Question

Suppose you have a 4x4 checkerboard with 16 squares. You put one penny on the first square, then 2 pennies on the next square then 2 to the second power pennies on the third square and so on until there are pennies on all the squares. How many pennies are on the 15th square?

a) 2^14
b) 2^15
c) 2^16
d) 2^13

Answer 1

On the 15th square of the checkerboard, there are 2^14 pennies, which is the answer to the student's question.

Step-by-step explanation:

The question pertains to a pattern where the number of pennies doubles on each square of the checkerboard. To determine how many pennies are on the 15th square, we start with one penny on the first square and double the amount for each subsequent square. Thus, the number of pennies on the 15th square would be:

2^0, 2^1, 2^2, 2^3, ... 2^14

Therefore, on the 15th square, we would have 2^14 pennies. The answer is option (a) 2^14.