Troll Party

[Brillig]

Today is a troll party. One of the troll puzzles was completed last
night forming a nine tile tower.

I went home for lunch today before noon and noticed that the shadow of
the sun was aligned not only with the north face but also with the
west face. This made me consider something that I'll call lunch hour.

Lunch hour is the period of time between the sun's aligning with the
west face to the time it aligns with the east face. If circular discs
are used instead of square tiles, then instead of faces, the alignment
is with the east and west tangent lines to the cone tangent to the
discs.

The length of lunch hour varies by latitude and by time of year.

Victor

[Helios]

I thought of a 9-disk "Tower of Hanoi" variant that takes 365 moves to complete. I previously had an 11-disk idea to accomplish this, but 9 disks is better.

These are the special rules of this variant;

1) Upper disks 8 and 9 are identically sized and either can be set atop of their counterpart.
2) The 2nd and the 5th disk are special. If either of these disks are moved, then an extra move of the next disk pending is immeadeatly made without being counted. Levels 2 & 5 can be indicated by a different color from the rest of the disks.

The addition of moves goes,

365 = 1 + ( 0 ) + 4 + 8 + ( 0 ) + 32 + 64 +  128 + 128