Pentomino-Pyramide
(Published on 11. June 2013, 21:48 by bromp)
Take seven of the nine solid pentominoes with the layouts ILNPUWXYZ, and build a step pyramid whose first step consists of 25 cubes, whose second step consists of nine cubes and whose third step consists of one cube, as in this picture: .
Solution code: The letters for the layouts of the solid pentominoes that form the second step of the pyramid, in alphabetical order.
Comments
on 14. September 2013, 15:26 by CHalb
Erstaunlich, wie logisch man hier vorgehen kann.
on 20. June 2013, 22:09 by pin7guin
Damit habe ich mich ganz schön schwer getan...
on 13. June 2013, 21:38 by bromp
@RALehrer: thanks a lot for your suggestion!
on 13. June 2013, 21:37 by bromp
Updated English version based on RALehrer's improvement suggestion.
on 13. June 2013, 14:40 by RALehrer
Bromp - one way to perhaps make it clear is to define a 3D analog/representation as an exact copy of the 2D pentomino, with thickness 1.
on 12. June 2013, 09:26 by bromp
@RALehrer: I am not a native English speaker, so if you can think of a better way to phrase this puzzle please let me know.
In 2D there are twelve objects that can be formed by glueing edges of five squares together, the twelve pentominoes. In 3D there are 29 different objects that can be formed by glueing sides of five cubes together (see for example http://mathworld.wolfram.com/Pentacube.html). Twelve of these are 3D analogues of the 2D pentominoes, and that's what I meant when I wrote 3D representation. Hope this makes it a bit clearer.
So, rotating is fine, folding is not - thanks for your help, Errorandy!
on 11. June 2013, 23:08 by Errorandy
@RALehrer: It´s not possible to "fold" the pentominos, the figures of the pentominos are still the same, only in 3D
on 11. June 2013, 21:52 by RALehrer
what do you mean by a 3-d representation? For example, if I "fold" the I, I get something that looks more like others - e.g., the N or V
