Checkers! (well sort of)

[Peppers]

Here's a simple puzzle that's like one that I did in gd class. Notice I said "like", so I hope the answer i got is the correct one.

 

--------------------
| | | | | |o| | | | | |
--------------------
|x| | | | | | |x| | | |
--------------------
| | |x| | |x| | | |x| |
--------------------
| | | | | | | | |x|x|x|
--------------------
|x|x|x| | | | | | | | |
--------------------

 

I really hope this shows up to look sort of like a checkerboard.

 

Anywho...rules...you start at the "o" and you may move only straight down or diagonally down at any one time. You cannot land on the "x" s but you may jump them (again, only straight down or diagonally down).

 

The question is: How many ways are there to get to the other side of the game board?

[Ducky Havok]

55?

[Peppers]

Uhoh, I got 56,... i'll check again

[Peppers]

Ya I still got 56.

[gnpatterson]

sorry I dont follow this problem and I get far more ways to do it

 

by writting in each box how many ways there are to get to it you can go down the grid row by row as shown here

 

| | | | | |o | | | | | |

------------------------------

| x| | | |1 |1 |1 |x | | | |

------------------------------

| | | x|1 |2 |x |2 |1 | |x | |

------------------------------

| | | 1| 3|3 |5 |3 |3 |x |x |x |

------------------------------

| x| x| x| 7|11|11|11|6 |3 |1 | |

------------------------------

| 1| 0| 8| 18|29|33|28|20|10| 4| 1|

------------------------------

 

this gives a total of 152 ways

 

(i get 50 at the previous row) PS what is gd (class)

[Ducky Havok]

Your numbers are wrong, that's the problem. In the row that you have 1,3,3,5,3,3, it should be 1,3,4,5,4,3. Also, you went one to many rows.

 

Oh yeah, Peppers, I recounted and got 56.

[Peppers]

PS what is gd

Geometry and Descrete Mathematics

[gnpatterson]

Thanks, spotted my mistake.

 

Is there any significance to this problem? I notice that you have placed a number of x's that do not interfere with the solution, do they have some meaning in a wider problem?

[Peppers]

I notice that you have placed a number of x's that do not interfere with the solution, do they have some meaning in a wider problem?

 

No, I sort of made this problem in about 3 seconds while I typed it out, I solved it later and also realized that it turned out pretty easy because most of the x's did absolutely nothing to the problem oh well, at least we all got it