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:

 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 Nico Looije 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:
 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 Nico Looije 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:

 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 Nico Looije The Netherlands 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:

 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 Nico Looije 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.