# Message #3292

From: Thomas Lehéricy <thomas.lehericy78@orange.fr>

Subject: Greetings

Date: Tue, 23 Feb 2016 11:15:46 +0100

Hello,

I am a postgraduate student in mathematics, and amateur cubist. 4D puzzles had already caught my attention a few years ago, but I never went as far as trying to solve them until recently. I have currently solved the 2^4 (one try, 199 moves), 3^4 (three… no, four tries, best 709 - but I’ll come back to that later) and 4^4 (one try, 1775 moves). I developped a Fridrich-like method (cross, then first layers, and finally the last layer), using the keyhole method to solve the first layers since it’s much more simple than standard F2L. After a successful (but very long) try with 4D commutators, I realized that the last face/cube behaved exactly like a 3D cube and could hence be solved the same way if he was correctly "oriented" - provided we take care of "undoing" the effects of the move on the other 3D faces. A way to solve the last face/cube was hence to solve it like a 3D cube, with "regrips" (cube rotations), so that we only turn the same "2D face". It would be like we only had the right to turn the lower face of a 3D cube, and had to rotate it every time to make sure the face we want to turn is facing down. Of course this can be optimized to minimize the number of regrips.

But Fridrich was never known to yield short solutions to the 3D cube, so I tried adapting another method - namely the human Thitlethwaite method. The likeness is probably only superficial, but my idea came from here: reducing the "legal" moves more and more while taking care of parity problems at each step. The cube won’t start looking solved until the middle of the solve, and even then it will seem to remain "half-solved" until the last ten moves. This method has the downside of being tedious and conterintuitive (parity problems are especially tiresome to spot), but I am confident that it can lead to solutions of length around or under 200 moves if implemented in a computer program.

I have recently done a solution in 205 twists using this method. However, I used a software at one point in the solve. The last step of my method requires to solve three 3D cubes with as few moves as possible, a bit like Matthew’s solution. As Matthew Sheerin stated in his message announcing his latest record (https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/3102), this step (solving a 3D 3x3x3) is difficult to optimize, and the way he did it (in around 40 moves, counting "regrips") is impressive. I am not experienced at all in 3D fewest move solving, so instead I used a solver to get short 3D solutions. The rest of the solution, taking into account adapting and including these 3D solutions to the global 4D solution, was done by me in around a week of time.

I don’t expect it to be valued the same as Matthew Sheerin’s solution (which is a beautiful solution by the way) since a software was used to help at one point in the solve. Melinda suggested to ask you for advice as to how it should be considered - a semi-record? What is your opinion?

Happy hypercubing,

Thomas