main body, and the puzzle were we scramble by the small letters (u, d, r, b), the tips. Let’s imagine that we have 2 Rubik’s cubes, connected by a stick from one’s center face to the other and we would regard this as one puzzle. Obviously, if we would generate a scramble we would want both cubes to be scrambled and not let one of them in a solved state. Right? We can now think of 5 or 10 Rubik's cubes connected like this. We would need to scramble all of them to be fair. We wouldn’t give to a competitor 4 cubes to solve and to another 5. Even if it sounds silly, we have to admit that the tip of the pyraminx is a puzzle itself…it’s crazy simple to solve, but it’s the simplest puzzle we can have (well…there’s also a 2D 1x1x2, but let’s not go into details). It has a solved state {0} and 2 scrambled states {1,2}. One could even do a competition on such a puzzle. The tip of the pyraminx is just one of the cubes in the example above. The same goes for the Pyraminx. If we look at a tip and the rest of the pyraminx it’s almost a 1x1x2 cube. You have to twist it, to get it solved. It’s a puzzle with only 3 states, but it's a puzzle itself. The tip is totally independent of the rest of the pyraminx which is the 2nd puzzle. So, there are 2 [i:2u92jmzb]different[/i:2u92jmzb] and [i:2u92jmzb]independent[/i:2u92jmzb] solves. Leaving the tip unscrambled is like giving a solved puzzle to the solver. Let’s extrapolate and imagine now another example. We have a huge ball with 100 tips. You have to solve the puzzle by bringing all 100 tips to the right position in order to solve this. Would it be fair to give to a competitor the puzzle scrambled with all 100 tips and to another one with only 75? This will obviously become just a matter of luck. It’s like giving someone to solve 100 puzzles and to another one 75! Of course, the pyraminx is more complex and has also the body which has to be solved by some algorithms and the tips by some others, but technically it is a puzzle with n tips, where n=4. As long as we can scramble a puzzle, why not do it? And why accept unscrambled tips? So, what I said in the beginning could be considered false. The Pyraminx is not 2 puzzles in 1, but 5 puzzles in 1. We have the main body + 4 tips, which compose the puzzle. Therefore, it would be fair to always scramble all the tips of a pyraminx, if we want to have a fair scramble, otherwise some will solve a different number of puzzles than others. Pyraminx is confusing because it's the only WCA puzzle which is actually made of more puzzles (we just don't see it like this) and also because n=4 it's a small number doesn't seem to influence the solve too much. Solving 1 tip is less then 0.5s but it actually could be a puzzle with much more tips like in the example above where it's obvious that all the tips should be scrambled in order to be fair with all competitors. I don’t pretend the regulations should be changed as we have to be consistent with the scrambles in the past and all the competitors must compete under the same rules, but I just wanted to point this out and see some other opinions about this issue. I hope I will not be the only one who sees the problem like this. Thanks for reading! EDIT: Slightly edited @ 13 Jan 2013 for some rephrasing.
Dene (2011-12-10 00:00:48 +0000)
I am inclined to agree that the way pyraminx is scrambled regarding the tips is an issue, but I don't know if scrambling all of the tips is the correct solution. Personally I think the best solution is to remove pyraminx as an official event, or else not scramble the tips at all, as they add nothing to the [i:3l1671oe]puzzle[/i:3l1671oe] factor.
Pedro_S (2011-12-10 20:26:15 +0000)
Agreed with Dene. No scrambling of the tips would be better, even phisically, since then we could use the Tetraminx, making grip better.
Alukret (2012-02-09 11:59:50 +0000)
remove pyraminx from official events? omg. pyraminx is the puzzle, older than a Rubik's cube, and we can't remove it because we respect the inventor, at least. ofc, pyraminx and 2x2 - easiest puzzles, and sometimes can be solved extremely fast, but averaging fixes case of luck. Radu, I start practising pyraminx last summer, like you I always scramble the tips, because better to be ready for bad scrambles. I think there is no dispute, Radu is totally right, and the man who coded a scramble program (Michael Gottlieb? or anyone else) should change some lines in his code.