+109 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?
If I understand your question, then I assume that she puts 2^k, k being the 1st, 2nd, 3rd....etc...squares. In other words, she puts: 2^1 grains of rice on the first square, 2^2 on the second square, 2^3 on the third square....and so on. If that is right, then you have the following grains of rice on each square from 1 to 10:
(2, 4, 8, 16, 32, 64, 128, 256, 512, 1024)
The sum of the first 8 squares =2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 =510 grains of rice.
The 10th square has: 2^10 = 1,024 - 510 = 514 grains of rice more that the first 8 squares combined.
