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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
avatar+101813 
+3

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

 

 

cool cool cool

 Jun 24, 2019
 #2
avatar+625 
0

Double Trouble? the song? wow guest...

 Jun 24, 2019
 #3
avatar+8406 
+2

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
avatar+101813 
+1

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

 

 

cool cool cool

CPhill  Jun 25, 2019
 #5
avatar+8406 
+2

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

hectictar  Jun 25, 2019

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