Livio's pentominoproblems
Livio published 3 beautiful pentomini problems. We like to put them on our site and this was his reply: "You have my permission to publish all my material on your site."

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.

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

Helmut Postl send us 26 solutions


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We hope that we recieve a solution from you!