Tiling

In 'Euclides' (the magazine of the Dutch Association of Mathematics Teachers ) in the magazine of April 2008 stood this
recreation pentominoes puzzle. The most joy you have when you find him yourself, but we made use of the great program of Aad van de Wetering Flat Poly that solves the problem incredibly fast.
Puzzle 1
Tile  a rectangle with one or more copies of the pentominoes and one or more copies of domino.
Try to make a rectangle with the smallest possible surface area.
Solve this puzzle for each of the pentominoes.

There are 12 problems to solve and the most are trivial.
The sum of the areas in our solution is 164.
Can you do better?

Good solvers obtain eternal fame
Mail to:
o.d.m@fulladsl.be

Name Country Puzzle 1
Frits Göbel The Netherlands 158
Aad van de Wetering The Netherlands 163
Helmut Postl Austria 158
Peter Jeuken The Netherlands 158
Lieke de Rooij The Netherlands 158

Puzzle 2
Make a rectangle from Z pentominoes and I-trominoes.

We found a solution with area 42.

Can you do better?

Good solvers obtain eternal fame
Mail to:
o.d.m@fulladsl.be
Name Country Puzzle 2
Aad van de Wetering The Netherlands 42
Helmut Postl Austria 42
Martin Friedeman The Netherlands 42
Peter Jeuken The Netherlands 42
Lieke de Rooij The Netherlands 42

George Sicherman: "Here is a square solution"

Puzzle 3
Make a rectangle from T pentominoes and O-tetrominoes.

We found a solution with area 80.
Can you do better?

Good solvers obtain eternal fame
Mail to:
o.d.m@fulladsl.be

Name Country Puzzle 3
Aad van de Wetering The Netherlands 80
Helmut Postl Austria 80
Martin Friedeman The Netherlands 80
Peter Jeuken The Netherlands 80
Lieke de Rooij The Netherlands 80
George Sicherman US 80

     George Sicherman:"Here is a complementary square for the T pentomino. (For 4-rotary symmetry, you will need a 14x14 square.)"


 George Sicherman emailed: "Making a rectangle from T pentominoes and square tetrominoes is moderately hard.  Making one from N pentominoes and square tetrominoes is harder!"
Puzzle
4
Make a rectangle from N pentominoes and O-tetrominoes.

George found a solution with area 160.
Can you do better?
Good solvers obtain eternal fame
Mail to:
o.d.m@fulladsl.be

Name

Country Puzzle 4
George Sicherman US 160
Aad van de Wetering The Netherlands 160
Peter Jeuken The Netherlands 160
Martin Friedeman The Netherlands 160

Aad sent us this beautiful picture. The smallest square with N-pentominoes and O-tetrominoes



Do you really like to see our solution? Send us an email.