Question 134
We consider a $100 \times 100$ square consisting of $10^4$ unit squares. We call tiles of type A the rectangular tiles $8 \times 1$ or $1 \times 8$ consisting of 8 unit squares. We call tiles of type B the rectangular tiles $4 \times 2$ or $2 \times 4$ consisting of 8 unit squares. Examine whether it is possible to cover the $100 \times 100$ square using $N$ tiles of type A and $N$ tiles of type B, for some positive integer $N$. (The tiles must be inside the initial $100 \times 100$ square and not overlapping.)