+102 A grid with 3 rows and 52 columms is tiled with 78 identical 2x1 dominoes. How many ways can this be done such that exactly two of the dominoes are vertical?
Details and assumptions
the dominies will cover the entire board. They are not allowed to jut over the board, or overlap with each other.
Rotations and reflectionscount as distinct ways.
+118667 A grid with 3 rows and 52 columms is tiled with 78 identical 2x1 dominoes. How many ways can this be done such that exactly two of the dominoes are vertical?
Details and assumptions
the dominies will cover the entire board. They are not allowed to jut over the board, or overlap with each other.
Rotations and reflectionscount as distinct ways.
I have not thought about it very hard (so I might not have considered everything) but it seems to me that the 2 have to be in either the 1st and second or 2nd and 3rd rows. And they cannot be seperated by an odd number of block.
So one must be in an even position and one must be in an odd position. There are 26 even positions and 26 odd positions.
So maybe
26*26*2*2 = 2704 ways
