BBC Article - Lego arrangements

Arrangements, combinations and permutations, probability, ...
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Eventhorizon
Posts: 19
Joined: Fri Sep 23, 2011 2:16 am

BBC Article - Lego arrangements

Post by Eventhorizon »

I read this morning a story about Lego on the BBC news app. It contained the following nugget:
915,103,765 - the number of ways to combine six two-by-four Lego bricks of the same color
That seemed surprisingly high a number to me.
Assume the following:
  • the bricks are indistinguishable (all the same color).
  • the bricks must be connected (i.e. 6 bricks side-by-side is not allowed).
  • the bricks are all lug-side up.
  • rotationally symmetric arrangements are the same.
How many arrangements are there?
What if we relax the rotational symmetry constraint?
What if the bricks were different colors? - I assume this will give us 6! times as many
Do any of these rules come in around the 915 million mark?
Ian
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traxex
Posts: 66
Joined: Thu Oct 19, 2017 1:30 pm

Re: BBC Article - Lego arrangements

Post by traxex »

A web search for the number came up with this page: http://www.math.ku.dk/~eilers/lego.html#howgetright.
Technically, everyone is full of himself.

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