I like to take a couple of sandwiches to
work with me for lunch. They are
nutritious, tasty and quick - the perfect
meal. Sadly, my lunchbox is ever so
slightly too small for two sandwiches,
which results in the sandwiches being
slightly compressed. Clearly the problem
lies with the
fillings: if I could only lose
those crucial few millimeters taken up by
ham, cheese, tomato or gherkin, my
lunch
would remain unsquished.

Here we have two example sandwiches.
Sandwich A (curved brackets) is filled
with
3mm of tomato and sandwich B (curly
brackets) is filled with 2mm of ham and
2mm of cheese: (|) {||}

If we remove the tomato, ham and
cheese,
we have this: () {} which saves
us
7mm but provides no sandwiches, as
without a filling a sandwich is merely two
slices of bread.

If we then place one inside the other like
this: ({}) we end up with a bread
sandwich, the filling being composed of
two slices of bread (note - the filling for
sandwich A is *not* sandwich B as
without
a filling this has reverted to being two
slices of bread). Sadly, one sandwich is
insufficient for lunch - I require two. So
instead we can interlock the two pairs of
bread like this: ({)} This will give
us two sandwiches, each with a filling
composed of half of the other sandwich,
complete with a 7mm saving in height.

Be sure to eat both sandwiches
simultaneously. If you try to divide the
two sandwiches like
this ({......)} you will find that
your
sandwich sandwich reverts to two pairs
of
bread slices, each with butter on the
outside of one face.

EDIT: Title provided by Ms. Wagster,
credit where credit's due etc. etc....

Wikipedia: http://en.wikipedia.org/wiki/Ham_sandwich_theoremhttp://en.wikipedia...am_sandwich_theorem "The ham sandwich theorem, also called the Stone–Tukey theorem after Arthur H. Stone and John Tukey, states that given n measurable "objects" in n-dimensional space, it is possible to divide all of them in half (according to volume) with a single (n - 1)-dimensional hyperplane." [zen_tom, Oct 21 2010]

A discovery of pure unadulterated genius.
If each sandwich is composed of half the other sandwich, then, according to maths:
1 Sandwich Sandwich (SwSw) = 2 Sandwiches (S).
Yet equally,
1/2 a SwSw = 1 and 1/2 S
meaning that
1 SwSw = is 1, 2 and 3 Sandwiches all at the same time!
Some people might furrow their brows at this point and ask from whence these virtual sandwiches have been magic'd.
Thankfully, due to the Laws of Thermodynamics, we can show that the mysterious and virtual superpositional quantum states can be actualised into a pile of cheese, ham and tomato, which might be described as a rudimentary pizza topping, located somewhere in [wagster]'s kitchen.

[Jinbish] - Of course a sandwich
sandwich is taller
than a ham sandwich - a sandwich
sandwich is in fact *two* sandwiches
whereas a ham sandwich is only one
sandwich. The point is that a sandwich
sandwich is more compact than two
ham sandwiches.

I have no idea what the f#ck you are on about,
however, i did at one time take 9 sandwiches to work , as well as three apples, a banana, and copious cans of coke.
I consumed the lot , 4 hours before we knocked off for the day, and was a shadow of myself before dinner.
My question is, " why don't ya just get a bigger tuckerbox man"?

There'll always be the trouble of the solitary red onion into the conceptual framework or Kantian epistemology if you so wish and thus fitting into the complex reality of the sandwich sandwich.

I believe that we need a diagrammatic representation other than ({'

[skinflaps] by applying a Lorenzian transformation, I think we might be able to form a set of equations that describe this unique structure in terms of a complex Minkowskian space, using the reciprocal sandwich tensor as a primary means of expressing i. If we solve the equations carefully, we should be able to cancel out any constants such as these single red onion and butter quandaries.

Diagrammatically, there's always the [] approach. Alowing, if we are ready for it, the potentiality for describing, in textual forms, the existance of an even more exotic form of sandwichery; The Sandwich Sandwich Sandwich:
[){](}

Hmm, symbiotic sandwiches - sounds good. Couldn't you make your sandwich problem-solving-space richer and more likely to result in tastier sandwiches (while still being constrained by your lunchbox and your need for two sandwiches) by relaxing the rule that a sandwich's internals must be delimited by bread? If a sandwich can be, for example, CBC (C=Cheese, B=Bread) or BCB - i.e. a cheese-based bread sandwich and a bread-based cheese sandwich, then CBCB provides two sandwiches and will be suitably economical of space to fit in your lunchbox.

Very nice solution [hippo]. By this logic
you could even have a ham and cheese
interlock: HCHC which would have a
thickness (using the above figures) of
only 8mm. Ultraslim lunching to go
with your Motorola Razr.

My name is Mr. JOHN MENSAH. I am the accountant of the International Commercial Bank - Ghana, First Light Branch Accra. I am a Ghanaian married with two kids.
I am writing to solicit your assistance in the noble transfer of US$3,800,000.00 (Three million, eight hundred thousand U.S. dollars). This fund is the excess of what my branch in which I am the accountant made as profit during the last year. I have already submitted an approved end of the last year report for the year 2004 and also submitted report of first quarter of this year 2005 to my Head Office here in Accra and they will never know of this Excess. I have since then, placed this amount of US$3,800,000.00 (Three million, eight hundred thousand U.S. dollars) on a SUSPENCE ACCOUNT without a beneficiary.
)

({+)} For those with big appetites, you could make a dagwood sandwich sandwich sandwich. This has the advantage of being three sandwiches, all of which contain three fillings apiece, using only one extra filling.

I find that by spreading the vagina jam very, very thinly and removing most of the hairs (does anyone know a better brand than Benfrost Farm?) my sandwiches are precisely 14mm, allowing two to fit snugly in a 3cm deep sanger box.

I do like sliced apple with it though, so sometimes a bread -jam-apple- bread -apple-jam- bread construction is called for, with the apple slices being 3.5mm thick.

Can't be bothered, [UB] - that bit was only there to introduce the concept (without making it sound like I'm the geeky type who considers various methods of sandwich construction just to pass the time).

For unsquished and healthier alternative than that tasteless white bread use 100% rye bread slices. Does not squish and much better for you. Well baked in Eastern European and Nordic countries.

I'm wondering which way up the sandwich would fall. Of course, if it was a mobius sandwich sandwich, it would get so confused on the way down that it would stop halfway and jump back into the safety of the lunchbox. Probably.

Wags, it seems to me that the problem is not with the sandwiches or their content but with the outdated slicing method used. As a systems manager I can tell you that the solution lays not with maths or geometry but with process re-engineering. If you cut your filled bread into smaller and more useful shapes then you would be able to fill your lunchbox more efficiently and avoid the unwanted squishing effect.

This would also have the effect of providing you with a box full of bite-size morsels, thus avoiding the problem of content slippage when you sink your teeth into the disorganised remains of what once passed itself off as a sandwich.

An additional benefit of this is that never again will your boss (or anyone else for that matter) arrive unexpectedly at your desk to find you with a half-eaten sandwich in your hand (or, more likely, half-way down your arm).

To summarise. I vote 'nay' to the sandwich sandwich and 'yeah' to spending several hours arsing about with a bread knife when you're in a hurry in the morning.

A mincer might do the trick, you could then transport the contents of your sandwhich in an icing bag, piping it onto your tongue whenever you feel hungry.

[zen_tom] - that's brilliant! And if you have a drink with your lunch - say, Diet Coke - and a piece of fruit or a yoghurt, you could mix that in too, to create a sort of lunch slurry. This can be put into a plastic bag which will then mould itself to whatever spare space is left in your briefcase, as opposed to a rectangular lunchbox which is not very economical in its use of space.

I don't want to sound like the marketing exec for Gillette, but has anyone considered a Sandwich sandwich sandwich sandwich? Perhaps with a cocktail-sandwich attachment when precision sandwich-eating in those tricky places...

I'm not keen on hippo's slurry as that would destroy the essential sandwichyness of the sandwich. At least the mincer would retain the bread-content-bread format although in a long, thin string of sandwichyness.

I had to read this twice; at first it looked
like you were breaking conservation of
luncheon meat. But this is far from bad
science. Add a pastry to your lunch.

You could manage a slurry sandwich, if you used the same technique the toothpaste people use. Instead of the red/blue stripes, you squeeze out your sandwich in an alternating bread/filling/bread string. [+]