Problem 662

[Sardaai]

Not a clarification, per se, but there's an odd inconsistency in the grid near the point (4, 5).

Yes, I do feel a bit ridiculous for noticing this, much less for making a forum post about it~

[Jochen_P]

Arrgh, cannot unsee this.

*Autistic screeching

[fpbosmans]

I don't seem to understand the problem. How is a path defined?
According to my understanding of the problem there are 36 paths between (0,0) and (3,4).

[vamsikal3]

<deleted post>

[fpbosmans]

Well, that is what I gathered, but still within the given constraints (x and y >= 0, so only going up and right) I don't see how you can come up with 278 paths

[v6ph1]

For a smaller example 2x2:

Expand

You can go:
0,0 - 0,1 - 0,2 - 1,2 - 2,2
0,0 - 0,1 - 1,1 - 2,1 - 2,2
0,0 - 0,1 - 1,1 - 1,2 - 2,2
0,0 - 1,0 - 1,1 - 2,1 - 2,2
0,0 - 1,0 - 1,1 - 1,2 - 2,2
0,0 - 1,0 - 2,0 - 2,1 - 2,2
--> 6 solutions only with step = 1

AND: (Two 1-steps and one 2-step)
0,0 - 0,1 - 0,2 - 2,2
0,0 - 0,2 - 1,2 - 2,2
0,0 - 0,1 - 2,1 - 2,2
0,0 - 1,0 - 1,2 - 2,2
0,0 - 1,0 - 2,0 - 2,2
0,0 - 2,0 - 2,1 - 2,2
(Two 2-steps)
0,0 - 0,2 - 2,2
0,0 - 2,0 - 2,2

--> in Total 14

For the 3x4-Example there are the following combinations usable:

Expand

1 x (3,4)
or combinations of the following:
3x(1,0), (1,0)+(2,0), (3,0)
4x(0,1), 2x(0,1)+(0,2), (0,1)+(0,3), 2x(0,2)

[fpbosmans]

I get it, very stupid of me! tnx!