Problem 1: In the summer, the Microsoft Asia Research Institute located on the fourth floor of the magma building made a large renovation of the office building patio. The original floor was paved with n × m
Square tiles, which have been damaged and aged, need to be updated. When the installers go to the store to buy new tiles, they find that the store currently only supplies rectangular tiles.
A rectangular tile is equivalent to the original two square tiles. The workers may not decide how much to buy. Readers may ask for help: can I use a 1 × 2 tile to cover n × m floors? Solution: first, N and m must be an integer multiple of 1 and 2, respectively. Otherwise, they cannot do it. If you think about it, there are no other conditions. This is a simple question: can p * q tiles cover M * n floors? Solution: ① M * n must be an integer multiple of p * q. ② the numbers in p and q must be smaller than or equal to M. The numbers in N must be smaller than or equal to M, N decimal places ③ if p * q is an even number, then M and N are not P, the side length of Q must be a combination of * + operations of p and q; if it is an odd number, you only need to meet the first two conditions;
For the method of Covering N * m floors with 1*2 ceramic tiles, see http://en.wikipedia.org/wiki/domino_tiling. The results are terrible!
