TimeSpaceLightForce

To make the spatial solutions we should first assign a fix axes reference. Naming the 8 cell : using Up Down Front Back Right Left orientation Cells : LUB BUR LUF FUR LDB BDR LDF FDR and since all dice showing only 3 of its faces on out sides.. Dice : (initial & final position) 312 214 263 365 315 [ ] 264 465 362 264 213 315 365 564 214 [ ] Turning : y-axis to yaw x-axis to pitch z-axis to roll Solution1: Straight forward moves 1. z FDR x FUR z FDR FUR:465 fixed 2. make a vacancy on upper deck next to 465..rotate lower deck until the correct sixer is below it . Another 3 moves max to fix BUR or LUF 3. repeat until all sixers are fixed. 4. with all oners on lower deck, if chiralty is correct, all the remaining dice can be fixed.. Not much of a challenge. So lets involve all the 6 sides and roll 25-dice in 3d

Can the light object cast an eclipsing shadow on the dark one??

in 2D the square can not pass through the circle... it will cut through instead, so you are correct to assume.

(a) the circle can pass through the square, (b) the sphere can pass through the cube or (a) & (b)

If the dark object can pass thru the light object, are they circle and square or sphere and cube?

...inside a cube the largest square that can fit in is not coplanar with the largest circle that can fit in.

I did not know that..when i had tried dismantling the 15 tiles and reassembled them 15 -1 i was able to do it back. Maybe this 7cube must be assembled first with all faces in same direction i.e. all blue top,orange down,red left,green right,yellow front,purple back.(or 1-6 if numbers) But wonder if the position of blocks adjacent to vacancy is different if it is slided up or down in initial position. this 3D rolling is new idea for me owing from your 8 cube. It is really interesting but somehow doubt if we are the first to tackle. Looking like a 2x2 Rubik with a missing cube... If we physically construct it the center mechanism must have a fix hold of all the 7 vertices. when rolling it shall pivot without twisting the binder.. that is rigid construction. Magnetic design involve magnetic strips on edges or center faces but + & - poles orientation is uncertain. But Rubber band might work.., knot 4 cuts tightly ,make a small holes on vertices of hollow cardboard cubes insert each rubber band end into the cube hole. A round bead as stopper will allow rolling without twisting..

There are no absolute speeds only relative..In this case , there were 3 inertial frames involved: the ground , the phalanx and the dog. they are all have a change in distance per time and whether they touches or not it does not matter..the dog in the platform will find it easier to run around the outside of the square but still relative to the observer on the ground the elevated dog has 3 variable speeds according to his own reference frame. Even if he is on a steady hot air balloon 1 m above the ground. Thus,any constant speed should be referenced.. I see that you computed it correctly .. using the constant speed relative to the ground and now its clear why K-man and my graph data differs. another good puzzle!

ok, why is a circular detector bigger than the square detector ?

Based on bonanova's rolling 8 blocks and with the same mechanics of rolling 1/4 on axis. This puzzle requires 7 blocks (dice) on 2 x 2 x 2. How it can be done? It would be more interesting to play and solve if there is a mini program for it but i can't find one.

I've seen one in a Escape the Room Game. Since we are just playing for the least rolls it might be helpful if we use the mini program http://www.jaapsch.net/puzzles/javascript/eightcubj.htm .Enjoy ..Don't press SOLVE.