[time-nuts] Solstice Puzzle

Brooke Clarke brooke at pacific.net
Sat Dec 17 01:39:59 EST 2011

Hi Nevelle:

Have each face of each cube contain an LED digit display.
They are battery powered.
If one is rolled like a dice an accelerometer (or better set of ball in a tube sensors) knows where the top and bottom 
faces are and so they are not to be turned on.
There's an assumption that after all six have been rolled someone will push them together into a sort of tight row.
To sense that they are now grouped into a row you use one LED on the four possible active faces to measure the light.
There are two possible answers, either three faces are open (an end cube) or two faces are open (a middle cube).
If a cube is an end it blinks an LED on the dark face with the I'm an end pattern.
If a cube is a middle cube it looks for a blinking LED.
When a middle cube sees a blinking LED it makes note of the code.
It remembers the code it's seen and adds one to it and blinks the opposite face unless the code is saying "in 4" meaning 
that the cube seeing this is the tail cube.
Now each cube has two IDs which is as it should be.  After a head end cube has received an "in 4" message then it knows 
it's also a tail end cube.

When the time is displayed the 10 hours digit will be on the face of a starting cube that's CW from the adjacent cube 
when looking down on the string.
If the cubes are numbered 1 to 6 left to right then the 10 hours digit will be on the 1 (left most) cube and on the 
front face.
When looking at the back of the string, i.e. cubes 6 to 1. the 10 hours digit will be on the 6 cube on the left facing 
to the back.
At this point the cubes assume they know where they are but they also know that they may be rearranged so . .
cube 1 not only displays the current 10 hour digit it also sends the position message to cube 2 and makes the light 
measurements to confirm that it's still an end cube.
If these fail then the cube un registers both it's IDs and we got back to the top.

If the tests pass (cubes are still in order) then cube 1 sends the 1 hour time to cube 2.  Cube 2 displays it and does 
the "have I been moved test" as above, if not it sends the 10 minutes message to cube 3, etc. etc.

It may be possible to detect movement with other sensors, such ball in a tube making it easier to tell when that's 
happened.  In any case when any cube knows that it has been moved it can cry out by blinking the LEDs on all faces in a 
we're being moved pattern.

Have Fun,

Brooke Clarke

Neville Michie wrote:
> At this time of the year many people look for frivolous puzzles to solve.
> My puzzle is to design a clock.
> This clock consists of 6 cubes, each has a digit display on one face.
> It does not matter how you arrange them, if they are in a line they will display the
> right time. (there may also be a nearby box containing a Rb or GPS time standard.)
> A second or two may be needed for them to reorganise if they are moved.
> It must be possible to design them, but an elegant design has eluded me.
> Merry Solstice,
> Neville Michie
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