I claim that no arrangement is possible in the case with cards ace through four.
_A_A_A_A_ (_ is any other card)
must be part of the arrangement. Now consider two cases:
the row starts and ends with aces - this is obviously not
possible, since that arrangement would only hold 7 cards, and we
there are cards to the left and right ...
@athin has found the mathematical pattern in the sequence and created a useful general way to display it pictorially (go see their post and upvote). However, a slightly more accurate diagrammatic rendering would be as follows:
This is because the sequence reflects:
The significance of 23 March in the hints is that:
The pattern emerges as:
Why does the ...
A similar answer to Quintec's (asserting that it is impossible):
Consider that you only have 12 cards that are not a 4, and that you need 12 total cards between the 4s. So the entire arrangement must look like
4 _ _ _ _ 4 _ _ _ _ 4 _ _ _ _ 4
As per Quintec's observation, somewhere in there we must have
_ A _ A _ A _ A _
But you can see that there ...
Partial answer, mostly observations but lots of them. Might be useful as a springboard if someone else can spot a unifying pattern between all of these.
Colours for circles are
Colours for numbers are
So we notice that
More observations, focusing now on the same-colour patterns:
My theory is that the number in each circle depends in ...