Attached are two solutions. The 6-piece solution is a solution with
the fewest possible pieces, the 8-piece solution has rotational
symmetry.

5 pieces do not suffice, because such a solution could not be
4-colored.

These were pretty.


-- Matt Elder

------------------------------------------------------------------------------------

Hi Ed,

The attached file contains the solutions to the holey dissections
problem of 12/06/04.

I added an additional solution to the four piece puzzle. The pieces
used for it are all identical, but they're not made from complete squares.

Warren Phillips

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Merry Christmas for You!
Here solutions for cuttings.

Juha Saukkola

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I found a 2nd solution which is attached. This one uses 4 size-1 Ls
and 2 size-4 Ls. The two large Ls touch in two places in addition to
each touching 3 small Ls.

Joseph DeVincentis

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Hi Ed,

I've attached solution for your Tesselated Holey Squares puzzle. XLS
and JPG...

(I only did 1 solution for each grid, though they're not necessarily unique)

Cheers,

Alan O'Donnell

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Claudio Baiocchi

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Patrick.Hamlyn's.square.almost-dissections.are.fun.
I've.been.doodling.with.them.on.the.Tube,.and.so.far.have:

+--+--+--+--+..+--+--+--+--+--+..+--+--+--+--+--+
|##|........|..|##|........|##|..|##|........|##|
+--+.....+--+..+--+--+--+..+--+..+--+........+--+
|..|.....|..|..|........|..|##|..|##|........|##|
+..+--+--+..+..+..+--+--+..+--+..+--+..+--+--+--+
|.....|.....|..|..|##|.....|..|..|..|..|........|
+.....+.....+..+..+--+--+..+..+..+..+--+--+.....+
|.....|.....|..|.....|..|..|..|..|........|.....|
+--+--+--+--+..+..+--+..+--+..+..+........+.....+
...............|..|...........|..|........|.....|
...............+--+--+--+--+--+..+--+--+--+--+--+

+--+--+--+--+--+--+..+--+--+--+--+--+--+..+--+--+--+--+--+--+
|..|...........|##|..|.....|........|##|..|........|.....|##|
+..+--+........+--+..+.....+........+--+..+........+.....+--+
|.....|........|##|..|.....|........|##|..|........|.....|##|
+.....+--+..+--+--+..+.....+--+--+..+--+..+..+--+--+.....+--+
|........|..|.....|..|........|..|.....|..|..|...........|..|
+.....+--+--+.....+..+--+--+..+..+--+--+..+..+--+--+--+--+..+
|.....|..|........|..|.....|..|........|..|..|...........|..|
+--+--+..+--+.....+..+--+..+--+--+.....+..+--+.....+--+--+..+
|##|........|.....|..|##|........|.....|..|##|.....|........|
+--+........+--+..+..+--+........+.....+..+--+.....+........+
|##|...........|..|..|##|........|.....|..|##|.....|........|
+--+--+--+--+--+--+..+--+--+--+--+--+--+..+--+--+--+--+--+--+..

+--+--+--+--+--+--+..+--+--+--+--+--+--+--+
|........|........|..|##|.....|..|##|.....|
+.....+--+........+..+--+.....+..+--+.....+
|.....|##|........|..|........|..|........|
+.....+--+--+--+..+..+--+.....+..+--+.....+
|.....|........|..|..|..|.....|.....|.....|
+--+--+.....+--+--+..+..+--+..+.....+--+..+
|.....|.....|.....|..|..|##|..|........|..|
+.....+.....+.....+..+..+--+..+.....+--+..+
|.....|.....|.....|..|.....|..|.....|..|..|
+.....+--+--+.....+..+.....+--+--+--+..+--+
|........|........|..|........|##|........|
+--+--+--+--+--+--+..+.....+--+--+........+
.....................|.....|..............|
.....................+--+--+--+--+--+--+--+

Haven't.done.the.7-piece.ones.yet.

>.Erich.Friedman:.Divide.a.square.into.L.tetrominoes.of.various.sizes
>.so.that.each.L.touches.exactly.4.others.

+--+--+--+--+--+--+--+--+--+--+--+--+
|...................................|
+...................................+
|...................................|
+...................................+
|...................................|
+...................................+
|...................................|
+--+--+--+--+--+--+--+--+...........+
|...........|.....|.....|...........|
+...........+..+--+..+--+...........+
|...........|..|..|..|..|...........|
+...........+..+..+..+..+...........+
|...........|..|..|..|..|...........|
+...........+--+..+--+..+...........+
|...........|.....|.....|...........|
+...........+--+--+--+--+--+--+--+--+
|...................................|
+...................................+
|...................................|
+...................................+
|...................................|
+...................................+
|...................................|
+--+--+--+--+--+--+--+--+--+--+--+--+

If.touching.at.a.vertex.doesn't.count,.there.are.solutions.like:
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
|...................................|.......................|
+...................................+.......................+
|...................................|.......................|
+...................................+.......................+
|...................................|.......................|
+...................................+.......................+
|...................................|.......................|
+...........+--+--+--+--+--+--+--+--+--+--+--+--+...........+
|...........|........|..........................|...........|
+...........+........+..........................+...........+
|...........|........|..........................|...........|
+...........+........+..........................+...........+
|...........|........|..........................|...........|
+...........+........+........+--+--+--+--+--+--+...........+
|...........|........|........|.................|...........|
+--+--+--+--+........+........+.................+...........+
|...........|........|........|.................|...........|
+...........+........+........+.................+...........+
|...........|........|........|.................|...........|
+...........+........+--+--+--+--+--+--+........+...........+
|...........|.................|........|........|...........|
+...........+.................+........+........+...........+
|...........|.................|........|........|...........|
+...........+.................+........+........+--+--+--+--+
|...........|.................|........|........|...........|
+...........+--+--+--+--+--+--+........+........+...........+
|...........|..........................|........|...........|
+...........+..........................+........+...........+
|...........|..........................|........|...........|
+...........+..........................+........+...........+
|...........|..........................|........|...........|
+...........+--+--+--+--+--+--+--+--+--+--+--+--+...........+
|.......................|...................................|
+.......................+...................................+
|.......................|...................................|
+.......................+...................................+
|.......................|...................................|
+.......................+...................................+
|.......................|...................................|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+

--.
Roger.Phillips............................................