Question

A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.

Answer 1

Answer: 512 grains on the 10th square. 1023 total grains on all 10 squares.

Explanation:

Two ways: add the number of grains on each square

1+2+4+8+16+32+64+128+256+512 = 1023

Or set up an equation using sigma: Σ

Put 10 on top and n=1 on the bottom. Next to it, put 2^(n-1).

Answer 2

The number of grains on the Nth square Is 2^(N-1). There are 512 grains on the 10th square alone, and 1,023 of them on all 10 squares together.