pentocubes

I used to teach math and I would challenge my geometry students to arrange 5 squares of paper into as many different shapes as they could.  There are 12 different ways to do this --with sides and corners touching.  If only the corners were touching, the shapes they created could not be taped together without the tape extending past the pieces.  This is a convoluted way of saying, they cannot just be connected at the corner or part of a side--there is always that one student who likes to be ‘creative’.  There are a total of 12 ways to combine 5 squares.

My students then used their 12 taped together pieces (or redrew them neatly on graph paper and cut them out).  The 12 different pieces fit together (no stacking them--this is cheating) to form a rectangle.  There are several different rectangles that are possible:  6x10, 5x12, 4x15, and 3x20.  (Notice that all these sizes multiply to get 60.) 

This is the 3D version of that challenge.  Each square here is a cube.  (There are other ways to connect 5 cubes but these are the 12 ‘flat’ shapes.)  These 12 pieces can be arranged to fit into boxes that correspond to the 4 rectangles mentioned above but they also fit into boxes taller than one cube high.  They are 2x3x10, 2x5x6, and 3x4x5.  (These sizes also multiply to get 60.)

Solitaire challenge--fit all 12 pieces into one of the boxes.  Solving all 7 challenges is moderately difficult.

Multi-player challenge--(2 or more players) Arrange all 12 pieces on the table so that all players have access to them.  Select a box to fill.  Take turns placing a piece in the box so that it is adjacent to more than one wall of the box or a wall and a previously played piece.  (Do not place a piece in the middle of a box and expect no one to nudge it aside while placing their piece.)  The piece must NOT extend over the top of the box.  The first player to be unable to play a piece completely inside the box is out.   Remove all the pieces from the box and play again--until there is only one player left--the winner.

I made the pieces from 1 cm cubes.  This was so that I could fit the 1x3x20 box on my print bed.  If you have access to a bigger printer or you do not wish to print this particular box, you can enlarge the pieces.  I like to print all the pieces in the same color filament--I think it makes it harder to memorize the solutions.  I also do not currently own 13 colors of filament (one for each of the puzzle pieces and a color to print the boxes.)  I have included separate files for each of the 12 pieces as well as a file that contains all 12 pieces together.

This is a good teacher gift for use in the classroom.