jmc

Question

A woman labels the squares of a very large chessboard 1 through 64. On each square k, the woman puts 2^k grains of rice. How many more grains of rice are placed on the 10^th square than on the first 8 squares combined?

Accepted Answer

The 10^th square receives 2^10=1024 grains. The first 8 squares receive 2+2^2++2^8=2(2^8-12-1)=2(256-1)=2(255)=510. Thus the 10^th square receives 1024-510=514 more grains than the first 8 combined.