How do you cut a doughnut into 12 pieces with only 3 cuts?

Lay the doughnut flat.  Cut it in half with a horizontal slice (like
you'd cut a bagel).  Then cut it in half with a vertical slice.  Now
take the two halves you've just made with your second cut, and
position them like this:
  __
 / _|
| /
| \_
 \__|
  __
 / _|
| /
| \_
 \__|

Now make your final cut vertically, so that each C shape above is
divded into 3 pieces.  Since each of those six pieces has been cut in
half horizontally, you have 12.

Pull knife from dr**  (oops, cut myself)
Pull knife from drawer
slice lengwise (bagel cut) at 33% of the width
slice down the mi**   (oops, cut myself)
slice down the middle
slice larger of two lengthwise sections in half
slice down the mi**   (oops cut myself)
slice down the middle again

THERE!
12 pieces and only three cuts!

-Fractl

(children, don't try this at home)

Fractl ... You cheated ... I counted 6 cuts.

As well as spilling blood all over the doughnut.

I followed racecar-ga's directions and it does work. However I STILL
couldn't eat it without licking my lips

I made 6 slices...but I only got 3 cuts.  (I suggest trying this with
a day-old chocolate frosted doughnut...the choco-coating is hard
enough to rinse the blood off before eating or serving to others).

With practice I was able to get it down to only 1 cut (2 if you count
ones on ther people as well).  I should be a chef!

-Iron Chef America: Fractl

This probably won't help much but cut the donut flat in a triangle of
cuts will yield 9 in a donut if you place the cuts directly tangent to
the inner circle.  I guess you could start going 3D on the problem and
achieve more slices that way...

..........reminds of a previous question of mine on GA where I asked "
how do you cut a pizza into 10 equal slices easily".

 John From Melbourne

Two transverse cuts, and one circumferential cut...

Cuts 1 and 2.  Lay flat on a tabletop, and make two cuts parallel to
the plane of the tabletop, at two different heights, through the
doughnut.
Cut 3.  Make a cut at a CONSTANT RADIUS through the donut.

I can't believe I just made $200.00!  Oh, wait...

I may be misinterpreting your instructions...but I count 6 there.

Racecar is correct.  At this point, there is only ONE CUT.
  ___
 / __|
| /
| \__
 \___|
  ___
 / __|
| /
| \__
 \___|

By cutting vertically through BOTH HALVES at the same time, you will
be left with six pieces in TWO CUTS:

  _   __
 /    __|
| /
| \   __
 \_   __|

  _   __
 /    __|
| /
| \   __
 \_   __|

Next, pick up the 2 pieces on the left, place them ON TOP of the small
pieces, and cut vertically once again: 12 PIECES IN 3 CUTS.

Yummy.

If, during the last cut, you try to slice the two larger parts before
the two sides of the hole merge you may be able to squeeze 14 pieces
out (not that that was the goal...)
If you allow cuts that aren't in straight lines one can get many more
than 12...but that is getting way off topic.

-Fractl