Question

You are given a penny on January 1, two pennies on January 2, four pennies on January 3, and eight pennies on January 4, and so on. 1.

Assuming the pattern continues, how many pennies do you get on the following dates? January 5 January 10 January 31

Answer 1

january 5 :12

january 10:22

Explanation:

Answer 2

• 16 pennies
• 512 pennies
• 1073741824 pennies

Explanation:

We can see a pattern:

• Days >> Pennies

• 1 >> 1= 2^0

• 2 >> 2= 2^1
• 3 >> 4 = 2^2
• 4 >> 8 = 2^3
• ...
• n >> 2^(n-1)

So

• January 5 fall on n = 5, therefore 2^4 = 16 pennies
• January 10 falls on n = 10, therefore 2^9 = 512 pennies
• January 31 falls on n = 31, therefore 2^30 = 1073741824 pennies