<s>[INST] how many ways to go from place a to place b through 9 squares 
Please see the image.  How many ways are there from M to N without passing through the sqaure more than once...
I counted upto 6 ways...is it the right answer??
 [/INST] The answer is $E$. Here are the paths:


*

*$(0,0) \rightarrow (1,1) \rightarrow (2,2) \rightarrow (3,3)$

*$(0,0) \rightarrow (1,1) \rightarrow (2,0) \rightarrow (3,1) \rightarrow (2,2) \rightarrow (3,3)$

*$(0,0) \rightarrow (1,1) \rightarrow (0,2) \rightarrow (1,3) \rightarrow (2,2) \rightarrow (3,3)$

*$(0,0) \rightarrow (1,1) \rightarrow (0,2) \rightarrow (1,3) \rightarrow (2,2) \rightarrow (1,1) \rightarrow (2,0) \rightarrow (3,1) \rightarrow (2,2) \rightarrow (3,3)$

*$(0,0) \rightarrow (1,1) \rightarrow (0,2) \rightarrow (1,3) \rightarrow (2,2) \rightarrow (3,1) \rightarrow (2,0) \rightarrow (1,1) \rightarrow (2,2) \rightarrow (3,3)$

*$(0,0) \rightarrow (1,1) \rightarrow (2,2) \rightarrow (1,3) \rightarrow (0,2) \rightarrow (1,1) \rightarrow (2,0) \rightarrow (3,1) \rightarrow (2,2) \rightarrow (3,3)$

*$(0,0) \rightarrow (1,1) \rightarrow (2,2) \rightarrow (3,1) \rightarrow (2,0) \rightarrow (1,1) \rightarrow (0,2) \rightarrow (1,3) \rightarrow (2,2) \rightarrow (3,3)$

*$(0,0) \rightarrow (1,1) \rightarrow (2,0) \rightarrow (3,1) \rightarrow (2,2) \rightarrow (1,1) \rightarrow (0,2) \rightarrow (1,3) \rightarrow (2,2) \rightarrow (3,3)$

*$(0,0) \rightarrow (1,1) \rightarrow (2,0) \rightarrow (3,1) \rightarrow (2,2) \rightarrow (1,3) \rightarrow (0,2) \rightarrow (1,1) \rightarrow (2,2) \rightarrow (3,3)$


I hope I didn't mess that up...
</s>