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PUZZLE FUN by Rodolfo Marcelo Kurchan

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:
#129Is 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 Iíve 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


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