UnSolved problems in 'PUZZLE FUN'

UnSolved problems in PUZZLE FUN

Follow UnSolved Problems from back issues of my magazine PUZZLE FUN.

Try to solve some problem that no one solve and send me Your, possibly partial, solutions. Your name, if you like, will appear here and in the journal!!

Cheer, Rodolfo M. Kurchan
PUZZLE FUN Editor

PUZZLE FUN | #2 | #5 | #6 | #7 | #12 | #16 | #18 | #19 |

PUZZLE FUN #2:

#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?

PUZZLE FUN #5:
Ramps pentominoes
A ramp is a road of pieces between an horizontal line and a vertical line.

Double and Triple Fence Probelms "Double fence" means that the fence should be double in all directions (i.a.d.: horizontal, vertical and diagonal). h.a.v cases will only requiere double horizontal and vertical directions.

#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.

Marcelo Iglesias and Hector San Segundo sent me independently this excellent idea: Construct two bridges, one inside another without contact between them in a way that the inside bridge should be the biggest possible. If there is a tie in the solutions, the best will be the one with the outside bridge with smallest area.

#252

Try for an outside double fence bridge h.a.v.

PUZZLE FUN #6:
Holes Pentominoes

#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

PUZZLE FUN #7:
Superposing pentominoes
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?

Superpose pentominoes in a way that each square is ocuppied as many times as the number indicates.
Example: I could cover this region for 6 pentominoes in this way:

Find these solutions:

#383

#384

PUZZLE FUN #12:
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.

PUZZLE FUN #16:
Packing
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.

n=1: r=4

n=2:r=10

n=3:r=9
or

PUZZLE FUN #18:
Inside Cube 7
This set consists in 13 pieces that are the combinations of 1x1, 2x2 and 3x3 squares allowing to put one lying over the other. The area is 138. Take out one of the two mirror images pieces for an area of 125.

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

(August 12, 1999) Patrick M. Hamlyn from Australia wrote: "A computer search reveals there are no solutions"
Five one floor pieces:
Six two floor pieces:
Two mirror pieces:
PUZZLE FUN #19:
The 3x3x3, 3x9 and 4x7 I part

#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?

The 3x3x3, 3x9 and 4x7 II part

#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.

Solutions, Hints, Ideas ... write to:

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

Web page processed by PUZZLE FUN Web Master - Mario Velucchi -- velucchi@bigfoot.com

Mario Velucchi / Via Emilia, 106 / I-56121 Pisa - Italy

Resources provided by Brad Spencer
800x600@16M optimized