Figure 1 A board missing two opposite corners Figure 2 A boa

Figure 1: A board missing two opposite corners. Figure 2: A board with some dominos. Consider a typical 8 times 8 checker board. Remove two opposite corners as shown in Figure 1. You have dominos each with dimensions 2 times 1 as seen in Figure 2. Prove or disprove the following statement: It is possible to cover the entire board using dominos, with no two dominos overlapping.

Solution

No it is not possible to cover entire board using dominos with no dominos overlapping.

It can be done if it allowed that one dominos to be overlapped.

It is also possible if total board is available without taking 2 corners

It is also possible if 4 corners are removed from 4 corners.