Cheer, **Rodolfo M. Kurchan**

PUZZLE FUN Editor

#129 | Is it possible to make a rectangle that use the 12 pentominoes that have at least 1 single, 1 double, 1 triple and 1 cuadruple?.Michael Reid found a closer solution to this problem using 10 pentominoes:1 single, 5 doubles, 3 triples and 1 quadruple: 320 = 15 x 39. Can someone find a solution using more pentominoes? |

A ramp is a road of pieces between an horizontal line and a vertical line.

#222 |
Find the biggest ramp with double fence h.a.v. symmetric (inside and outside border) |

#226 |
Find the biggest ramp with triple fence h.a.v. symmetric (inside and outside border) |

#239 |
Find the biggest bridge with double fence i.a.d. only with the inside border symmetric. |

#247 |
Find the biggest bridge with triple fence h.a.v.but with the inside border symmetric. |

#252 |
Try for an outside double fence bridge h.a.v. |

#308 |
The most quantity of symmetric pentominoes F inside a rectangl |

#315 |
The most quantity of pentominoes L inside a rectangle |

#316 |
The most quantity of symmetric pentominoes L inside a rectangle |

#323 |
The most quantity of pentominoes N inside a rectangle |

#324 |
The most quantity of symmetric pentominoes N inside a rectangle |

#327 |
The most quantity of pentominoes T inside a rectangle |

#328 |
The most quantity of symmetric pentominoes T inside a rectangle |

#335 |
The most quantity of pentominoes V inside a rectangle |

#336 |
The most quantity of symmetric pentominoes V inside a rectangle |

#339 |
The most quantity of pentominoes W inside a rectangle |

#340 |
The most quantity of symmetric pentominoes W inside a rectangle |

#343 |
The most quantity of pentominoes X inside a rectangle |

#344 |
The most quantity of symmetric pentominoes X inside a rectangle |

#347 |
The most quantity of pentominoes Y inside a rectangle |

#348 |
The most quantity of symmetric pentominoes Y inside a rectangle |

#351 |
The most quantity of pentominoes Z inside a rectangle. |

#352 |
The most quantity of symmetric pentominoes Z inside a rectangle |

I've recieved and idea from Ariel Arbiser (Buenos Aires, Argentina) to superpose pentominoes. I've made pairs of pentominoes that are superposed in 1 square, and with this area of 54 I could make the rectangle of 6 x 9.

#377 |
Can you make a 3 x 18 rectangle?. If you can, try to make it symmetric. |

#378 |
Is it possible to put the 6 squares in a way that the rectangles have only one solution? |

Example: I could cover this region for 6 pentominoes in this way:

Find these solutions:

#383 | #384 |

A building is a figure that has as many doors and windows as you want. The object is to have the buildings with the most quantity of "holes".(doors and windows).

The idea of "buildings" came to me after I’ve seen the letter that Michael Reid sent to me in September 18 of 1994.

#454 |
Find the symmetric rectangular building with the most quantity of trominoes I. |

#455 |
Find the building with the most quantity of trominoes L. |

#456 |
Find the symmetric building with the most quantity of trominoes L. |

#458 |
Find the symmetric rectangular building with the most quantity of trominoes L. |

#462 |
Find the symmetric rectangular building with the most quantity of trominoes of any shape. |

#463 |
Find the building with the most quantity of tetrominoes L. |

#464 |
Find the symmetric building with the most quantity of tetrominoes L. |

#466 |
Find the symmetric rectangular building with the most quantity of tetrominoes L. |

#467 |
Find the building with the most quantity of tetrominoes I. |

#468 |
Find the symmetric building with the most quantity of tetrominoes I. |

#471 |
Find the building with the most quantity of tetrominoes S. |

#472 |
Find the symmetric building with the most quantity of tetrominoes S. |

#474 |
Find the symmetric rectangular building with the most quantity of tetrominoes S. |

#475 |
Find the building with the most quantity of tetrominoes T. |

#476 |
Find the symmetric building with the most quantity of tetrominoes T. |

#478 |
Find the symmetric rectangular building with the most quantity of tetrominoes T. |

#479 |
Find the building with the most quantity of tetrominoes O. |

#480 |
Find the symmetric building with the most quantity of tetrominoes O. |

#484 |
Find the rectangular building with the most quantity of tetrominoes of any shape. |

#485 |
Find the symmetric building with the most quantity of tetrominoes of any shape. |

#486 |
Find the symmetric rectangular building with the most quantity of tetrominoes of any shape. |

#487 |
Find the building with the most quantity of pentominoes of any shape. |

#489 |
Find the building with the most quantity of different area holes. |

#491 |
Find the building with the most quantity of different squares area holes. |

Pablo Coll asks which is the smallest area in which we can put the pentominoes without contact and without contact with the edge of the area. In the example we show his solution of area 172.

#555 |
2 sets of pentominoes, with the condition that there is no contact between pieces of the same set. |

#556 |
Find the smallest possible rectangle made with n pentominoes so that it results biggest than the smallest possible rectangle made with any other n pentominoes.For example for n=2 with the pentominoes I and Y the smallest rectangle is 2x7= 14 so the rest is 4, but my best solution is with the pentominoes X and I that the smallest rectangle I can find is the 4x5=20 with rest = 10. Here I show my best solutions until n=3. For n=12 of course you make a complete rectangle, and I think that n=11 is the same. |

#576 |
Is it possible to pack the 12 pieces in a 5x5x5 cube? |

Six two floor pieces:

Two mirror pieces:

#590 |
If we add a monomino to the solution of problem 589) (to make a 3x9 rectangle
and a 3x3x3 cube with unique solution using 1 domino, 1 tromino, 1
tetromino, 1 pentomino, 1 hexomino and 1 heptomino) we could probably make a
4x7 rectangle. If this new rectangle had not a unique solution, could you
find another set that has a unique solution for the 3x3x3, 3x9 and 4x7,
adding a monomino?If you don't find a solution with unique solutions for the 3 cases, which is the set that has the less quantity of solutions? |

#591 |
If you couldn't find a unique solution to problem 590), can you find a set
without restrictions, (that means that you can use as many pieces as you
want and of the sizes you want) so you have a unique solution to the 3x3x3
the 3x9 and to the 4x7, adding a monomino.Anyway, you are very restricted because the pieces should be inside the 3x3 square, and you cannot repeat any piece; so the possible pieces would be from a domino to an octomino. |

**Rodolfo Marcelo Kurchan** / Lavalle 3340 21"3" / (1190) Buenos Aires - Argentina

**eMail: rodolfo@kurchan.com.ar
http://www.bigfoot.com/~velucchi/pfun/pfun.html**

last revision:

Mario Velucchi's Web Index
| visitors since March 08, 1999 |

Resources provided by Brad Spencer 800x600@16M optimized |