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# Double Trouble

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1009
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1.

In how many patterns can six identical L-shaped pieces, each consisting of three unit squares, be placed to perfectly cover a fixed 3 by 6 board? One such pattern is shown.

2.

How many paths are there from C to D on the grid shown, if every step must be down or to the right?

Jun 23, 2019

#1
+121056
+4

2.       We have the following moves  (R R R R  D D D D D D)

So in the set....we can choose any 4 of the 10 positions for the R's to occupy  or, alternatively, any 6 of the 10 positions for the D's to occupy

So....the nuber of possible paths  =  10C 4  = 10C6  =  210 possible paths

Jun 24, 2019
#2
+1709
+7

Double Trouble? the song? wow guest...

Jun 24, 2019
#3
+9312
+5

1. We will have to fit the pieces into 3 compartments like this:

If we try to place a piece between these compartments, it will create an unfillable area.

Within each of these compartments, there are only 2 ways to fit the pieces:

So the total number of possibilities   =   2 * 2 * 2   =   23  =  8

They are:

1.  AAA

2.  AAB

3.  ABA

4.  ABB

5.  BAA

6.  BAB

7.  BBA

8.  BBB

And here is a picture of them:

Jun 24, 2019
#4
+121056
+1

Very nice, hectictar......you are very good at this sort of thing  !!!

CPhill  Jun 25, 2019
#5
+9312
+4

Thanks.....there is still a LOT more I have to learn though....

hectictar  Jun 25, 2019