In Klondike solitaire, what is the fewest number of cards that can be placed in a beginning setup to...

Problem

In Klondike solitaire, what is the fewest number of cards that can be
placed in a beginning setup to guarantee the player will not be able to
win?

The rules:

7 piles
Deal in 'standard' solitaire way
From deck show every 3rd card, then repeat (if the last portion of
cards is not a multiple of 3 - kill remaining 1 or 2 cards and restart)
Aces placed in 4 piles (by suit) - cards may be moved freely from Aces
stack to main stack (as long as normal rules are followed).

So, for example, I could easily place 50 of the cards where I wished,
and have the remaining two placed randomly in the two remaining spots,
and guarantee a loss.  I feel I could also do this with 49 cards, 48
cards, etc...  But what is the SMALLEST number of cards that you can
place, with the rest placed randomly (or in the most opportune way for
the player), that will guarantee no solution?

The best we could come up with (without delving very deeply into it)
is this:

Place each of the original top 7 cards (eg: 2 2 2 2 4 4 4).  Then place
every third card in the deck so that it is not an Ace or 3.  This would
need the placing of 14 cards (7 top ones and every third of the
remaining 23).

Is it possible to do it better?

-- Stephen Dillinger <driver@mcs.com> (April 1994)