A basic DNA code-like sequencing below
has a lacking last letter : What is it?
C T T T C G A
---------------------------
A A G C G G T T
---------------------------
G T A C T T A C
---------------------------
G C T G A G C G
--------------------------
C A C A C A A _
--------------------------

I see, I mixed up the adavance of the hour hand with the elapsed time for each cycle. And I calculated period incorrectly for the second part in my previous post.
Still, after the corrections, I get a different answer. My hour and minute hands will meet a lot sooner.
Why rejecting the occurences where the clock hands meet at 12 in a mid-cycle?
I see nothing in the OP prohibiting that. In fact, the clock hands will meet again at 12 on a mid-cycle before they do so after a whole number of cycles.

@captainEd, the pic is not the start, both @ 12 o'clock is the start where the hands are moving clockwise, eventually the MH overtakes the HH causing it to stop but the MH keeps going until it reached the stopped HH again where then it reverses its direction (like bumping) while causing the HH to move again(resume running clockwise) . No double interpretations is intended here.

A peculiar Grandfather's clock has both its hour and minute hands
running in proper rates. Starting at 12 o'clock both runs clockwise.
But the hour hand stops when the minute hand passes over it.
And the minute hand turn its direction back when it is over the stopped
hour hand causing the hour hand to run clockwise again.
How long will it take for both hands to be on 12 o'clock again?

Hai! That is yes..5 coins w/ 2 double diamater. Looks like a parallelogram with line in the middle.
OP should say "same coin" but i guess no one use 4 half-cut coins (or bitable coins) to make 8 diameters.
My angles were more...90 degrees .
Sorry if I'm going on a completely different tangent than what the OP intended, to be honest, I'm not sure what the OP intends , but seeing your response to witzar made me think 'outside the box' (or plane of the box ) type solutions were acceptable.
Oui! congrats Y-san .. merci

Hai! That is yes..5 coins w/ 2 double diamater. Looks like a parallelogram with line in the middle.
OP should say "same coin" but i guess no one use 4 half-cut coins (or bitable coins) to make 8 diameters.