Pentomino Odd Pairs Update

Livio Zucca's Pentomino Odd Pairs studies the problem of finding a compatibility figure for two pentominoes with an odd number of tiles. Many of the solutions are complex. Solutions were contributed by Gabriele Carelli, Dario Uri, Giovanni Resta, Silvio Sergio, Paolo Licheri, Odette De Meulemeester and T.I.D. Ronse (now K.S.O. Glorieux Ronse), Remmert Borst, Helmut Postl, Ricardo Montiel, and Zucca. See the bottom of this page for a table of current results.

No solution is given for L+X. Here is one with 137 tiles:

No solution is given for T+W. Here is one with 21 tiles:

Some of the solutions can be improved. Here is a solution for F+X with 11 tiles, improving one with 21:

Here is a solution for F+Z with 7 tiles, improving one with 11:

Here is a solution for I+N with 9 tiles, improving one with 11:

Here is a solution for I+T with 29 tiles, improving one with 71:

Here is a solution for I+U with 23 tiles, improving one with 27:

Here is a solution for I+V with 13 tiles, improving one with 27:

Here is a solution for I+W with 17 tiles, improving one with 21:

Here is a solution for N+T with 7 tiles, improving one with 9:

Here is a solution for T+V with 9 tiles, improving one with 11:

Here is a solution for T+Z with 9 tiles, improving one with 11:

Here is a solution for U+Z with 13 tiles, improving one with 25:

Here is a solution for V+Z with 11 tiles, improving one with 13:

Here is a solution for W+Z with 13 tiles, improving one with 23:

Here is a solution for X+Y with 7 tiles, improving one with 9:

Table

The orange cells represent figures shown on this page.

 FILNPTUVWXYZ
F*1335357751137
I13*79529231317×525
L37*53575513737
N595*375353337
P3533*3533933
T529573*139212559
U72375513*117×713
V713533911*11×711
W51755321711*?713
X11×13733925××?*7?
Y3533357777*5
Z7257739131113?5*

Last revised 2010-02-21.

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Col. George Sicherman [ HOME | MAIL ]