Imagine you have a 4 x 2 blue lego, a 4 x 2 red lego and a 2 x 2 yellow lego. How many ways, excluding rotations, can you put the legos together (you must use all the pieces)?

When I first saw this I had the image of 3 bricks having an elevation of 3 high.

This is not stipulated in the dialogue.  For instance, I might align the Red with the Blue, exactly, and place the Yellow in any of 5 positions along their common 'join'; I am allowing myself the right to allow my Yellow to have two free interlocks each end (half the brick overhangs) while locking to both the Red and Blue by one peg.

I can swap the positions of my Red and Blue, and I can also adjust how much of my Red and Blue align.

Oh! Let me also place my Yellow on the lower level.  For whatever I have with it above, I double with it below.

With those thoughts, it is possible to reduce one's work load by swapping colour as appropriate, but ensure that the effect has not  created a rotational image.

The difficulty with this problem is only in the tedium to ensure that one has envisaged all translations of pieces allowable under the rules as given.

Leming, seeing the possibilities of attachment, and 2 or 3 levels, I am not going to be seduced by a diagrammatical display of my result, should I ever get that far.

Posted by brianjn on 2006-10-07 02:29:30