HexoPento
These are 10 flippable two-side hexominoes. Colors are the same on both sides. Cover a 10x6 rectangle so that you see the 12 pentominoes.

Gabriele Carelli:"Excelent puzzle with unique solution!"
Numbering the pieces from left to right and top down we have:
A - Pieces 6 and 10 have only 4 different "relationships", in any case the light gray pieces form an L, the light green form a T or a V
B - Pieces 3 and 7 has only 2 possible "relationships", in both "relationships" the blue squares form the I. Two other "relationships" seems possible but force the purple or the blue squares to form an L pento but such pento is formed by the light gray pieces (see above).
C - Pieces 2 and 8 have only 4 possible "relationships"
Putting in a whole A, B and C and following a logical path we can reach the unique solution
Odette De Meulemeester: "It's really an excellent puzzle but the solution isn't unique"
If you want to see the solutions you can click on the words, but first searching for yourself.
Helmut Postl (27-06-2017) : "Now I got my program finish. The two 6x10-rectangles are indeed the only ones. And there are no other rechtangles."


12 Pentominoes "X".
These are 12 flippable two-side Pentominoes "X". Colors are the same on both sides. Cover a shape so that you see the 12 different Pentominoes. The resulting Pentominoes are colored according to the 4-Color Theory.

We find a solution:

Livio Zucca:"There is at least another solution. Odette's solution coincides with mine. I have no idea how many there can be, nor what can be the exhaustive method to find them."
Helmut Postl:"The "4x3"-arrangement of the X-pentos has also only one solution. I tried different arrangements, with no new solutions so far."


We like to hear comments

 

12 Pentominoes "F".

These are 12 flippable two-side Pentominoes "F". Colors are the same on both sides. Build an open chain as in the example, so you can see the 12 different Pentominoes.


We found a sulution.

XUTFZLYPVINW
Livio Zucca:"Nice solution. Is different from mine. You are the first to do this."

Helmut Postl send us 26 solutions

XUTYVILZFPNW	XUTYVILZFPNW
XUZYVILTFPNW	XUZYVILTFPNW
XUTFZLYPVINW	XUTFZLYPVINW
XUTFZLYPVINW	XUTFZLYPVINW
XUZFTLYPVINW	XUZFTLYPVINW
XUZFTLYPVINW	XUZFTLYPVINW
XLYTZUFPVINW	XLYZTUFPVINW
XYLTZUFPVINW	XYLZTUFPVINW
XYLTZUFPVINW	XYLZTUFPVINW
XTLYZUFPVINW	XZLYTUFPVINW
XZLYTUFPVINW	XTLYZUFPVINW
XZLYTUFPVINW	XTLYZUFPVINW
XZLYTUFPVINW	XTLYZUFPVINW

We hope that we recieve a solution from you!

 

 

 

 

 

 

 

 

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