Question

A man places 1 penny on the square of a chess board, 2 pennies on the next square, 4 pennies on the third square, and continues this pattern. How many pennies will be on the 14th square?(1 point)
Responses

8,192 pennies
8,192 pennies

28 pennies
28 pennies

256 pennies
256 pennies

16,384 pennies

Answer 1

The pattern described is a doubling of the number of pennies placed on each square of the chessboard.

1. On the 1st square: \(2^0 = 1\) penny
2. On the 2nd square: \(2^1 = 2\) pennies
3. On the 3rd square: \(2^2 = 4\) pennies
4. On the 4th square: \(2^3 = 8\) pennies
5. On the 5th square: \(2^4 = 16\) pennies
6. On the 6th square: \(2^5 = 32\) pennies
7. On the 7th square: \(2^6 = 64\) pennies
8. On the 8th square: \(2^7 = 128\) pennies
9. On the 9th square: \(2^8 = 256\) pennies
10. On the 10th square: \(2^9 = 512\) pennies
11. On the 11th square: \(2^{10} = 1024\) pennies
12. On the 12th square: \(2^{11} = 2048\) pennies
13. On the 13th square: \(2^{12} = 4096\) pennies
14. On the 14th square: \(2^{13} = 8192\) pennies

Thus, the number of pennies on the 14th square is **8,192 pennies**.