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