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## #1 2006-03-26 13:56:58

MareyaRoberts
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### Use your logic and Maths knowledge to solve this Question?!!

Hello guyzz..
I got a question that i couldnt myself solve. Lets if you people can get the solution. I think it needs some logical before applying some basic maths concepts. It might be related to "combindations".  Here is the question:-

The lego company regularly publishes the number of ways to combine 6 identicallly coloured (2 x 4) blocks of height 6 ( the number is 102981500).

1. How many ways can you combine 3 identically coloured ( 2 x 4) lego blocks of height 3 ( 90 and 180 degree rotations do not count as separate configuration).

2. Repeat part 1 of the question if the blocks are 3 different colours.
3. Repeat part 1 of the question if 2 blocks are white and one is red.

Lets see who is gonna be the smartest person here.

## #2 2006-03-28 05:06:37

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Use your logic and Maths knowledge to solve this Question?!!

Here's something to read on this subject.
http://www.math.ku.dk/~eilers/lego.html
or click me, same thing

This webpage says that the number if 6 high is 102981504, so Lego was off by 4 because
way back when they computed it, the calculators didn't go out to nine digits, only eight, was surmized.   (The web page also explains other setups where two or more legos are on the same level, but that is not directly the problem stated here.   There is paired symmetry mentioned, but I havn't worked on it yet.)

Last edited by John E. Franklin (2006-03-28 05:24:05)

igloo myrtilles fourmis

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## #3 2006-03-28 05:33:13

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Use your logic and Maths knowledge to solve this Question?!!

If you place a 2x4 lego on a table, then note that it is the same if you turn it 180 degrees (half a turn).
So hence if you build up and out forward, it is the same as building up and out backward.
Hence up and out forward on the right side is the same as up and out backward or the left side.
And so forth...  Hence this is how the pairs are counted.
However, I don't understand all of the LONER symmetrics yet.   One I can think of is just crisscrossing the 2x4's to make plus signs.
Good luck!

igloo myrtilles fourmis

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