You all know I love maths.
In one of the older posts, I said I will test the properties of the "Frame" magic,
which was first invented by Juozas Granskas.
Here is the result:
Pantazis_Z8.jpg [ 128.81 KiB | Viewed 650 times ]
Note that this puzzle has *exactly* eight flat states, and I made it such each state
is one of the numbers 0, 1, 2, 3, 4, 5, 6, and 7, which correspond to the cyclic group
of eight elements Z8.
Everything in this puzzle is cruciallly important, even the way it is firstly strung.
And each solved state will use three tiles to represent one number on the left
with a background of the same color.
But the most amazing thing, is that, to go to the next or previous number, the EXACT
(slightly complex) sequence is needed.
Aaaah... I always loved cyclic groups, especially the Z8 (aka C8).
PS. To see an interesting difference, the four square-tile magic is not related to a cyclic group,
but to the Dihedral group D8 (or D4).
PS2. Will try to make a video of the "countdown" from 7 to 0.