What is the solution to Alcatraz?

Additional material

Hints (without the spoiler):

The objective is to free the ball trapped in a cage composed of 2 plastic
slabs which are connected by 2 plastic bars and 4 metal bars.  Although
there are several openings in the cage, between pairs of bars, the
diameter of the ball exceeds the smallest dimension of each opening and
so the obvious ploy of simply drawing out the ball through an existing
opening doesn't work.

Several other ploys suggest themselves:

1) Could the ball be shrunk?  Well, if the ball is in fact metal as it
   appears to be then I would say that any attempt to employ this method
   would violate one of the primary rules of mechanical puzzle solving,
   which prohibits marring the puzzle.

2) Could the entire cage be disassembled?  This would allow the ball to
   be freed, but finding how to accomplish it (without again marring the
   puzzle) would certainly be a superset of finding how to remove at
   least one slab or bar.

3) Could any opening be made large enough to pass the ball?  This would
   seem to be easier to investigate than (2).  Note that this doesn't
   necessarily mean that a piece must be removed, or disconnected from
   the rest of the structure, only moved aside enough for the ball to
   pass.

Each *plastic* bar is in fact solidly anchored at each end to a slab and
cannot be moved.  What about the metal bars?  They appear solid - neither
stretchable nor compressible - and in fact they are, and the solution
doesn't require their deformation.

Each metal bar is embedded at both ends in a slab, but each can be freely
rotated about its axis, so they are not solidly attached to the slabs
like the plastic bars are.  The only way for a non-compressible bar to be
freed from the structure would be to have one end retract into a slab to
permit the other end to be freed from its mooring in the opposite slab.

Unfortunately, if you try pushing, pulling, or screwing (clockwise or
counterclockwise) each bar, you'll find that the solution won't be quite
so easy.  Applying a maxim from Sherlock Holmes, we must conclude that
there must be some hidden mechanism whereby a bar can be retracted.
Where would such a mechanism reside and how could it be actuated?  Well,
since it's *hidden* it might be inside any of the components - but we
can rule out the ball itself since it's not connected to the relevant
structures.  That leaves the plastic bars, the slabs, and the metal bars.

How might the hidden mechanism be actuated?  I think it is safe to rule
out any mechanism that would require the application of an electric or
magnetic field, since this would violate another mechanical puzzle rule,
namely that the puzzle contains within itself all materials needed for
its solution, which requires only manipulation.  In what manner can the
plastic bars, slabs, and metal bars be manipulated?

Each component of the structure might be manipulated relative to the
rest of the structure, or in conjunction with the structure as a whole.
You should already have tried pushing, pulling, and screwing (spinning)
the metal bars, and found that there doesn't seem to be any other way to
manipulate any of them relative to the rest of the structure.  Also, you
can assume that the plastic bars also cannot be manipulated relative to
the rest of the structure, and neither can the slabs.  That leaves only
manipulations of the structure as a whole.

How might the structure be manipulated as a whole?  Well, it can be
moved "in place" about its own x, y, and z axes, (roll, pitch, and yaw)
and it can be (simultaneously) translated through space along some
curve, and with some continuously varying acceleration.  In fact, it can
undergo a series of such continuous movements.

If you've seen a lot of mechanical puzzles, you'd know that there is one
whose solution involves a simple in-place application of yaw (in other
words, spinning the puzzle on the table) to obtain the solution - the one
with 4 ball bearings in a box with depressions in the corners, whose
object is to get each ball in its own depression.  Tilting the puzzle to
get one ball at a time usually disturbs the positions of the other balls
and frustrates the puzzler.  There is another puzzle where yawing
(spinning) is used to allow its disassembly - in this case to move (by
the centrifugal force resulting from the spinning) some internal pins
which hold the puzzle together.

So you might try manipulating Alcatraz in this fashion.  You'll have to
be careful to try each bar at each end without disturbing the structure
after yawing it, lest whatever internal mechanism you've actuated by
yawing is reset by jostling.  Also, remember to try each possible yaw
axis.

Want to try that now before reading farther?

When you're done, you'll find that simple yawing doesn't work in this case.  (Sorry.)  And since you've
tried each axis, you've also ruled out simple pitching and rolling.  But
maybe we're on the right track, with regard to moving some internal pins,
or something that is blocking a metal bar from retracting at either end.
Such a block would have to reside in a slab.  How might such a block be
moved, if not by simple yawing, pitching, or rolling?  In what direction
would it have to move to clear the mooring of a metal bar so as to make
the mooring deeper to permit retraction of the bar into the mooring?

Also, what would prevent the mechanism from actuating accidentally - in
other words, could the mechanism be such that accidental jostling is not
enough to actuate it?  What difference would there be between accidental
and deliberate jostling?

The spoiler:

The Alcatraz puzzle is kind of an "all or nothing" puzzle in the sense
that either you find the trick, whereupon the puzzle is solved, or you
struggle on without success and without any sense of incremental
accomplishment.  It seems to generate more than an average level of
frustration - one person to whom I lent my copy actually bent two metal
bars while physically forcing out the ball with a tool!

However, such deformation of the puzzle is not required, and it *is*
possible to achieve incremental progress - it's just that such progress
happens to consist of obtaining negative information - determining what
*doesn't* work - and most people don't approach a problem from the
direction of trying to rule out what won't work - they want to just
fiddle with it until something works.

The mechanism in the Alcatraz puzzle is designed to much reduce the
likelihood that the solution will be found by random fiddling.

Arguably, the simplest motion through space is in a straight line, and
the simplest acceleration increases and then abruptly stops (increasing,
peaking, and then decreasing represents, I think, a more complicated
function).  Why not try a simple manipulation such as this, first?

It would seem that such a motion could indeed have the desired effect of
moving an internal block - accelerating the structure in a straight line
(along some axis to be determined by trial and error), and then suddenly
stopping (for instance, by smacking the structure down on a suitably
mar-proof surface) would cause an internally free block to continue
moving in the original direction of motion of the structure, hopefully
away from the base of a metal bar.

But if the block is free to move internally, why wouldn't simple
pitching of the structure achieve the same result?  Here's where the
Alcatraz mechanism is clever.  It turns out that the block is held in
place by a magnet, so that motion without sufficient force to overcome
the magnetic attraction won't dislodge the block!

A friend of mine found this (*after* we had both independently solved
the puzzle, by the way) by x-raying the structure, and also measuring its
own (weak) magnetic field with an appropriate instrument.  Even if you
don't have a magnetometer handy, you can still find the field using a
more common instrument - you know that kid's toy where there's a face on
a card behind a plastic cover, and inside there are iron filings, and you
draw a beard or hair on the face using a magnet?

If this doesn't work for you, then either you have to hit it harder, or
it might be that you have a different version of the puzzle where some
other bar comes free - try rapping the "Z" end instead.

To reset the puzzle, replace the ball in the cage, replace the free end
of the bar in its mooring hole, and invert the puzzle to slide the
internal block back against the internal magnet.

Now go torture a friend.

-- Robert R. Stegmann <rob@redacam.redac.com>

When the plate slides out of the way, the metal post can move further
into the block, exposing its other end.  Now the post can be swung out of
the way of the ball.  After the end of the post has been put back into
the hole, the puzzle can be tipped so that the steel plate will slide
back and be trapped by the magnet again.

I haven't taken one of these apart, but this all follows pretty well from
what I see and hear as I open the puzzle.

-- Mike Corrigan <corrigan@vnet.ibm.com>

[ Editor: a reply to a 1993 request for help with the puzzle, sold as
"Escape From Alcatraz". ]

Basically, one of the bars slides upwards (into the plate that says
"Alcatraz") -- not much, but enough that the bottom end comes free.  The
problem is that there's a widget in the top plate which prevents the bar
from moving.  The widget is held in place with a magnet.  You have to
bang the thing around until it comes loose, then slide the bar up.  (You
can probably free it up with a magnet, but it's not necessary.)  It's
very tricky, since if you bang too hard, the widget will bounce back
into place.

I don't know exactly what the guts look like.  (I tried looking up the
patent, but it didn't say much more than the above... :-)  I watched
someone stumble on the solution by repeatedly banging the thing in some
random way and then manipulating all the bars.  I was then able to find
a set of motions that usually works.  Then someone else found a set of
motions that almost always works.

More specific spoilers....

Hold the gizmo in your right hand, thumb on top, 3-4-5 fingers on the
bottom, with your right forefinger on the north-east corner bar.  (That
is, the top plate looks like

 -----------*
|  ALCATRAZ |
 -----------

then your forefinger should be on the * bar.  At least, that's where it
is on my copy.  You can tell that's the key bar because there's a faint
circular mark on the north side of the east edge of the top plate.)
Now bang it sort of hard into your left palm, west side first.  Right
after impact, try to slide the key bar up with your finger (press in,
slide up.)  Now try it again sixty or seventy times.  Eventually you'll
get it.

To close it, reseat the bar and shake the gizmo.

Now keep it on your bookshelf and make everyone else hate you.

-- Andrew C. Plotkin <ap1i+@andrew.cmu.edu>