Ramps pentominoes
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.
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 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 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 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.
